Citation
Optical studies of ion-molecule collisions

Material Information

Title:
Optical studies of ion-molecule collisions N2+ + O2
Creator:
Murray, Lambert Edward, 1949-
Publication Date:
Copyright Date:
1977
Language:
English
Physical Description:
xi, 167 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Electron emission ( jstor )
Emission spectra ( jstor )
Energy ( jstor )
Forced migration ( jstor )
Molecular excitation ( jstor )
Population estimates ( jstor )
Projectiles ( jstor )
Visible spectrum ( jstor )
Wave excitation ( jstor )
Wavelengths ( jstor )
Collisional excitation ( lcsh )
Collisions (Nuclear physics) ( lcsh )
Dissertations, Academic -- Physics -- UF
Physics thesis Ph. D
Scattering (Physics) ( lcsh )
Genre:
bibliography ( marcgt )
non-fiction ( marcgt )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 163-166.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Lambert Edward Murray.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
022210167 ( ALEPH )
04213816 ( OCLC )
AAG8797 ( NOTIS )

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OPTICAL STUDIES OF ION-MOLECULE COLLISIONS:
N2 + 0








By

Lambert Edward Murray




















A Dissertation Presented to the Graduate Council of
the University of Florida in Partial
Fulfillment of the Requirements for the Degree of
Doctor of Philosophy



UNIVERSITY OF FLORIDA

1977















ACKNOWLEDGMENTS

The author wishes to thank the members of his super-

visory committee, especially Professors T. L. Bailey and

C. F. Hooper, for their assistance and encouragement

throughout his graduate program. He wishes to give special

credit to Dr. Ralph C. Isler, the chairman of his committee,

for his counsel, his assistance, and his patience during the

course of this research.

The author is also indebted to Helen Dickman for her

fine work in typing this paper.

Finally the author wishes to thank his wife, McKay,

for her patience, understanding, and constant encouragement

during the course of his graduate program.



























ii
















TABLE OF CONTENTS


ACKNOWLEDGMENTS . . . .

LIST OF TABLES . . . . .

LIST OF FIGURES . . . .

ABSTRACT . . . .

Chapter

I. INTRODUCTION . . . .

II. EXPERIMENTAL APPARATUS . .

Collision Apparatus .

Vacuum System . .

Ion Source . .

Beam Transport and Detect

Ion Beam Characteristics

Optical Detection System .

Spectroscopic Arrangement

Detectors . . . .

Pulse Counting System .

III. PROCEDURE . . .


Operational Definition of the Excitation and
Emission Cross Sections . . .

The Relationship of the Excitation Cross
Section to the Emission Cross Section . .

Target Excitation . . . .


i i i


Page

ii

v

vii

x



1


. . . 31









Chapter Page

Projectile Excitation . . . . . 38

Determination of Emission Cross Sections 41

The Emission Cross Section as a Function
of Energy . . . . . . . .. 42

Relative Emission Cross Sections . .. 45

Calibration of the Optical Detection
System . . . . . . . . 46

Dependence of the Emission Cross Section
on Polarization . . . . . . . 57

IV. RESULTS . . . .. .......... .. . 66

Identification of Observed Spectral Features . 66
o
Spectral Features Above 2500 A .. ... . 66

Spectral Features Below 1500 A . . . 79

Emission Cross Sections of the Molecular
Features of 112 and N2 . . . ... . 80

Emission Cross Sections of the Molecular
Features of 02 . . . . . .. . 103

Emission Cross Sections of Atomic Features . 108

Polarization Measurements . . . . . 126

V. DISCUSSION . . . . . . . . .. .. 128

Ion Beam Excited State Population . . . 128

Excitation of the N 2 B 2E State . . 132

Comparison with Charge Transfer Data . . . 144

Production of Excited Dissociation Fragments 150

VI. CONCLUSION . . . . . . . . . 160

REFERENCES . . . .... . . .. . 163

BIOGRAPHICAL SKETCH .. ..... .... . .. .167

















LIST OF TABLES


Table Page

I. Absolute emission cross sections for the
(0,0), (0,1), (1,2), and (2,3) bands of
the first negative system of N2+ arising
from col visions of N2 w ii th 02 . . . . 83

II. Absolute emission cross sections for the
(0,0), (1,0), and (2,1) bands of the second
positive system of N2 arising froni collisions
of N2 with 02 . . . . . . ... . 86

I Absolute emission cross sections for various
N2+ first negative and N2 second positive
vibrational bands arising from collisions of
N2 with 02 at a collision energy of 4.0 keV 96

IV. Absolute emission cross sections for the N +
first negative system at a beam energy of 4.0
keV . .. . . . . . . . . . 97

V. Absolute emission cross sections for the N2
second positive system at a collision energy
of 4.0 keV . .. . . . ... . 98

VI. Absolute emission cross section of the entire
N2+ first negative system as a function of
collision energy . . . .... . 101

VII. Absolute emission cross section of the entire
N2 second positive system as a function of
collision energy .. .... .. . . 102

VIII. Absolute emission cross sections for the
observed band sequences of the 02+ first
negative system at 4.0 keV . . . . . 104

IX. Absolute emission cross sections for lines
below 1750 A arising from excited dissociation
fragments resulting from collisions of N2+
with 02 at 4.0 keV . . .. . . 109









Table


Page


X. Absolute emission cross sections for lines
above 3000 A arising from excited dissocia-
fion fragments resulting from collisions of
N2+ with 02 at 4.0 keV . . . . . . 110

XI. Absolute emission cross sections for several
excited dissociation fragments as a function
of collision energy arising from collisions of
N2+ with 02 . .. . . . ... . 122

XII. Relative population of the vibrational energy
levels of the X and A states of N,' at the
collision chamber . . . . . . 131

XIII. The minimum energy defect for direct excitation
Q ,and for charge exchange excitation Qe, and
tge experimentally observed thresholds E for
the resonance lines of NI, NII, 01, and 6?I
which were observed. . . . .. . . 151

XIV. Emission cross sections of several NI and NII
lines arising from dissociative collisions of
N with 02 and with Ar at a collision energy
o 4.0 keV . . . . . . . . .. . 154


















LIST OF FIGURES


Figure Page

1. Schematic of collision apparatus . . . . 6

2. Schematic of vacuum system ... . .. . 8

3. Schematic cross section of ion source . . . 12

4. Dependence of ion beam current upon coil current
for H2+ . . . . ... . . .... 16

5. Dependence of the N2+ ion current upon electron
bombardment energy with a potential of 2.5 keV
applied to the ion chamber . . . . .. 18

6. Dependence of the N2+ ion beam current upon the
potential applied to the ion chamber with an
electron bombardment energy of 50 eV . . . 20

7. (a) Experimental configuration for determining the
mean energy of the ion beam and the energy spread.
(,) Dependence of the ion beam current upon the
retardation potential Vr .. . . . . ..23

8. Schematic of spectroscopic arrangement . . . 26

9. Schematic of pulse counting system . .. . 30

10. Dependence of the relative count rate on target
gas pressure . . . .. . 44

11. Relative detection efficiency as a function of
wavelength for the vacuum monochromator and the
EMI 9558Q phototube .. . .... . .. 48

12. Relative detection efficiency as a function of
wavelength for the Ebert mount monochromator and
and the EMI 9558Q phototube . . . ... . 50








Figure

13. Relative detection efficiency as a function of
wavelength for the vacuum monochromator and the
EMR phototube .. ......

14. Relative detection efficiency as a function of
wavelength for the vacuum monochromator and the
M EI . . . . . . . . . . .

15. Experimental arrangement for determining the
instrumental polarization

16. Instrumental polarization of the Ebert mount
monochromator as a function of wavelength


17. Emission spectra between 2500 and
from collisions of N2+ with 02 at
energy of 4.0 keV . .

18. Emission spectra between 3300 and
from coll visions of N2+ with 02 at
energy of 4.0 keV . .

19. Emission spectra between 4200 and
from collisions of N2+ with 02 at
energy of 4.0 keV .

20. Emission spectra between 4900 and
from col visions of N2+ with 02 at
energy of 4.0 keV . .

21. E mission spectra between 1525 and
from collisions of N2+ with 02 at
energy of 2.5 keV . .

22. Emission spectra between 1200 and
from col visions of N2+ with 02 at
energy of 4.0 keV . .


3400 A arising
a col vision


4300 A arising
a collision


5050 A arising
a collision


6200 A arising
a collision


1270 A arising
a collision


680 A arising
a collision


23. Absolute emission cross sections for the production
of the (0,0), (0,1), (1,2), and (2,3) bands of the
first negative system of N2+ as a function of beam
energy . . . . .

24. Absolute emission cross sections for the production
of the (0,0), (1,0), and (2,1) bands of the second
positive system of N2 as a function of beam
energy . . . . .

25. The (0,1)/(0,0) branching ratio of the N21 first
negative system for N2+ + 02 collisions as a
function of collision energy


v iii


Page








Figure Page

26. The emission cross section as a function of ion
beam energy for the entire N2+ first negative
system and the entire N2 second positive system . 100

27. The emission cross sections of the Ai = -1 band
sequence of the first negative system of 02 as
a function of collision energy . . . . . 106

28. Energy level diagram of NI . . . . . 112

29. Energy level diagram of N I . . . . .. .. 114

30. Energy level diagram of 01 . . . . . 116

31. Energy level diagram of 01i . . ...... 118

32. Absolute emission cross sections of excited
dissociation fragments arising from N2 + 02
col visions as a function of ion beam energy . . 121

33. Relative populations of the vibrational levels of
the N+ B Z1 state as a function of ion beam
ene rgy . . . . . . . . . . 135

34. Selected potential energy curves of N2 and N2 . 141

35. Total cross sections for the production of 02+ and
for the production of all slow ions in collisions
of N2+ with 02 . . .. . .. .. . 142

36. Selected potential energy curves of 02 and 02 . 148

37. Emission cross sections of the NI 1200 A line
arising from the 3s "P + 2p3 'S transition, and
the Nil 1085 A line arising from the 2s2p3 DO
2p2 3P transition compared to calculated cross
sections using the Landau-Zener formula . . . 159















Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy


OPTICAL STUDIES OF ION-MOLECULE COLLISIONS:
N2 + 02



By

Lambert Edward Murray

August, 1977


Chairman: R. C. Isler
Major Department: Physics

Inelastic collision processes of the N2 + 02 system

have been examined by studying emissions of the spectral

features in the range from 600 to 8000 A at ion impact ener-

gies from threshold to 7 keV. Emission cross sections of the

vibrational bands of the N2+ first negative (B 2E+ X 2+)

and N second positive (C n -* B 3 ) systems as well as the

emission cross section of the 02 first negative (b 4 -

a n ) system have been determined as functions of energy.

The relative population of the vibrational levels of the

N2 B state have also been determined and compared with pre-
+ +
vious measurements for the N2 + He and N2 + Ne systems. The

relative population appears to be describable in terms of








the Franck-Condon principle at the higher energies, in agree-

ment with other experiments. Thresholds and emission cross

sections have been determined as functions of impact energy

for lines originating from several excited configurations of

NI(3s 4p, 3s 2P, 3s' 2D, 3d 'P), NI (2p3 2DO), 01(3s 3So),

and 01I(2p4 4P), resulting from collision induced dissociation.

Emission cross sections for additional lines originating from

excited configurations of NI, Nil, 01, and Oil have also been

determined at 4 keV. In contrast to collisions which produce

ground state dissociation fragments, the cross section for

the production of excited dissociation fragments appears to

be relatively small.















I. INTRODUCTION

As a beam of projectiles traverses a gaseous target both

elastic and inelastic collisions can occur. When molecular

reactants are involved, the inelastic collisions may result

in excitation, ionization, or dissociation of either the pro-

jectile or the target, or both, as well as electron transfer

from one reactant to the other. In addition, reactive colli-

sions, resulting in the appearance of new molecular species,

may also occur. Ideally, experiments designed to.study these

processes should be performed by preparing both the projectile

and the target in a single state and then determining the

separate cross sections for each set of final states which

are produced. However, experimental limitations usually pre-

vent the achievement of such well-defined conditions.

The most important technique used to determine the cross

sections of the various interaction channels as well as their

angular dependence is the direct detection of the products

emerging from the collision region. However, it is often

quite difficult in this type of experiment to isolate, for

separate study, a given interaction channel from the several

possible. In such cases where the collision process leads

to an excited state which subsequently emits a photon due

to spontaneous decay, optical techniques may be utilized








to determine precisely which states have been populated dur-

ing the collision process as well as the energy thresholds

and cross sections for populating the various states, thus

providing added detail about the total cross sections for

individual interaction channels.

This dissertation reports measurements of emission cross

sections resulting from collisions of N2 with static gas 02

targets for ion beam energies from threshold to 7 keV in a

spectral range from 600 to 8000 A. Although this system is

relatively complex theoretically, the data should be of con-

siderable interest because of the importance of these mole-

cules in atmospheric processes. The only other spectroscopic

observations which appear to have been made for this system

are those reported by Liu and Broida.1 Their measurements,

however, consist only of the absolute emission cross sections

for the production of the N2 first negative system and of

two 0. lines (3947 and 4368 A) at an ion beam energy of 0.90

keV.

The measurement of emission cross sections arising from

excited dissociation fragments are of particular interest.

Few spectroscopic measurements of these features have been

made at energies less than 10 keV for any collision system.2

Most of these have involved the dissociation of H2 and H2'

although a number of measurements of the dissociation of N2

and N2 in collisions with various other species have been

made by Doering3 (N2+ + N2), Neff4 (Na+ + N2, Ne+ + N2),

Hollstein et a 5 (He+ + N2), and Holland and Maier6

(He + N2). The only spectroscopic measurements of the




3



dissociation of 02 within this energy range appear to be

those of Hughes and N 7 for H impact on 02. Of these

measurements, only those of Holland and Maier included de-

terminations of the thresholds for the production of emis-

sions from any excited dissociation fragments.















II. EXPERIMENTAL APPARATUS

Collision Apparatus

A schematic diagram of the collision apparatus used in

these experiments is shown in Fig. 1. It consists of three

principal sections: (i) a chamber for the production of

ions by electron bombardment; (ti) a differential pumping

chamber which contains a system of electrostatic lenses for

accelerating and focusing the ion beam, as well as a low

resolution Wien filter; and (iii) a collision chamber which

contains the target gas.

The system has been modularly constructed to make use

of the High Voltage Engineering Corporation's 4-inch beam

line components and coupling flanges. Each module has been

constrLcted from type 303 stainless steel, and the electri-

cal feedthroughs, ion gauges, leak valves, and observation

windows are mounted on conflat flanges and are sealed into

the various modules with oxygen-free, high-conductivity cop-

per gaskets.


Vacuum System

The source and lens chambers, which achieve ultimate

pressures of 1-2 X 10-7 torr, are coupled to a 2-inch mer-

cury pumping system by 1/4-turn butterfly valves. These

pumping systems (shown in Fig. 2) consist of a liquid nitro-

gen cooled vapor trap, a thermoelectrically cooled baffle,



















































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and a mercury vapor diffusion pump. These pumps are connected

through a liquid nitrogen trap and a molecular sieve trap to

a mechanical backing pump.

The collision chamber, which reaches an ultimate pres-

sure of 2-3 X 10-6 torr, is evacuated continuously through

the beam entrance hole (0.075 in.) in the bulkhead which sep-

arates the collision chamber from the lens chamber, and

through the slits of the vacuum monochromator, which is coup-

led to an open observation port opposite the observation win-

dow shown in Fig. 1 (see also Fig. 8). In addition a small

oil diffusion pump, employed as the low pressure reference

of a capacitance pressure sensor, is used in the initial evac-

uation of the collision chamber. This pump is not open to

the collision chamber while measurements are being made.

Airco pure grade N2 and 02 gases of quoted purity

99.9% and better than 99.5%, respectively, have been used

with no further purification. These gases are admitted to

the source and col vision chambers by means of Granville-

Phillips Variable Leak valves. Standard Bayard-Alpert type

ionization gauges and a Granville-Phillips ionization gauge

controller are used to monitor the pressure in the three

chambers of the system. In addition, a Datametrics Electron-

ic Manometer and capacitance type Barocel Sensor are used to

measure the pressure of the various gases in the collision

chamber. This is done to facilitate comparison measurements,

since the calibration accuracy of this type device is inde-

pendent of gas composition.








Ion Source

A schematic diagram of the electron bombardment ion

source is shown in Fig. 3. Except for the molybdenum grid,

all parts shown are type 304 stainless steel or boron nitride.

In order to produce a beam, the source chamber is first

evacuated, and then the butterfly valve is almost completely

closed until the pressure rises to about 2 X 10-6 torr. This

serves to minimize fluctuations in pressure in the ion cham-

ber and thus helps to maintain beam stability. The gas to

be ionized is then leaked into this section until the pres-

sure is between 10-3 and 10-4 torr. The optimum pressure for

the production of N2 was found to be about 4 X 10- torr.

The bombarding electrons are produced from a cathode

which is directly heated by current from a well-regulated

dc power supply. The cathodes are produced by painting an

RCA triple carbonate (Ba, Sr, Ca) mixture on a strip of

0.010 .n. nickel mesh 1/8 in. wide and 3/4 in. long. These

carbonates are converted to oxides by heating the cathode to

900-1000C in a vacuum. After conversion begins, electron

emission is stabilized by drawing approximately 40 mA for

about an hour.

The electrons emitted from the cathode are drawn through

the molybdenum grid by a potential difference, which can be

varied from 0 to 250 V, applied between the ion chamber and

the cathode. The electrons are then focused toward the exit

aperture of the ion chamber by an axial magnetic field which

is produced by a narrow coil wrapped around the ion chamber.

This coil consists of 275 turns of #27 copper wire with a
































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heavy formvar coating. Currents as large as 2 A are used in

the coil to produce fields of about 120 G in the region of

the extraction aperture. In order to prevent the disinte-

gration of the insulation, the coil is cooled by circulating

oil around the coil and through a simple water cooled heat

exchanger.


Beam Transport and Detection

Ions created in the ion chamber are drawn out by an

extractor potential 15-20 V lower than the potential applied

to the ion chamber itself. These ions are focused and ac-

celerated toward the collision chamber by a system of cylin-

drical electrostatic lenses. The potential applied to each

lens is adjusted empirically for maximum current in the

collision chamber. In addition, a low resolution Wien filter

is employed to eliminate N2 and N from the ion beam.

The ion beam is monitored by a General Radio type 1230-A

dc amplifier and electrometer which is connected to a Faraday

cup mounted in the collision chamber. To determine the possi-

ble effect of secondary electron emissions on the measurement

of the ion current, a potential was applied to the Faraday

cup to suppress secondary electron emission. The ion cur-

rent was measured as a function of this suppressor potential

and, within experimental error, was found to be independent

of this potential.


Ion Beam Characteristics

The dependence of the ion beam current as measured in

the collision chamber upon the magnetic field in the ion









chamber (and thus upon the coil current), the electron bom-

bardment energy, and the potential applied to the ion cham-

ber are shown in Figs. 4-6.

Although Fig. 4 is a plot for H2, ions, this plot rep-

resents the general dependence of the ion beam current.upon

the coil current which has been noted for all ions produced

in this source. While performing a measurement, the coil

current is adjusted to a region where the ion current varies

smcothly with coil current. In order to increase the sta-

bility of the ion beam, the output of the electrometer which

monitors the ion beam has been used to provide an error sig-

nal to the programming terminals of the power supply which

supplies current to the coil. Using this technique, fluc-

tuations in the ion current have been reduced to less than

0.25% while measurements are being made.8

The dependence of the N2 ion beam current on electron

bombardment energy is shown in Fig. 5 for bombardment ener-

gies between 20 and 40 eV. To obtain sufficient accuracy in

cross section measurements, the electron bombardment energy

was always maintained above 30 eV.

The ion beam energy is established by applying a posi-

tive potential of up to 7 keV to the ion chamber while the

collision chamber is maintained at ground potential. Figure

6 shows the variation of the ion current as a function of this

applied potential. To determine the actual energy of the

ions as they enter the collision chamber, a simple double

retardation screen was placed just beyond the entrance aperture

















































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Figure 5

Dependence of the N2 ion current upon electron
bombardment energy with a potential of 2.5 keV
applied to the ion chamber.
















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of the col vision chamber (see Fig. 7a). A plot of ion cur-

rent versus retardation voltage (solid curve) is shown in

Fig. 7b for an H + ion beam with a potential of 40 V applied

to the ion chamber and an extractor potential of 15V. The

mean energy of the ions is taken to be the potential at which

the ion current has fallen to 1/2 maximum (or where -dl/dV is

a maximum), in this case approximately 12.5 eV lower than the

applied potential. Additional tests have shown that the mean

energy of the ions is 12.3 0.5 eV lower than the potential

applied to the ion chamber, even at zero extractor voltage.

Unless otherwise noted, the beam energies quoted herein have

been corrected to give the actual energy of the ions entering

the collision chamber.

The energy spread of the ion beam, taken to be the full

width at half maximum of the change in ion beam current as

a function of retardation potential, is seen in Fig. 7b to be

approximately 3.5 eV, or about 9% of the applied potential

at 40V. Additional measurements have shown that the energy

spread is approximately 8 eV for an applied potential of

180 V for extractor potentials from 0 to 65 V. The energy

spread, therefore, is taken to be less than 5% of the beam

energy for an applied potential higher than about 200 V.

Optical Detection System

Spectroscopic Arrangement

Two types of monochromators have been utilized for the

detection of optical emissions arising within the collision

chamber: a I-meter normal-incidence vacuum instrument



















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(McPherson model No. 225) and a 1/4-meter Ebert mount instru-

ment (Jarell-Ash model No. 82-410). The vacuum instrument,

equipped with a magnesium floride coated, 600 grooves/mm
0
grating blazed for 2000 A, has a linear reciprocal dispersion

of 16.6 A/mm in the first order. This instrument is coupled

directly to the collision chamber through an open observa-

tion port (see Fig. 8). The Ebert mount instrument is mounted

on the opposite side of the collision chamber from the vacuum

instrument, separated from the collision chamber by a quartz

observation window. Light arising from the collision chamber

passes through this window and is focused upon the entrance

slit by a quartz lens. This instrument, equipped with a 1180
0
grooves/mm grating blazed for 6000 A, has a linear reciprocal

dispersion of 33 A/mm in the first order. All observations

have been made at 90" to the direction of the beam.

The entrance slits of both instruments are mounted verti-

cally, perpendicular to the beam direction, to minimize the

effect of possible variations in the beam diameter. Although

the beam is not collimated, it is estimated that distortions

of relative cross sections owing to these variations are less

than 5% over the entire range of beam energies.

The length of the beam from which light can be detected

(the observation length k) as well as the solid angle sub-

tended by the detection system is determined by the optical

limiting stops of each detection system. For the vacuum

monochromator system the limiting stops are the ruled area

of the grating (height 56 mm, width 96 mm, located 120 cm











































c

E

Q)

(U
C



U



ci



f0
L
-CO 0

U








0
u




E
SU
(U
r-










U
4-1





















rc





ft:
I
0







C)
0 <


LLI



-J i-
Or


0
or








from the beam) and the entrance slits of the monochromator.

For the Ebert mount system the limiting stops are the diam-

eter of the quartz lens and the entrance slits of the mono-

chromator. The observation length, 2, of the vacuum mono-

chromator system may be taken as 1.92 cm and will be in

error less than 3% for a slit width of 500p or less, while

the observation length of the Ebert mount system will be

approximately equal to the entrance slit width. The distance

L from the bulkhead which separates the collision and lens

chambers to the region of optical detection is approximately

1.25 cm for the vacuum monochromator and 2.21 cm for the

Ebert mount system.

Detectors

In order to observe emission spectra over a range from

600 to 8000 A, four different detectors were used: (i) an

EMI 9558Q photomultiplier tube was used from 2500 to 8000 A;
0
(ii) an EMI 6256S tube was used from 1500 to 3000 A; (iii)

an EMR 542G-09-18 tube was used from 1200 to 1700 A; and

(iv) a Bendix mouel 306 magnetic electron multiplier (MEM)

was used below 1200 A. The vacuum monochromator was employed

for all measurements below 5000 A, while the Ebert mount mon-

ochromator was employed only for measurements above 5000 A.

Although the dark count rate for the EMR tube and for

the MEM is less than 1 per second at room temperature, both

EMI tubes had to be mounted in a liquid nitrogen cooled

housing to reduce their dark count rate to about 50 per sec-

ond. To further reduce the dark count rate to a minimum of








3 per second, a permanent donut-shaped magnet was placed

about I inch from the tube face. This was done to deflect

the electrons which are thermally emitted from the unused

portion of the photocathode toward the walls of the tube,

thus preventing them from passing through the dynode chain.


Pulse Counting System

The output pulses from the detectors pass through a

preamplifier (located as closely as possible to the detector

to reduce the input capacitance) into a linear amplifier and

then a pulse-height discriminator (see Fig. 9). The ampli-

fication and the threshold of the discriminator are adjusted

to give the best signal-to-noise ratio. To obtain emission

spectra, the output of the discriminator is integrated by a

linear rate meter and then displayed by a strip chart recorder

while the monochromators are scanning the wavelength region

of interest. Relative emission rates for the various spectral

features are obtained by summing the output pulses of the dis-

criminator over a convenient time interval using a preset

timer-scaler combination.




















































2-



QJ





0,







U,


ZI u,
04

ic ci





U



In
2



U
In






30


















I a:
rn UJ



rt. u I
I-..
(n








L;Ij
~~L J




I-


cc,
C) w







_IJ
Ld z


0-_D



C rn

H -4 EL'














III. PROCEDURE
Operational Definition of the Excitation
and Emission Cross Sections

When a projectile beam of density Nb (particles/cm3)

and velocity v (cm/sec) is incident on a target gas of

density N (particles/cm3), the number of excited molecules

produced per unit time per unit.volume in a particular ex-

cited state is given by

dN.
--= N N avo ,
dt (a b ( -1)

where Ni may be the density of excited molecules in the

target Nai or in the beam bi. The constant of proportional-

ity o. is called the total cross section for exciting state i

and has the units of square centimeters. As the projectile

beam of cross sectional area A traverses a finite length Z of

the target region, the total number of excited molecules pro-

duced per unit time in state i is given by


N. = / / NaNb dA dx (111-2)
Z iA a b i

If the density of the target gas is uniform over the volume

At, then

N. = oia f [f Nbv dA] dx (1 1-3)
SA

where Ib(x) = f Nbv dA (I11-4)
A

is the flux integrated over the cross sectional area of the








projectile beam at a position x. The integrated flux of the

projectile beam as a function of position is given by


I((X) = I1(0) exp(-N a ), (111-5)

where o is the total cross section for all processes which

remove a projectile from the beam. This leads to the expres-

sion

SIb (0)
N. [.l-exp(-N a0 )]
o ( 111-6)
o


for the number of excited states i produced per unit time in

a finite distance R. If N a << the so-called thin target
ao
criterion, this last equation reduces to


Ni = iI (O)N a, (11 -7)


and the operational definition of the total cross section

for the production of state i becomes


N.
S. =a
SIb(O)Na ( 11 -8)


The assumption of single-collision conditions, i.e.,

when no projectile undergoes more than one collision as it

traverses the target chamber, has been implicit in this deri-

vation. Thus, whenever equation (1l1-7) is shown to be sat-

isfied, i.e., when N. is linearly dependent upon both N and
a
Ib(0), it is assured that the experiment is being carried out

under single-collision conditions. Under these conditions

Na is approximately uniform and IbT() = Ib(0) = NbvA so that
a D b b








Ib and NA may be monitored at any convenient point within

the target chamber.

The emission cross section is defined analogous to the

excitation cross section by the relation


G . -
1 NaI b ( I 1-9)


where J.. is the total number of photons emitted per second
s1J
in the transition i j from a length of the beam path

through the target region. In this expression the assump-

tion is also made that N and Ib are sufficiently tenuous

to assure that they may be monitored at any convenient point

within the coll vision chamber.


The Relationship of the Excitation Cross
Section to the Emission Cross Section

Although collisionally induced emission cross sections

may be of practical interest in and of themselves, they are

of most value when they can be related in an unambiguous way

to excitation cross sections. The comparison of the emission

cross section to the excitation cross section is, however,

complicated by several factors: (i) the emission cross sec-

tion is related to all processes which populate and depopulate

an excited state i, not just to the direct excitation of this

state; (ii) 'f the lifetime of an excited state is very long,

the excited particle may drift a considerable distance before

emission occurs, and the emission cross section may depend

upon the point at which observations are made; and (iii) if








the emission is anisotropic, the measured emission cross

section will depend upon the position of observation. The

remainder of this section demonstrates how the emission and

excitation cross sections can be related to each other in a

systematic way, and follows the presentation by E. W. Thomas.9

When the beam-static target configuration is employed,

the assumption generally made in relating the total emission

cross section to the total excitation cross section is that

the projectile experiences only a small change in energy and

direction as a result of a collision, while the target re-

coils only with a small velocity and at an angle of approx-

imately 90 to the beam direction. Therefore, t, a first

approximation, the direction and speed of the projectile as

well as the position of the target remains unchanged by col-

lision. Two different approaches to the comparison of the

emission cross section with the excitation cross section are,

therefore, required depending upon whether the projectile or

the target is the emitting species.


Target Excitation

There are four processes which act to populate a given

state i of the target molecule: (i) direct collisional exci-

tation by the projectile, (ii) cascades from all higher states

k which are excited during the collision process, (iii) ab-

sorption of resonant photons, and (iv) transfer of internal

energy by collisions with other target particles. Therefore

the number density of the target particles in state i increases








at a rate given by


dNa
= N vo .i + Zk N Ak + f.A oN + i o .a' (111-10)
dt as D k>I ak kI + so as x es ax
dt


The first term of this equation represents the rate of direct

coll isional excitation which has already been discussed. The

second term represents the rate of populating state i by cas-

cade from all higher states k, where Nak is the density of

target particles in state k and Aki is the radiative transi-

tion probability for the decay of state k to state i. The

third term represents the rate of repopulation of state i by

absorption of resonant photons, where A. Ni is the rate of

depopulation to the ground state by spontaneous radiative de-

cay and fi is the fraction of resonant photons which are ab-

sorbed within the target region. The last term represents

the rate of population of state i by collisional transfer of

internal energy by collisions with other target particles

where c = o N is the collisional frequency and N is
x 2. xt Xa ax
the density of target particles in all other states x.

The number density of the target particle in state i

decreases at a rate given by


dN
at
N . . + .
dt ai, j< 1, at x zx (111-11)

where the first term represents the rate of depopulation due

to spontaneous radiative decay to all lower states j, while

the second term represents the rate of depopulation due to

collisional transfer.








Once a steady state is reached, the rates of population

and depopulation must be equal, and the expression for the

equilibrium excited state density NA i is given by
aa


a b + k>i ak ki x x, ax
a E . A .. fiA + Z C (1 -12)
3] 3 < io

The number of photons of wavelength A emitted per unit time

in all directions from a length R of the beam path is given by


J.. = N -A ..A, (11 -13)
,3 ai 3

where A is the cross sectional area of the beam and A..(sec-)
'3
is the radiative transition probability for the uecay of state

i to state j. Making use of equations (111-12) and (Ill-13),

the expression for the emission cross section [see equation

(111-9)] becomes

A.A NY + T7 A / + Cn A
ij. a Nb"i k>i ak ki x xi ax
S.. = A..
N I A f A t + E c

(1 11-14)


This equation can be simplified to give
A A
oi + Zk>.i Oki + C iYx

SA .A. + c (111-15)
3j

where ki, the emission cross section for the cascade transi-

tion, has replaced the cascade term N kA ki A(N I b )-1, and
where is defined by the relation a
where y is defined by the relation y = AN (N Sa N 1b
x o: x a b








In this equation the emission cross section is related

to terms describing photoabsorption and collisional transfer,

both of which depend upon the construction and operating con-

ditions of the apparatus. As stated earlier, measurements of

emission cross sections may be of interest in and of them-

selves, but are most useful if they can be related in an un-

ambiguous way to the excitation cross section, that is, if

S.. is independent of the construction and operating condi-

tions of the apparatus. Since the photoabsorption and colli-

sional transfer terms are obviously dependent upon the tar-

get density, at sufficiently low pressures within the colli-

sion chamber, their effect should be negligible. Under these

conditions, equation (111-15) reduces to


A .
o [ +
S . A.. '7 i' ('I -16)


Here .. is no longer dependent upon target density, and J.

can be shown to be linearly dependent upon both Na and Ib [see

equation (Ii -9)]. Therefore, when J.. is shown to be linearly

dependent upon both N and I (and J . 0 as Na 0), the
a b L a
emission cross section a.. is independent of the construction

and operating conditions of the apparatus. The excitation

cross section can then be determined, if the transition prob-

abilities are known, by measuring the emission cross section

a.. and all emission cross sections due to cascade, according

to the equation,
EJ A.
S C. = 0i ki Oki
A .k (I 1 1-17)








If this equation is summed over all j
the excitation cross section becomes


S= E . (111-18)
i ji ki' (I I-18)

Thus the emission cross section can also be determined by

measuring the emission cross sections for all transitions

into and out of a given state.

Only in a relatively small number of cases is it possi-

ble to evaluate an excitation cross section explicitly in

this way, either because of the limited spectral range of a

practical detection system or because of the limited accur-

acy of calculated transition probabilities. However, in many

cases the cascade terms may be shown to be quite small, thus

simplifying the comparison of the emission and excitation

cross section.

As mentioned earlier, this treatment of target excita-

tion is based upon the assumption that the excited target

emits from the same place where it is excited. There is

presently no evidence to indicate that this assumption is

violated for projectiles colliding with atomic targets. This

may, however, not be true for excited fragments produced by

the dissociation of molecules. However, as will become clear

from the following treatment of projectile excitation, if

the lifetimes of the excited states are short (of the order

of 10-8 sec.), then this assumption may still be quite ade-

quate.








Projectile Excitation

The mechanisms leading to the population and depopula-

tion of an excited state of the projectile are essentially

the same as for the target. However, since the number den-

sity of the emitting species in a projectile beam is small,

absorption of resonant photons and collisional transfer of

excitation energy have generally been neglected. The rate

of population of the excited state i in the projectile beam,

then, is given by


dNbi ,
dt Na Nb + k>i N Ak i N. 2 Aij


(1 11-19)

where the terms on the right hand side represent the rate of

direct excitation, the rate of cascade from all higher lev-

els k, and the rate of spontaneous radiative decay into all

lower levels j, respectively.

Since the excited projectile has an appreciable velocity

and may move a considerable distance before emitting a photon,

the density of excited states in the projectile beam, and

thus the intensity of photon emissions, will depend upon the

penetration of the projectile beam through the target region.

To facilitate the calculation of ,N i as a function of pene-

tration, the time variable is converted to distance by the

relation x = vt where x is the distance penetrated by the pro-

jectile in time t. As a first approximation to the solution

of equation (111-19), the cascade term is neglected, giving









VuaNb o .
Nb =- [1-exp (-x/vri) ,
S . A (111-20)


subject to the boundary condition Nbi = 0 at x = 0. In this

equation T is equal to [z. A..]-1 and is the lifetime of

state i. The total number of photons emitted in all direc-

tions from a beam of cross sectional area A and of length Z

is given by


L+Z
J. = I I N .A dA dx. ( 11-21)
-3 L b


In this equation L is the penetration of the bean, through

the target chamber before reaching the observation region

(that region from which photons can be detected by the appa-

ratus), and 2 is the length of the beam within the observa-

tion region. Upon integration of equation (111-21), the

emission cross section becomes


oiA .A
o .. -
S Z .A. (111-22)
3<1- -3


where
VT.
A = 1 {exp (-L/wvr)cl-exp(-Z/VTi)]}


(111-23)
is a correction term due to the projectile velocity and the

lifetime of the excited state. When VT << the correction

term A = 1 and the excitation cross section would again take

the form of equation (111-16) except for the fact that the








cascade terms will also depend upon the position of excita-

tion and the lifetime of the higher levels. We will, how-

ever, define a corrected emission cross section 0.. by the

equation


i3 A (111-24)


Again the treatment of projectile excitation is based

upon the assumption that the speed and direction of the

projectile remains unchanged as it passes through the target

region.

Determination of Emission Cross Sections

To determine the emission cross section for the i j

transition it is necessary to relate the output signal S..

(counts per unit time) of the optical system to the total

number of photons J.. emitted per unit time from a length Z

of the beam path through the target region. In any practi-

cal experiment only a portion of these photons are detected.

If the emission is isotropic, the number of photons entering

the optical system per unit time S is given by
S J J


S..= J..
-0 4 1 (1 1-25)


where Q is the solid angle subtended by the optical system.

The output signal S .., therefore, is given by


S.. = S.. K(, A = J. -- K(),
-' -3 t3O 4'i ( 11-26)


where S.. is the number of photons entering the optical system
7-'J








per unit time and K(A) is the detection efficiency at the

wavelength X of the i j transition. The expression for

the emission cross section then becomes, from equation (Ill-9),

S.. 47T
7,3
J K(X) Na bt (I 1-27)


The ion beam flux Ib integrated over the cross sectional

area of the beam is related directly to the ion beam current

I measured by the Faraday cup, and at low pressure the target

gas density Na may be related to the gas pressure P in the

target chamber by the ideal gas law. If the observation length

z and the solid angle Q remain unchanged during a series of

measurements, the emission cross section may be written


a i =
K(A) (I1 -28)


where the relative emission rate a.. is defined by the relation

sj


i3 P I (111-29)


and where A is a constant as long as the observation length

., the solid angle 2, and the temperature of the target gas

remain unchanged.

To insure that the determination of emission cross sec-

tions was independent of secondary processes, i.e., that a.
z3
is independent of both Na and Ib, measurements of relative

count rates were made as a function of target gas pressure.

Figure 10 is a plot of relative count rate versus target
































T3





E


-1


C1



















O-
CZ



cJ









cn
C











C Z


- 0
o










0:
C .-





- 0

0
H 0


CU C LU




















77

















CL






(UQO
C; Wrvj




to LO I

I N UII-IWV 3L.8 L~o 3UV-3








gas pressure for the excitation of (a) the Av = 0 band se-

quence of the first negative system of 02 (b) the (0,0)

band of the first negative system of N2 and (c) the 1200 A

line of NI. The relative emission rate for these three fea-

tures is linear for pressures below 4 X 10-4 torr. Thus all

measurements of relative cross sections were made with a tar-

get gas pressure of less than 4 X 10-4 torr. In addition,

the relative emission rate was found to be linear with ion

beam current over the entire range of currents used.


The Emission Cross Section as a Function of Energy

When the emission cross section of a particular transi-

tion is measured as a function of ion beam energy, both A

and K(x) remain unchanged for all measurements and the rela-

tive emission rate o.. is directly proportional to the abso-

lute emission cross section. Relative emission rates are

measured as a function of energy by computing the ratio of

the net output signal to the product of the ion beam current

and the target gas pressure for each potential applied to the

ion chamber [equation (111-29)]. The net output signal is

taken to be the difference of the output signal obtained with

a target pressure P and the background signal obtained when

the target gas has been removed.


Relative Emission Cross Sections

The ratio of absolute emission cross sections for two

different spectral features measured at the same ion beam

energy is given by









ij ij kZ

kl kl Kij (111-30)


as long as the observation length k, the solid angle 0, and

the temperature of the target gas remain unchanged while the

two features are compared. This expression, then, defines

the relative emission cross sections for the two features,

where o.. and okZ are obtained as described above at a par-

ticular beam energy, and the ratio K(iz)/KK( j .) is obtained

by taking the ratio of the relative detection efficiency at

the two wavelengths. The determination of this relative

detection efficiency is described in the following section.


Calibration of the Optical Detection System

The relative detection efficiency is determined by the

expression

K(\I) I(Xi) Io(\2J

K(\2) I(12) I (A) (111-31)

where I(A1)/1(>2) is the relative intensity of two spectral

features measured with the optical detection system and

Io(A )/o1 0(2) is the known relative intensity of the same

two spectral features.

For wavelengths greater than 2800 A the relative detec-

tion efficiency was determined using a calibrated tungsten

ribbon lamp (Eppley model No. EPS-1055) as a light source.

Plots of the relative detection efficiency of the vacuum mono-

chromator system and of the Ebert mount system, both using










































GJ0


ca C
U'%
Cc











rru


C:4
dlo



















ru 0.
uu
U-'




















0
44g

















Q):
U Li





















u
I~n







-o
>c
(Ul





im
E




4- 0

CO

CE

44E
dI:

44 0
dim
-o

di


En

diE
Id:




48







8











,I,
/ o




o






p i p
I
t' t
r s






- I O






















C
+J

3
0
E







L
-Q








O



0




--r
1 4.








0 m







"J
C-
C 2.

















uc
u 4o
E:
441


c





0
o U











aCE
* -U
0
>- 44







"0

o C
0

E


ao




50



O
-- rF~ TI i-T---- 1 TITTTF-ni-i- i--- o



/
o0
/ o
/





0
-




/










0 0 1




0 c 0
A- ,N Ki fic;.asci 1]A,
*\i
-- -- J- J.L.i.,_L_ -.i .^UJ LL L- -J L _-



^ -: 00
































Figure 13

Relative detection efficiency as a function of
wavelength for the vacuum monochromator
and the EMR phototube.













G-







L .


El
-4



0 3;

li
LL\








L--








1200 1400 100 1800

WAVELENGTH (A
























E


2



.j
> 0





-c





c

O iL
LC





















c C .-
O *- U





m J
-x

> -c

S0)

1- E
00
>)>-










CD
U -- U
4i C





U .) >

0)
















c Z ..
>- SE







U LU
0l








o i
0) E












>C
O
WE





'U


0r

























o








-o

CO







S0 0 Uo 1O -


AOW,1OiU-3 NO!1O213G 3Al?V13a








the EMI 9558Q tube, are shown in Figs. 11 and 12, respectively,

for this spectral region. Here the error in determining the

relative detection efficiency is estimated at less than 5%.

Because there are no standard sources for the vacuum

ultraviolet region of the spectrum, the relative detection

efficiency in this region must be determined by branching

ratio techniques. In the region between 1200 and 1750 A the

relative emission rates of two pairs of NI lines (1493, 1744;

1243, 1412 A) obtained from ion beam collisions are compared

with tabulated transition probabilities10 to obtain the var-

iation in detection efficiency of the system. A plot of the

relative detection efficiency of the vacuum monocaromator

with the EMR tube is shown in Fig. 13 for this spectral reg-

ion. The results for these two sets of points are connected

by assuming that the variation in detection sensitivity is

linear between pairs of points when plotted on a semilogarith-

mic scale. There is some freedom allowed in determining the

intersection point of the two linear segments. The particular

choice made here results in a curve which is very similar to

the quantum efficiency curve for the EMR tube alone. It

should be pointed out that the quantum efficiency of the EMR

tube falls off very sharply below 1200 A, so that the detection

efficiency plotted in Fig. 13 cannot be extrapolated to lower

wavelengths. Although the absolute transition probabilities

of the NI lines may be in error by as much as 50%, the ratios

should be much less uncertain. However, the assumption that

the response curve is linear between pairs of calibration points








when plotted on a semilogarithmic scale, and the freedom

allowed in fitting the two linear segments of this curve lead

to an estimated overall uncertainty in the determination of

relative cross sections of approximately 50% for the entire

spectral range from 1200 to 1750 A. The uncertainty in ob-

taining relative cross sections for the spectral range from

1200 to 1400 A, however, is expected to be much less than 50%.

In Fig. 14 a plot of the relative detection efficiency

of the vacuum monochromator with the MEM is shown for the

spectral region between 600 and 1200 A. For the region be-

tween 1000 and 1200 A the molecular branching ratio method

was utilized. 1 Here, the relative detection efficiency has

been obtained by comparing the relative emission rates of the

1Q lines of the 2-v" progression of the Werner system of H2

produced in a microwave light source to the transition prob-

abilities given by Allison and Oalgarno.12 The light inten-

sity was sufficient to achieve 0.30 A resolution. To obtain

the relative detection efficiency below 1000 A, the relative

emission rates of two pairs of Oi lines (796,718; 673,616 A)

have been compared with tabulated transition probabilities.

This was done for Oil emissions resulting both from He ions

bombarding 02 and from a microwave light source. The detec-

tion sensitivity curve was obtained as before by assuming a

linear variation of sensitivity between pairs of points on a

semilogarithmic scale. Again, using this technique some free-

dom is allowed in determining the intersection points of the

various linear segments. Since the results differ somewhat









depending upon the source of the 011 emissions and upon the

choice of intersection points, a smooth response curve was

constructed by averaging different possible curves. This

average curve is what is presented in Fig. 14. The slope
o
of the relative response curve between 650 and 750 A is seen

to agree well with the slope of the relative quantum efficien-

cy of the MEM in this region (represented by x in Fig. 14).

The relative quantum efficiency of the MEM was obtained by

simultaneously comparing the response of the MEM at various

wavelengths to that of a photomultiplier tube coated with

sodium salicylate under the assumption that the response of

the sodium salicylate does not vary with wavelength over this

region.

The errors in calculating the absolute transition prob-

abilities of the Werner system are quoted as less than 6%.

Again, the ratio of transition probabilities is expected to

be even more accurate. Thus, within the spectral region from

1000 to 1200 A the uncertainty in determining the relative

spectral response is expected to be less than 5%. Assuming

that it does not fall off too rapidly below 1000 A, the

relative detection efficiency is expected to be in error

by less than 20% down to 900 A. The quoted error in the

transition probabilities given for the Oil lines is greater

than 50% so that below 900 A the uncertainties increase and

are probably as high as 70 100% at 700 A.








Dependence of the Emission Cross
Section on Polarization

In any practical experiment only a portion of the photons

emitted from a length of the ion beam are detected. If the

emission of these photons is anisotropic, the number of pho-

tons entering the detection system per unit time will depend

not only upon the solid angle Q subtended by the detection

system, but also upon the angle of observation, 0, measured

relative to the beam direction. It can be shown13 that the

rate of photon emission from a length I of the ion beam per

unit solid angle in a direction e is given by

ij 3-Pcos28
Iij( 4d 3-P (111-32)



where P is the polarization fraction defined by


I. J




In this last equation I.. and I.. are the number of photons

emitted per unit solid angle per unit time in the direction

0 = 90 with planes of polarization respectively parallel

and perpendicular to the beam direction.

The number of photons S.. actually entering the detec-
tJ
tion apparatus, then, is given by

S.. -= f i'( ) di ( 1 -34)


If observations are made at right angles to the beam direction,

and if 0 varies only slightly over the solid angle 0, then








S.. is given by


S.. = I..(900) = I... ( 11 -35)


In order to relate the output signal of the detection

system to the photons entering the system, the detection

sensitivity of the optical system must be known for polar-

ized light. It should be obvious that the count rate S..
"3
is given by
i N L L
S.. = [K I.. + K i .], (111-36)


where K K is the detection sensitivity for light polar-

ized respectively parallel and perpendicular to the beam

direction. Since the total number of photons entering the

detection apparatus I.. is given by


I.. = I.. + I.. = T..(C + 1), ( 1-37)
'-3 zj 1-3 '3

where C = I../ i., and the detection sensitivity for unpolar-

ized light is given by

i L L
K + K K (a+1)
K(W) = ---- ----
2 2 (111-38)

N L
where a = K /X then equation (111-36) can be written


(Ca + 1)
S..= 2K(A) I..
o3 o (a+- ) (C+I) (1 1-39)


Using equation (111-32), with 0 = 90, this equation becomes

0 3 2(C+1) K(X)
St. t 4n 3-P ( a+.(C+ ) (111-40)
sO '_ 4,1 3-P (a+1) (C+1) (1 1 1-40)








and the emission cross section becomes


o. .= - F.
"S NI N I1, (il -41)
a b a

where

(a+1)(C+1) 3-P

2(C+1) 3 (111-42)

is the correction due to the effect of polarization. This

correction term can also be written



1-P/3
r =
P(a-1)
S+
(a+1) ( 1-43)

It is clear from this last expression that if P = 0, F = 1,

and if a = 1, F = 1-P/3. Therefore, in order to actually

determine the emission cross section, the polarization frac-

tion must be determined. From equations (111-33) and (111-35)

it is clear that the polarization fraction can be written

r *-t
S.. S..
P = i AL.
S.. + si. (1 1-44)


As discussed previously the output signal S.. is determined

by the detection efficiency of the optical system. This de-

tection efficiency depends upon the polarization, so that

equation (111-44) becomes

Ir II L I tL JL
itt
= ./K (Ki /K )

S ./K + Si /K o +o (K /K )

( 1 -45)



























0


Cu
N










CL

Cu


0
2























4-
r







E
Cu
I-







2 C-
3 Cu

LCO C
-u

0L a









E
Cu

Dc
C
Cu

Cu

CU


C
Cu
0

Cu




x
w

























LM


cfli l


c- c n

o L
- -)
I c


rl
N


-I




0

.N
Z



Ij



-J
C
^ CL


cr


I <
O 0
2 [-



fd 0
, o


LJ
co












0 LJ
F- "
0 0



S -1

C C
(1_ 0
































Figure 16

Instrumental polarization of the Ebert mount
monochromator as a function of wavelength.















2.0 i-r r -E -i r i-T 1-









1.5 ,:

0$ /




- 4


S.0







0.5 -










4000 5000 5000
WAVELENGTH (A)


7000







n L
where a and a are the relative emission rates for light

polarized respectively parallel and perpendicular to the

beam direction, and where the ratio K /K is called the

instrumental polarization for the detection system, a.

The arrangement for determining the instrumental polar-

ization is shown in Fig. 15. Light from an Eppley tungsten

ribbon lamp was depolarized by a diffuser and focused by a

quartz lens through a polarization analyzer onto the entrance

slit of the monochromator. The analyzer was mounted so that

the polarization axis could be fixed either parallel or per-

pendicular to the beam direction. The output signal of the

photomultiplier was then measured at each wavelength with

the polarizer first parallel, then perpendicular. When the

incident light is unpolarized, the ratio of the output sig-

nals measured with the polarizer first parallel and then per-
L
pendicular to the beam direction, S /S is clearly equal to

the instrumentation polarization K /K A plot of the in-

strumentation polarization as a function of wavelength is

shown in Fig. 16 for wavelengths between 4000 and 7500 A.

Therefore, to determine the polarization of a given

spectral feature as a function of beam energy, the relative

emission rates for the two orientations of the analyzer are

computed for each potential applied to the ion chamber, and

equation (111-45) is evaluated using the instrumental polar-

ization plotted in Fig. 16.















IV. RESULTS

Identification of Observed Spectral Features

Spectral scans arising from N2+ + 02 collisions are

shown in Figs. 17-22 for the wavelength region between 700

and 6200 A. These scans have not been corrected for varia-

tions in the sensitivity of the optical detection system as

a function of wavelength.


Spectral Features Above 2500 A

In Figs. 17, 18, and 19 a spectral scan from 2500 to

5050 A taken with 5 A resolution is shown for a collision

energy of 4 keV. The most prominent features in this spec-

tral region are the vibrational bands of the second positive

system of N2 (C 3 B 31 ) and of the first negative sys-
S a g
tem of N + (B 2+ X 2Z+), the (0,0) band of this latter
2 u g
system being off scale in Fig. 18. The locations of many

of the band heads of these systems are indicated although not
0
all of those indicated are clearly resolved. With 5 A reso-

lution both of these systems have the appearance of single-

headed bands which are degraded toward shorter wavelengths.

Also present in this spectral region (most prominent at the

shorter wavelengths) is the second negative system of 02

(A 21 .- X 2H ). This is an extensive system of double-
u g
headed bands which are degraded to the red. Below 3000 A

other spectral features also appear to be present, but because





















0 -








NC
E >





O
u a)

0 .C



UC C4
C: _






0
U ) -u


(D- C
Oc









0 m0

- "--
4-

E



C T 4







O 0
or
o 1- .







-I-
















m 0
0 m)

























' C
"- 0 0








-E
-o












m
oJ-
U ^
CL .-







LUl f
Ea~





















0









2,


0





2 3S/SN~0t


C)
0





N,










2;if































a

N

2


u---,-




-r -.











CC











--C





















--4
2K
:4Km












O-'"d Y fl I






















C1O



r>
o -












-c- t

+ -0




0 C
O C














o"ro 0
0

C -L:0


O0 O







*- -4
C4-' 0
**O-






to-- -u
3C:



cc

0
0 o -
o L





C >

-2 C
o o
o -r

( 4- 0
0 --



3LO

C a"O




S- O

auto
0 0--4
1) u=






i -


E
UJ





70




(;
o










--- f U L






S..

-- 0- 4 -,9
-r .4 3 s IK













3- In AV't
s o o I



4,-- '5^
0 "

-/ I
-- I~




).3f- .IN L
s- ^ "
s. r~y












^ ^ 2__ ^
o IXo < -
























-c


+

C
+ fU

Z 01

Oa *



0 c
C U>


0 0
c






aE C-
O r










C
. OT
0 0







U-0





cn- .--





















U
0
ro r
C L..











E
0Cu
o o




-U --
04-






OQO
0r0



U -













-- IO
LE













A".
r

io







-- /
I')
a
N
ri-
zn t ho







0
a a
N L




















g--
Z ---




aQ
rit
^ / <









41J t 5






2

_. _
it" _.









... -
Si,-





N C
o 0- 0 ---it
Tr ~ fi fl.







'0



- -) C)-



o ot
26 -


-Q N- 0. .
a o.
/ t :- 1dO d r ^IU
t-< H 1= ^^
0u 0 0I '- ~-





<' '. -- TK- -
(i -1.^
> n ^.



a ~f0




?3S/SNOI~o:-ud do) dtij~'!li ri.Mi iir"





















Co



















-TD
0
m c
0e
+*-




















"-- CD
(o

4-f -


























L C
CA







00
-- 3










04-'
O0
0 C-u
cc



*-o >





















<- 0
L C






















mi
4- C
















CY



U-c-
fO
CO
o I- 0

C'i

-c c

C .2
r 0








a) L






0
U -



u-




(U r







LU













~p- 'ro:
0u






PH





a ~ O

0,










I~U)


a *.2





to







a -. r
c.J I







,2



too


*1-




















N
0


.:C -
c




c-j
c
+ m

C


-D
0
C 1
O

inc




0
0 >
o o<


E -


















4
OJ










































lu
c

-c~c
CL 3
0- i
C -a
0 -- ini


O Q04





L\ -


in 4 a






CL-





ri





U -


a uO





in
0E
c l-

"u
3: <






76








Ct C
H H --- .--^
,, "* J I









60 -









zI
^ H ------- ------c--~-------- *'.


F'^l.s-'-----;i -- -- --- --- --------




3/
c 7I /-^^
^-" '

H H
_^ _ _______


33S,'SNOJ.OHcd 2JO tSI'nLN 3AiIJ.U-1u


0
ro


U
-_
uJ






















0















Q)
0
+










Q))

0)
4- Z













cn c
A_-






CD,

Clo




LA 0
0u T
---0)
E )

























LiD
o -


0-o
.0 L






O 01





C 000



004



C"

>- 4
0a) 0




0-

0)0)





U-
0)0
0.

00
Oc
04-
40


Fl





78




V -
1-n ,g + '












N o
H


0 0 0

-- --- ------- 0
N H- 0















L L
Z a
-, N H -e












-- -- ^- - _
ci







0 N N c' I-



''r- ^ ------ '"----W-- _
-42















a C)



^ __


3SS/SNOI&OHd J0 aiZWru-i JAIN173U


M-.








of the relatively low signals and extensive nature of the 02

second negative emissions, these could not be unambiguously

identified.14

In Fig. 20 a scan from 5000 to 6200 A is shown taken

with a resolution of 8.5 A. This scan was also taken at a

collision energy of 4 keV. The width of the rotational struc-

ture and the consequent overlapping of the different bands of

the first negative system of 02 (b 4Z a ) together

with the relatively low signal make it impossible to identify

the individual bands. For this reason only the band sequences

(Av = 0, -1, -2) have been identified.

The atomic lines observed in the spectral region above

2500 A arise, except for four 01 lines, from transitions of

the atomic ions of oxygen and nitrogen. These lines appear

to be relatively weak compared to the molecular bands of N2

and N2 but this is due in part to the decrease in detection

sensitivity at the higher wavelengths.

Above 6200 A no additional features were identifiable.


Spectral Features Below 1500 A

Figures 21 and 22 show a spectral scan from 1500 to 700 A

taken with 5 A resolution, the collision energy being respec-

tively 2.5 and 4 keV. The most prominent features in this

spectral region are the resonance lines of both NI and 01.
0 0
Both of these features (the 1200 A line of NI and the 1303.5 A

line of 01) are off scale in Fig. 21. Other atomic lines

arising from excited dissociation fragments are also identi-

fied.15








Below 700 A a spectral feature was observed at approxi-
0
mately 673 A. This feature appeared to be broad enough to be

two unresolved lines and probably arises from the 2s3s 2pO -

2p2 3p transition of NII and the 2p23s 2p 2p3 2pO transition

of O l .

The only spectral features observed in the wavelength
0 o
region between 1500 and 2500 A (not shown) were the 1743.6 A

line of NI, which arises from the same upper state as the
0 o
1493.3 A line, and, at wavelengths greater than 2200 A, the

second negative system of 02


Emission Cross Sections of the Molecular
Features of N and N2

The emission cross sections for the (0,0), (0,1), (1,2),

and (2,3) bands of the first negative system of N2 are plot-

ted in Fig. 23 and listed in Table I as a function of ion

beam energy, while emission cross sections for the (0,0),

(1,0),. and (2,1) bands of the second positive systems of N2

are presented in Fig. 24 and Table II. The relative emission

rates for the individual features were determined at a much

larger number of impact energies than indicated in these

figures, and a smooth curve was visually fit to these origin-

al data points. Within experimental error there appears to

be no structure in the relative emission rates as a function

of energy for any of these spectral features so that the

values for the emission cross sections derived from this

smooth curve are averaged values and may well be more accu-

rate than individual data points. The error bars in Figs.







































C- a
Oa)


a-E

0*4 I.
U) a)

u*- a
a~ U-
-0 E
oala
U a
a~C 4OJ

a) 4
-~ 0




U) C

o n 4-







a) itl

a) c'



' -0


a--
a)- E





E '-U)


a) >
0 *
-~ a-
0-
U)
vl0
















O
---T Il--T-1- -ic
o x





00 <<
0 4 -
o ox < --
o x oo i,.

o o l :< --
oo Lu
0 o -



"- 0
+a -
00 0
-C;- -a] 0



- 3c
<


1 ilf I I I I I -
Q q q q q o
(uw O I)-o














Table 1. Absolute emission cross sections for
the (0,0), (0,1), (1,2), and (2,3) bands of
the first negative system of N2+ arising
from collisions of N2+ with 02.

Cross Section
Energy
(key) (10-18 cm2)
(keV)0) (0, 1 2) (2____
(0,0) (0,1) (1,2) (2,3)


0.25
0.30
0.35
0.40
0.50
0.60
0.70
0.80
0.90
1 .00
1.25
1.50
1.75
2.00
2.50
3.00
3.50
4.00
5.00
6.00
7.00


0.07
0.14
0.27
0.45
0.79
1.14
1.53
1.88
2.27
2.67
3.63
4.64
5.61
6.48
8.15
9.64
11.05
12.38
14.52
16.49
18.35


0.05
0.09
0.18
0.35
0.49
0.63
0.77
0.91
1.20
1.49
1.78
2.02
2.50
2.94
3.32
3.66
4.28
4.84
5.34


0.05
0.09
0.18
0.28
0.41
0.53
0.63
0.75
1.00
1.23
1 .44
1.65
2.05
2.38
2.72
3.08
3.63
4.22
4.75


0.05
0.09
0.17
0.24
0.33
0.41
0.47
0.53
0.67
0.78
0.88
0.96
.1 0
1 .24
1.33
1 .40
1 59
1.74
1 .85































-W
-0ol
C:





'4-
-0


aa




0o


WO
C3
C




-u u










00(
uu
75










0.. E
aj




OW




in,


UZ







0 (1)
inC





0


u
(1)









-C
C:4
0
2- u









0


Sla
0
-on





85










0



0 < -- x -
O

o < x < ~

xI
W <
-0- -1- ---




c 'x4 0
O
0C0


a C.



oJ


IJ 1 I -1 2 ___
o o q o o oq o
L jo ro o


(WO o 801).-o














Table II. Absolute emission cross sections for
the (0,0), (1,0), and (2.1) bands of the
second positive system of N2 arising
from collisions of N2+ with 02.


Cross Section
(10-18 cm2)


Energy
(keV)


(0,0)


0.30
0.35
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.25
1 .50
1 .75
2.00
2.50
3.00
3.50
4.00
5.00
6.00
7.00


0.02
0.04
0.05
0.1 1
0.18
0.23
0.32
0.39
0.50
0.78
1.10
1.38
1.69
2.30
2.77
3.19
3.57
4.26
4.80
5.30


(1,0)


0.02
0.05
0.08
0.12
0.18
0.25
0.34
0.41
0.64
0 .89
1.16
1.40
1.87
2.24
2.58
2.92
3.37
3.81
4.22


(2.1)


0.03
0.08
0 .11
0.16
0.22
0.28
0.45
0.63
0.77
0.91
1.1 1
1.42
1 .64
1.88
2.20
2.51
2.02








23 and 24 indicate the estimated error in determining the

relative cross section of a particular band as a function

of energy.

As can be seen in Figs. 23 and 24, the relative emis-

sion rates of the N2 first negative and of the N2 second

positive bands increase monotonically above an ion-beam

energy of about 0.20 keV. Below this energy the relative

emission rate levels off, and, within experimental error,

becomes constant as far down as 80 eV. The emission rate

of the (0,0) band of the N2+ first negative system remained

constant as far down as 33 eV.

It was impossible to determine whether this constant

signal resulted from emissions of the feature under observa-

tion or from the background continuum which was observed at
o
all wavelengths above 2500 A. Therefore, the energy thresh-

old for the emission cross section could not be determined.

The observed background above 2500 A may be due in part

to unresolved molecular emissions of the second negative

system of 02 In addition, no emissions from the 02 mole-

cule were identified, so that some of this apparent background

may result from unresolved 02 emissions. However, this seems

unlikely since the relative emission rate of the background,

measured at 3200, 3400, 4015, 4300, and 4900 A, was found to

be fairly constant with both wavelength and collision energy,

although there was a slight increase in the observed back-

ground at 4300 and 4900 A for energies above 4 keV. The

emission rates for all spectral features above 2500 A have

been corrected for this observed background.









In order to determine the variation of the emission

cross section for a particular molecular band as a func-

tion of energy, the relative emission rate of the band head

was measured with a 5 A band width for various ion beam ener-

gies. The relative emission rates obtained in this way

should be free of significant error unless there is consider-

able overlap of the head of one band by the rotational struc-

ture of an adjacent band and unless the rotational-energy dis-

tribution in the upper state varies significantly with pro-

jectile velocity.

To determine the amount of overlap of the head of one

band by the rotational structure of an adjacent band for the

Av = -1 band sequence of the first negative system of N2 a

high resolution scan was taken with a beam energy of 3 keV

and a target pressure of 4 X 10-4 torr. This scan indicated

that the rotational structure was relatively compact, extend-
0 0
ing only over about 40 A for the (0,1) band, 30 A for the

(1,2) band, and 20 A for the (2,3) band. The error in the

relative emission rate due to overlap was estimated at less

than 3% for this system. A high resolution scan of the

Av = +1 band sequence of the second positive system of N2

was also taken at a beam energy of 3 keV. Again the rota-

tional structure of the bands appeared relatively compact

and the error in the relative emission rates due to overlap

was estimated to be no greater than 6%.

In experiments conducted by Bregman-Reisler and Doer-

ing16 on the excitation of N2 in collisions with He and Ne,







the energy distribution among the rotational levels of the

first negative (0,0) band of N2 was found to be velocity

dependent below about 1.2 X 107 cm/sec (an ion-beam energy

of approximately 2 keV). The excitation of high rotational

states was found to increase with decreasing ion velocities

and the intensity maximum of the band contour became broader

and moved toward higher values. Such a shift in the intensity

maximum of the band contour would tend to make the relative

emission rate of a particular band measured in the manner

described above appear to decrease more rapidly than it ac-

tually does at lower energies. However, the magnitude of

the error resulting from such a shift could not b precisely

determined in all cases due to poor resolution, and no at-

tempt has been made to correct for it.

Because of a limited observation length Z, emission

cross sections arising from excited states of the projec-

tile must be corrected for both the projectile velocity and

the lifetime of the excited states according to equation

(111-23). The cross sections presented in Figs. 23 and 24

as well as in Tables I and II have been corrected using

66 nsec17 as the lifetime of all vibrational levels of the

N2+ B 2E state and 38.4 nsec18 as the lifetime of all vibra-

tional levels of the N2 C 31u state. This correction amounts

to less than 3% below 1 keV, but as much as 30% at 7 keV for

the N2 first negative system, while for the N2 second posi-

tive system it amounts to less than 3% below 3 keV and only

as much as 10% at 7 keV.




Full Text

PAGE 1

OPTICAL STUDIES OF ION-MOLECULE COLLISIONS N 2 + 2 By Lambert Edward Murra A Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doc tor of Philosophy UNI VERS ITY OF FLOR I DA 1977

PAGE 2

ACKNOWLEDGMENTS The author wishes to thank the members of his supervisory committee, especially Professors T. L. Bailey and C. F. Hooper, for their assistance and encouragement throughout his graduate program. He wishes to give special credit to Dr. Ralph C. Isler, the chairman of his committee, for his counsel, his assistance, and his patience during the course of this research. The author is also indebted to Helen Dickman" for her fine work in typing this paper. Finally the author wishes to thank his wife, McKay, for her patience, understanding, and constant encouragement during the course of his graduate program.

PAGE 3

TABLE OF CONTENTS Page ACKNOWLEDGMENTS LI ST OF TABLES LI ST OF FIGURES ABSTRACT Chapter I. INTRODUCTION ...... II. EXPERIMENTAL APPARATUS Collision Apparatus Vacuum System Ion Source Beam Transport and Detection Ion Beam Characteristics Optical Detection System Spectroscopic Arrangement Detectors Pulse Counting System III. PROCEDURE Operational Definition of the Excitation and Emission Cross Sections The Relationship of the Excitation Cross Section to the Emission Cross Section . . . Target Excitation 1 k it 10 13 13 21 21 27 28 31 31 33 3^

PAGE 4

Chapter Page Projectile Excitation 38 Determination of Emission Cross Sections ... h 1 The Emission Cross Section as a Function of Energy k 2 Relative Emission Cross Sections kS Calibration of the Optical Detection System 46 Dependence of the Emission Cross Section on Polarization 57 IV. RESULTS 66 Identification of Observed Spectral Features . . 66 o Spectral Features Above 2500 A . . _ . . . . 66 Spectral Features Below 1500 A 79 Emission Cross Sections of the Molecular Features of N„ + and H 80 Emission Cross Sections of the Molecular Features of 103 Emission Cross Sections of Atomic Features . . . 108 Polarization Measurements 126 V. DISCUSSION 128 Ion Beam Excit'ed State Population 128 Excitation of the N„ + B 2 l + State 132 l u Comparison with Charge Transfer Data \kk Production of Excited Dissociation Fragments . . 150 VI. CONCLUSION 160 REFERENCES 163 BIOGRAPHICAL SKETCH 1 6 7

PAGE 5

LIST OF TABLES Table Page I. Absolute emission cross sections for the (0,0), (0,1), (1,2), and (2,3) bands of the first negative system of N 2 + arising from collisions of N ? + with 2 83 II. Absolute emission cross sections for the (0,0), (1,0), and (2,1) bands of the second positive syst em of N „ arising from collisions o f N 2 + w i t h 2 . . 8 6 II. Absolute emission cross sections for various N 2 + first negative and N 2 second positive vibrational bands arising fro m collisions of N 2 wit It 0o at a collision energy of 4.0 keV . 9 6 IV. Absolute e n 1 ission cross sections for the Nn + first negative system at a beam energy of 4.0 keV 97 V. Absolute emission cross sections for the N2 second positive system at a collision energy o f 4 . k e V 9 8 VI. Absolute emission cross section of the entire ^2 + first negative system as a function of collision energy 101 II. Absolute emission cross section of the entire N „ second positive syste n 1 as a function of collision energy 102 II. Absolute emission cross sections for the observed band sequences of the 2 + first negative syste m a t 4 . k e V 104 IX. Absolute emission cross sections for lines below 1750 A arising from excited dissociation fragments resulting from collisions of N2 + w i t h 2 a t 4 . k e V 10 9

PAGE 6

Table Page X. Absolute emission cross sections for lines above 3000 A arising from excited dissociafion fragments resulting from collisions of N 2 + with 2 at k.O keV 110 XI. Absolute emission cross sections for several excited dissociation fragments as a function of collision energy arising from collisions of N 2 + wi th 2 1 22 XII. Relative population of the vibrational energy levels of the X and A states of N* at the collision chamber 131 XIII. The minimum energy defect for direct excitation 0. , and for charge exchange excitation Q g , and the experimentally observed thresholds E lL for the resonance lines of Nl, Nil, 01, and which were observed 6^ 151 XIV. Emission cross sections of several Nl and Nil lines arising from dissociative collisions of N ? + with 2 and with Ar at a collision energy o v, i .. .i 0„ and with A r at .f k .0 keV 15*

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LIST OF F IGURES Figure Page 1 . Schematic of collision apparatus 6 2 . S c h e rn atic of v a c u u m system 8 3 . Schematic cross section of ion source 12 4. Dependence of ion beam current upon coil current for H 2 + 16 5 . Dependence of the No ion current upon electron bombardment energy with a potential of 2.5 keV applied to the ion chamber 18 6. Dependence of the N 2 + ion beam current upon the potential applied to the ion cha m ber w i t h an electron bombardment energy of 50 eV 20 7 . (a) Experimental configuration for determining the mean energy of the ion beam and the energy spread. (,j) Dependence of the ion beam current upon the retardation potential V r 23 8. Schematic of spectroscopic arrangement 26 3 . Schematic of pulse counting system 30 10. Dependence of the relative count rate on target gas pressure 4 4 11. Relative detection efficiency as a function of wavelength for the vacuum monochromator and the EMI 9558Q phototube 48 12. Relative detection efficiency as a function of wavelength for the Ebert mount monochromator and and the EMI 95 58 Q phototube 50

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Figure Page 13Relative detection efficiency as a function of wavelength for the vacuum monochromator and the EHR phototube 5 2 1 4 . Relative detection efficiency as a function of wavelength for the vacuum monochro m ator and the MEM 5 if 15Experimental arrangement for determining the instrumental polarization 62 16. Instrumental polarization of the Ebert mount monochro m ator as a function of wavelength 64 17. E n ission spectra between 2500 and 3 4 A arising from collisions of N2 + with O2 at a collision energy of 4.0 keV 68 18. E m ission spectra between 3300 and 4300 A arising from collisions of N o + with O2 at a collision energy of 4.0 keV . . 70 19. Emission spectra between 4200 and 5050 A arising from collisions of N 2 + w i t h 2 at a collision energy of 4.0 keV 72 20. Emission spectra between 4900 and 6200 A arising from collisions of N2 + with O2 at a collision energy of 4.0 keV 74 21. Emission spectra between 1525 and 1270 A arising from collisions of N 2 + with O2 at a collision energy of 2.5 keV 76 22. Emission spectra between 1200 and 680 A arising from collisions of N 2 + with O2 at a collision energy of 4.0 keV 78 23Absolute emission cross sections for the production of the (0,0), (0,1), (1,2), and (2,3) bands of the first negative system of N^ + as a function of beam energy 82 24. Absolute emission cross sections for the production of the (0,0), (1,0), and (2,1) bands of the second positive system of N2 as a function of beam energy 85 25. The ( , 1 ) / ( , ) branching ratio of the N ? + first negative system for N2 + + ? collisions as a function of collision energy 9 3

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Figure Page 2 6. The emission cross section as a function of ion beam energy for the entire N2 + first negative system and the entire No second positive system . . 100 27. The emission cross sections of the A V = 1 band sequence of the first negative system of 0y + as a function of collision energy 106 28. Energy level diagram of Nl 112 29. Energy level diagram of MM 114 30. Energy level diagram of 01 116 31. Energy level diagram of Oil 118 32. Absolute emission cross sections of excited dissociation fragments arising from N2 + O2 collisions as a function of ion beam energy . . . . 121 33Relative populations of the vibrational levels of the N „ B 1 1, state as a function of ion beam energy 135 3^. Selected potential energy curves of N „ and N • • ' ^ ' 35Total cross sections for the production of 02 + and for the production of all slow ions in collisions of N 2 + with 2 U2 36. Selected potential energy curves of O2 and O2 . 1 ** 8 37Emission cross sections of the Nl 1200 A line arising from the 3s l+ P •> 2p 3 '* S ° transition, and the Nil 1085 A line arising from the 2s2p 3 3 D° -> 2p' 3 P transition compared to calculated cross sections using the Landau-Zener formula 159

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Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy OPTICAL STUDIES OF ION-MOLECULE COLLISIONS: N 2 + + 2 By Lambert Edward Murray August, 1977 C ha I rman : R . C . I s 1 er Major Department: Physics Inelastic collision processes of the N. + system have been examined by studying emissions of the spectral o features in the range from 600 to 8000 A at ion impact energies from threshold to 7 keV . Emission cross sectionsof the vibrational bands of the N first negative ( B 2 T + •* X 2 Y. + ) .2 u g and N, second positive (C 3 n -> B 3 n ) systems as well as the 1 u 9 emission cross section of the 0„ first negative (b h T,~ -> 2 g a II ) system have been determined as functions of energy. The relative population of the vibrational levels of the N 2 B state have also been determined and compared with previous measurements for the N+ He and N„ + Ne systems. The relative population appears to be describable in terms of

PAGE 11

the F ra nek-Condon principle at the higher energies, in agreement with other experiments. Thresholds and emission cross sections have been determined as functions of impact energy for lines originating from several excited configurations of Ml (3s 4 P, 3s 2 P, 3s' 2 D, 3d 4 P), Nll(2p 3 2 D°), I (3s 3 S°), and 0ll(2p 4 4 P ) , resulting from collision induced dissociation Emission cross sections for additional lines originating from excited configurations of Nl, Nil, 01, and Oil have also been determined at 4 keV. In contrast to collisions which produce ground state dissociation fragments, the cross section for the production of excited dissociation fragments appears to be relatively smal 1 .

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I . I NTRODUCTION As a beam of projectiles traverses a gaseous target both elastic and inelastic collisions can occur. When molecular reactants are involved, the inelastic collisions may result in excitation, ionization, or dissociation of either the projectile or the target, or both, as well as electron transfer from one reactant to the other. In addition, reactive collisions, resulting in the appearance of new molecular species, may also occur. Ideally, experiments designed to. study these processes should be performed by preparing both the projectile and the target in a single state and then determining the separate cross sections for each set of final states which are produced. However, experimental limitations usually prevent the achievement of such well-defined conditions. The most important technique used to determine the cross sections of the various interaction channels as well as their angular dependence is the direct detection of the products emerging from the collision region. However, it is often quite difficult in this type of experiment to isolate, for separate study, a given interaction channel from the several possible. In such cases where the collision process leads to an excited state which subsequently emits a photon due to spontaneous decay, optical techniques may be utilized

PAGE 13

to determine precisely which states have been populated during the collision process as well as the energy thresholds and cross sections for populating the various states, thus providing added detail about the total cross sections for individual interaction channels. This dissertation reports measurements of emission cross sections resulting from collisions of N_ with static qas 2 y 2 targets for ion beam energies from threshold to 7 keV in a spectral range from 600 to 8000 A. Although this system is relatively complex theoretically, the data should be of considerable interest because of the importance of these molecules in atmospheric processes. The only other spectroscopic observations which appear to have been made for this system are those reported by Liu and Broida. 1 Their measurements, however, consist only of the absolute emission cross sections for the production of the N first negative system and of two 0, lines (39^7 and A368 A) at an ion beam energy of 0.90 keV. The measurement of emission cross sections arising from excited dissociation fragments are of particular interest. Few spectroscopic measurements of these features have been made at energies less than 10 keV for any collision system. 2 Most of these have involved the dissociation of Hand H* although a number of measurements of the dissociation of N and N 2 in collisions with various other species have been made by Doering 3 (N 2 + + N 2 ), Neff 4 (Na + + N Ne + + N„), Hollstein et al . 5 (He + + Nj, and Holland and Maier 6 (He + N 2 ). The only spectroscopic measurements of the

PAGE 14

dissociation of 2 within this energy range appear to be those of Hughes and N 7 for H + impact on 0„ . Of these measurements, only those of Holland and Maier included de' terminations of the thresholds for the production of emissions from any excited dissociation fragments.

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I I . EXPERIMENTAL APPARATUS Collision Apparatus A schematic diagram of the collision apparatus used in these experiments is shown in Fig. 1. It consists of three principal sections: (i) a chamber for the production of ions by electron bombardment; (M) a differential pumping chamber which contains a system of electrostatic lenses for accelerating and focusing the ion beam, as well as a low resolution Wien filter; and (ill) a collision chamber which contains the target gas. The system has been modularly constructed to make use of the High Voltage Engineering Corporation's A-inch beam line components and coupling flanges. Each module has been constrLCted from type 3 3 stainless steel, and the electrical f eedthroughs , ion gauges, leak valves, and observation windows are mounted on conflat flanges and are sealed into the various modules with oxygen-free, h i g h -cond uc t i v i ty copper gaskets. Vacuum System The source and lens chambers, which achieve ultimate pressures of 1-2 X 10~ 7 torr, are coupled to a 2-inch mercury pumping system by 1/4-turn butterfly valves. These pumping systems (shown in Fig. 2) consist of a liquid nitrogen cooled vapor trap, a t he rmoe 1 ec t r i ca 1 1 y cooled baffle, k

PAGE 17

r }; A y , £i. ; .— -LL n m J==fn J I II L 1 8 § a: O I* ° u I I ii to 1: rr -: I « I: F \ u rfY i A"^i i :: e] II "I i t r? -= ; / hi =* lii "JJUJL ^ «in ! — L §3y i: UJ ( *\ r L__„. s X .*d w. -J 1 5 ufc t: L?

PAGE 19

LU cc

PAGE 20

and a mercury vapor diffusion pump. These pumps are connected through a liquid nitrogen trap and a molecular sieve trap to a mechanical backing pump. The collision chamber, which reaches an ultimate pressure of 2-3 X 10~ 5 torr, is evacuated continuously through the beam entrance hole (0.075 in.) in the bulkhead which separates the collision chamber from the lens chamber, and through the slits of the vacuum monoch rom ato r , which is coupled to an open observation port opposite the observation window shown in Fig. 1 (see also Fig. 8). In addition a small oil diffusion pump, employed as the low pressure reference of a capacitance pressure sensor, is used in the initial evacuation of the collision chamber. This pump is not open to the collision chamber while measurements are being made. Airco pure grade N 2 and gases of quoted purity 99.9% and better than 99-5%, respectively, have been used with no further purification. These gases are admitted to the source and collision chambers by means of GranvillePhillips Variable Leak valves. Standard Baya r d -A 1 per t type ionization gauges and a Granville-Phillips ionization gauge controller are used to monitor the pressure in the three chambers of the system. In addition, a Datametrics Electronic Manometer and capacitance type Barocel Sensor are used to measure the pressure of the various gases in the collision chamber. This is done to facilitate comparison measurements, since the calibration accuracy of this type device is independent of gas composition.

PAGE 21

1 Ion Source A schematic diagram of the electron bombardment ion source is shown in Fig. 3Except for the molybdenum grid, all parts shown are type 30A stainless steel or boron nitride In order to produce a beam, the source chamber is first evacuated, and then the butterfly valve is almost completely closed until the pressure rises to about 2 X 10" 5 torr. This serves to minimize fluctuations in pressure in the ion chamber and thus helps to maintain beam stability. The gas to be ionized is then leaked into this section until the pressure is between 10" 3 and 10 -t * torr. The optimum pressure for the production of N ~ was found to be about k X 1 ~ 4 torr. The bombarding electrons are produced from a cathode which is directly heated by current from a well-regulated dc power supply. The cathodes are produced by painting an RCA triple carbonate (Ba, Sr, Ca) mixture on a strip of 0.010 n. nickel mesh 1/8 in. wide and 1/k in. long. These carbonates are converted to oxides by heating the cathode to 900-1000°C in a vacuum. After conversion begins, electron emission is stabilized by drawing approximately kQ mA for about an hour. The electrons emitted from the cathode are drawn through the molybdenum grid by a potential difference, which can be varied from to 250 V, applied between the ion chamber and the cathode. The electrons are then focused toward the exit aperture of the ion chamber by an axial magnetic field which is produced by a narrow coil wrapped around the ion chamber. This coil consists of 275 turns of #27 copper wire with a

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1 2 CO i

PAGE 24

I 3 heavy formvar coating. Currents as large as 2 A are used in the coil to produce fields of about 120 G in the region of the extraction aperture. In order to prevent the disintegration of the insulation, the coil is cooled by circulating oil around the coil and through a simple water cooled heat exchanger . Beam Transport and Detection Ions created in the ion chamber are drawn out by an extractor potential 15-20 V lower than the potential applied to the ion chamber itself. These ions are focused and accelerated toward the collision chamber by a system of cylindrical electrostatic lenses. The potential applied to each lens is adjusted empirically for maximum current in the collision chamber. In addition, a low resolution Wien filter is employed to eliminate Nand N + from the ion beam. The ion beam is monitored by a General Radio type 1230-A dc amplifier and electrometer which is connected to a Faraday cup mounted in the collision chamber. To determine the possible effect of secondary electron emissions on the measurement of the ion current, a potential was applied to the Faraday cup to suppress secondary electron emission. The ion current was measured as a function of this suppressor potential and, within experimental error, was found to be independent of this potential. Ion Beam Characteristics The dependence of the ion beam current as measured in the collision chamber upon the magnetic field in the ion

PAGE 25

\k chamber (and thus upon the coil current), the electron bombardment energy, and the potential applied to the ion chamber are shown in Figs, k 6 . Although Fig. k i s a plot for H ions, this plot represents the general dependence of the ion beam current. upon the coil current which has been noted for all ions produced in this source. While performing a measurement, the coil current is adjusted to a region where the ion current varies smcothly with coil current. In order to increase the stability of the ion beam, the output of the electrometer which monitors the ion beam has been used to provide an error signal to the programming terminals of the power supply which supplies current to the coil. Using this technique, fluctuations in the ion current have been reduced to less than 0.25% while measurements are being mnde. 8 The dependence of the N„ ion beam current on electron bombardment energy is shown in Fig. 5 for bombardment energies between 20 and kO eV. To obtain sufficient accuracy in cross section measurements, the electron bombardment energy was always maintained above 30 e V • The ion beam energy is established by applying a positive potential of up to 7 keV to the ion chamber while the collision chamber is maintained at ground potential. Figure 6 shows the variation of the ion current as a function of this applied potential. To determine the actual energy of the ions as they enter the collision chamber, a simple double retardation screen was placed just beyond the entrance aperture

PAGE 27

16 LU or. UJ Cl. < H .

  • PAGE 28

    Figure 5 Dependence of the N„ ion current upon electron bombardment energy with a potential of 2.5 keV applied to the ion chamber.

    PAGE 29

    10 •.-G UJ c: o 10 i i i i — r ft o © « I L ._L 1 J L 50 20 50 40 ELECTRON BOMBARDING ENERGY (eV)

    PAGE 30

    c

    PAGE 31

    20 Fnnm r 1 t TT ~i "~TTfTrrT~r r -LLLLL 1 1 i I i I I J_LLJ_L_L _j o < — _j s (v) lN'jjjyno mo

    PAGE 32

    21 of the collision chamber (see Fig. 7a). A plot of ion current versus retardation voltage (solid curve) is shown in Fig. 7b for an H ion beam with a potential of ^0 V applied to the ion chamber and an extractor potential of 15V. The mean energy of the ions is taken to be the potential at which the ion current has fallen to 1/2 maximum (or where -dl/dV is a maximum), in this case approximately 12.5 eV lower than the applied potential. Additional tests have shown that the mean energy of the ions is 12-3 ± 0.5 eV lower than the potential applied to the ion chamber, even at zero extractor voltage. Unless otherwise noted, the beam energies quoted herein have been corrected to give the actual energy of the ions entering the collision chamber. The energy spread of the ion beam, taken to be the full width at half maximum of the change in ion beam current as a function of retardation potential, is seen in Fig. 7b to be approximately 3-5 eV, or about S% of the applied potential at AOV. Additional measurements have shown that the energy spread is approximately 8 eV for an applied potential of 180 V for extractor potentials from to 65 V. The energy spread, therefore, is taken to be less than 5% of the beam energy for an applied potential higher than about 200 V. Optical Detection System Spectroscopic. Arrangement Two types of monoch roma to r s have been utilized for the detection of optical emissions arising within the collision chamber: a 1-meter normal-incidence vacuum instrument

    PAGE 33

    2 **O > -^ uo O — ro c >~ .i_ CJI 4-> 4-> L. u C in 3 (D (U 3 o ro a) E — — .c 0) TO -C XI X> nj v1_

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    23 fO H > olx> /1J C UJ O 2 U-l O c S 1 1 N A d V W 1 1 6 W V F— I !f W N k\\ 1 1 1 1 !:i t i i j Uii,

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    Ik (McPherson model No. 225) and a 1/4-meter Ebert mount instrument (Jarell-Ash model No. 82-410). The vacuum instrument, equipped with a magnesium floride coated, 600 grooves/mm grating blazed for 2000 A, has a linear reciprocal dispersion o of 16.6 A/mm in the first order. This instrument is coupled directly to the collision chamber through an open observation port (see Fig. 8). The Ebert mount instrument is mounted on the opposite side of the collision chamber from the vacuum instrument, separated from t he . co 1 1 i s i on chamber by a quartz observation window. Light arising from the collision chamber passes through this window and is focused upon the entrance slit by a quartz lens. This instrument, equippeo with a 1 1 8 O grooves/mm grating blazed for 6000 A, has a linear reciprocal dispersion of 33 A/mm in the first order. All observations have been made at 90° to the direction of the beam. The entrance slits of both instruments are mounted vertically, perpendicular to the beam direction, to minimize the effect of possible variations in the beam diameter. Although the beam is not collimated, it is estimated that distortions of relative cross sections owing to these variations are less than 5% over the entire range of beam energies. The length of the beam from which light can be detected (the observation length z) as well as the solid angle subtended by the detection system is determined by the optical limiting stops of each detection system. For the vacuum monoch roma to r system the limiting stops are the ruled area of the grating (height 56 mm, width 96 mm, located 120 cm

    PAGE 37

    26 o

    PAGE 38

    27 from the beam) and the entrance slits of the monochromator. For the Ebert mount system the limiting stops are the diameter of the quartz lens and the entrance slits of the monochromator. The observation length, I , of the vacuum monochromator system may be taken as 1.92 cm and will be in error less than 3% for a slit width of 500y or less, while the observation length of the Ebert mount system will be approximately equal to the entrance slit width. The distance L from the bulkhead which separates the collision and lens chambers to the region of optical detection is approximately 1.25 cm for the vacuum monochromator and 2.21 cm for the Ebert mount system. Detectors In order to observe emission spectra over a range from 600 to 8000 A, four different detectors were used: (i) an EMI 9 5 5 8 Q photomultiplier tube was used from 2500 to 8000 A; (ii) an EMI 62 56 S tube was used from 1500 to 3000 A; (iii) o an EMR 5^2G-09"18 tube was used from 1200 to 1700 A; and (iv) a Bendix moael 3 06 magnetic electron multiplier (MEM) was used below 1200 A. The vacuum monochromator was employed for all measurements below 5000 A, while the Ebert mount mono ochromator was employed only for measurements above 5000 A. Although the dark count rate for the EMR tube and for the MEM is less than 1 per second at room temperature, both EMI tubes had to be mounted in a liquid nitrogen cooled housing to reduce their dark count rate to about 50 per second. To further reduce the dark count rate to a minimum of

    PAGE 39

    28 3 per second, a permanent donut-shaped magnet was placed about I inch from the tube face. This was done to deflect the electrons which are thermally emitted from the unused portion of the photocathode toward the walls of the tube, thus preventing them from passing through the dynode chain. Pulse Counting System The output pulses from the detectors pass through a preamplifier (located as closely as possible to the detector to reduce the input capacitance) into a linear amplifier and then a pulse-height discriminator (see Fig. 9). The amplification and the threshold of the discriminator are adjusted to give the best signal-to-noise ratio. To obtain emission spectra, the output of the discriminator is integrated by a linear rate meter and then displayed by a strip chart recorder while the monoch roma tor s are scanning the wavelength region of interest. Relative emission rates for the various spectral features are obtained by summing the output pulses of the discriminator over a convenient time interval using a preset timer-sealer combination.

    PAGE 41

    30

    PAGE 42

    III. PROCEDURE Operational Definition of the Excitation and Emission Cross Sections When a projectile beam of density N (particles/cm 3 ) and velocity v (cm/sec) is incident on a target gas of density N q (particles/cm 3 ), the number of excited molecules produced per unit time per unit. volume in a particular exc i ted state is g i ven by dlt. = N N.va , dt ( I I I -1 ) where N i may be the density of excited molecules in the target l^. or in the beam ^_.. The constant of proportionality a i is called the total cross section for exciting state i and has the units of square centimeters. As the projectile beam of cross sectional area A traverses a finite length I of the target region, the total number of excited molecules produced per unit time in state i is given by N . = / / N N va . dA dx Z I A a b ^ (I I 1-2) If the density of the target gas is uniform over the volur A I, then where N. : = o t N a f [f N b v dA] d: I^(x) = f N.v dA (I I 1-3) (I I 1-4) is the flux integrated over the cross sectional area of the 31

    PAGE 43

    32 projectile beam at a position x . The integrated flux of the projectile beam as a function of position is given by I h (x) « I h (0) exp(-N a o* o x), (I I 1-5) where o q is the total cross section for all processes which remove a projectile from the beam. This leads to the expres% b exp (-N a I) a o (I I 1-6) for the number of excited states i produced per unit time in a finite distance I . I f N o Z<<] , the so-called thin target criterion, this last equation reduces to a .1,(0) N I, i b a ' (Hl-7) and the operational definition of the total cross section for the production of state i becomes N . 1,(0)11 I b a (111-8) The assumption of single-collision conditions, i.e., when no projectile undergoes more than one collision as it traverses the target chamber, has been implicit in this derivation. Thu'.;, whenever equation (l I 1-7) is shown to be satisfied, i.e., when N. is linearly dependent upon both A 7 and v a 1-^(0), it is assured that the experiment is being carried out under s i ng 1 eco 1 1 i s i on conditions. Under these conditions A 7 is approximately uniform and I-,(x) = 1,(0) = N,vA so that •b'

    PAGE 44

    33 I b and ''a may be monitored a t any convenient point within the target chamber. The emission cross section is defined analogous to the excitation cross section by the relation '3 10 N I,i a b I I -9) where J^. is the total number of photons emitted per second in the transition i -»j from a length I of the beam path through the target region. In this expression the assumption is also made that N and J, are sufficiently tenuous to assure that they may be monitored at any convenient point within the collision chamber. The Relationship of the Excitation Cross Section to the Emission Cross Section Although co 1 1 i s i ona 1 1 y induced emission cross sections may be of practical interest in and of themselves, they are of most value when they can be related in an unambiguous way to excitation cross sections. The comparison of the emission cross section to the excitation cross section is, however, complicated by several factors: (i) the emission cross section is related to all processes which populate and depopulate an excited state i, not just to the direct excitation of this state; (ii) r f the lifetime of an excited state is very long, the excited particle may drift a considerable distance before emission occurs, and the emission cross section may depend upon the point at which observations are made; and (iii) if

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    34 the emission is anisotropic, the measured emission cross section will depend upon the position of observation. The remainder of this section demonstrates how the emission and excitation cross sections can be related to each other in a systematic way, and follows the presentation by E. W. Thomas. 5 When the beam-static target configuration is employed, the assumption generally made in relating the total emission cross section to the total excitation cross section is that the projectile experiences only a small change in energy and direction as a result of a collision, while the target recoils only with a small velocity and at an angle of approximately 90° to the beam direction. Therefore, to a first approximation, the direction and speed of the projectile as well as the position of the target remains unchanged by collision. Two different approaches to the comparison of the emission cross section with the excitation cross section are, therefore, required depending upon whether the projectile or the target is the emitting species. Target Excitation There are four processes which act to populate a given state i of the target molecule: (i) direct collisional excitation by the projectile, (ii) cascades from all higher states k which are excited during the collision process, (iii) absorption of resonant photons, and (iv) transfer of internal energy by collisions with other target particles. Therefore the number density of the target particles in state i increases

    PAGE 46

    35 at a rate given by dm dt NN.vo. + I. . If A. . + f .A . N . + I c N ( I l l 1 n a b i k>t ak kt J t to at x xi N ax' U ' ° The first term of this equation represents the rate of direct collisional excitation which has already been discussed. The second term represents the rate of populating state i by cascade from all higher states k, where N , is the density of target particles in state k and A ki is the radiative transition probability for the decay of state k to state i. The third term represents the rate of repopulation of state i by absorption of resonant photons, where A. N . is the rate of to at depopulation to the ground state by spontaneous radiative decay and /\ is the fraction of resonant photons which are absorbed within the target region. The last term represents the rate of population of state i by collisional transfer of internal energy by collisions with other target particles where ^ • = ° -^ # is the collisional frequency and N is * (M| _ ]]) where the first term represents the rate of depopulation due to spontaneous radiative decay to all lower states j, while the second term represents the rate of depopulation due to co 1 1 i s i ona 1 transfer.

    PAGE 47

    36 Once a steady state is reached, the rates of population and depopulation must be equal, and the expression for the equilibrium excited state density N is given by a b i, k>i ak k% 1 A. . f .A . + I c 3i ak ki x xi a: 13 13 N'l. I a j : . -A . . 3<1 13 i vo + I a (I I 1-14) This equation can be simplified to give a . + Z * . a, . + I c .y i k>i ki -*• ~ • X XI X a . . = A. . 13 13 T, .. A . . f .A . + I c . 3
    PAGE 48

    3 7 In this equation the emission cross section is related to terms describing pho toa bso r p t i on and collisional transfer, both of which depend upon the construction and operating conditions of the apparatus. As stated earlier, measurements of emission cross sections may be of interest in and of themselves, but are most useful if they can be related in an unambiguous way to the excitation cross section, that is, if a., is independent of the construction and operating conditions of the apparatus. Since, the pho toa bso r p t i on and collisional transfer terms are obviously dependent upon the target density, at sufficiently low pressures within the collision chamber, their effect should be negligible. Under these conditions, equation (111-15) reduces to A . . 1>3 . . A . . 0<1 id t k>i< kr 1 111-16' Here a., is no longer dependent upon target density, and J.. can be shown to be linearly dependent upon both A 7 and I, [see equation (lll-9)j. Therefore, when J., is shown to be linearly dependent upon both N and I, (and J.. + as A 7 -> 0) , the emission cross section a., is independent of the construction and operating conditions of the apparatus. The excitation cross section can then be determined, if the transition probabilities are known, by measuring the emission cross section °ij and a11 emission cross sections due to cascade, according to the equation, I . . A . i-O £ 7 • a, . . k>i ki (111-17!

    PAGE 49

    If this equation is summed over all ji °ki( ) Thus the emission cross section can also be determined by measuring the emission cross sections for all transitions into and out of a given state. Only in a relatively small number of cases is it possible to evaluate an excitation cross section explicitly in this way, either because of the limited spectral range of a practical detection system or because of the limited accuracy of calculated transition probabilities. However, in many cases the cascade terms may be shown to be quite small, thus simplifying the comparison of the emission and excitation cross section. As mentioned earlier, this treatment of target excitation is based upon the assumption that the excited target emits from the same place where it is excited. There is presently no evidence to indicate that this assumption is violated for projectiles colliding with atomic targets. This may, however, not be true for excited fragments produced by the dissociation of molecules. However, as will become clear from the following treatment of projectile excitation, if the lifetimes of the excited states are short (of the order of 10" 8 sec.), then this assumption may still be quite adequate.

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    Z3 Projectile Excitation The mechanisms leading to the population and depopulation of an excited state of the projectile are essentially the same as for the target. However, since the number density of the emitting species in a projectile beam is small, absorption of resonant photons and collisional transfer of excitation energy have generally been neglected. The rate of population of the excited state i in the projectile beam, then, is given by dVt hi a b i "k>i bk ki N bi 1 j
    PAGE 51

    40 vN N,a . a d % b % [ 1 -e.ro (-x/vx ) ] 3 < t to subject to the boundary condition N. (iii -20; at x = . In this equation t. is equal to [z. . i4..] _1 and is the lifetime of •* t-J state t. The total number of photons emitted in all directions from a beam of cross sectional area A and of length I is given by Jji = f f N h .A . . dA dx. K7 L A ittj 11-21) In this equation I is the penetration of the bean, through the target chamber before reaching the observation region (that region from which photons can be detected by the apparatus), and I is the length of the beam within the observation region. Upon integration of equation ( I I 1-21), the emiss-ion cross section becomes a . . = to a .A . .A i to I . .A . . 0
    PAGE 52

    k\ cascade terms will also depend upon the position of excitation and the lifetime of the higher levels. We will, however, define a corrected emission cross section o.. by the equation * 'Z-J o . . = 1-0 ( I I 1-24) Again the treatment of projectile excitation is based upon the assumption that the speed and direction of the projectile remains unchanged as it passes through the target region. Determination of Emission Cross Sections To determine the emission cross section for the i ->• g transition it is necessary to relate the output siqnal S . (counts per unit time) of the optical system to the total number of photons J . emitted per unit time from a lenqth I of the beam path through the target region. In any practical experiment only a portion of these photons are detected. If the emission is isotropic, the number of photons entering the optical system per unit time S '. . is qiven by 13 T-J kv (I I 1-25) where it is the solid angle subtended by the optical system. The output signal • ., therefore, is given by J . . K(\), ... S . . K ( A i>3 tQ X ° ^ (111-26) where £.. is the number of photons entering the optical system

    PAGE 53

    kl per unit time and K ( X ) is the detection efficiency. at the wavelength A of the i + j transition. The expression for the emission cross section then becomes, from equation (111-9), S . . i<3 K(X) N I, I a b (I I 1-27: The ion beam flux J, integrated over the cross sectional area of the beam is related directly to the ion beam current I measured by the Faraday cup, and at low pressure the target gas density A 7 may be related to the gas pressure P in the target chamber by the ideal gas law. If the observation length I and the solid angle ft remain unchanged during a series of measurements, the emission cross section may be written 'J a . .A ^0 K(\) (I I 1-21 where the relative emission rate a . . is defined by the relation "Z-J tj P I a (I I 1-29; and where A is a constant as long as the observation length I, the solid angle ft, and the temperature of the target gas rema in unchanged . To insure that the determination of emission cross sections was independent of secondary processes, i.e.. that a-. to is independent of both N and I-,, measurements of relative count rates were made as a function of target gas pressure. Figure 10 is a plot of relative count rate versus target

    PAGE 55

    kk hto io *t ro cc (3ii no A^vyne^v) 3i ?y inooq 3Aiivi3a

    PAGE 56

    A3 gas pressure for the excitation of (a) the Ay = band sequence of the first negative system of _ + , (b) the (0,0) band of the first negative system of N + , and (c) the 1200 A line of Nl. The relative emission rate for these three features is linear for pressures below 4 X 10 -l+ torr. Thus all measurements of relative cross sections were made with a target gas pressure of less than A X 1 " k torr. In addition, the relative emission rate was found to be linear with ion beam current over the entire range of currents used. The Emission Cross Sectio n as a Function of Ener SX When the emission cross section of a particular transition is measured as a function of ion beam energy, both A and K ( X ) remain unchanged for all measurements and the relative emission rate a., is directly proportional to the absolute emission cross section. Relative emission rates are measured as a function of energy by computing the ratio of the net output signal to the product of the ion beam current and the target gas pressure for each potential applied to the ion chamber [equation (111-29)]. The net output signal is taken to be the difference of the output signal obtained with a target pressure P^ and the background signal obtained when the target gas has been removed. Relative Emission Cross Sections The ratio of absolute emission cross sections for two different spectral features measured at the same ion beam energy is given by

    PAGE 57

    u 13 IJ K(X kl } 'kl kl K(X iJ J ( I I 1-30 as long as the observation length l , the solid angle 0, , and the temperature of the target gas remain unchanged while the two features are compared. This expression, then, defines the relative emission cross sections for the two features, where a., and a are obtained as described above at a particular beam energy, and the ratio K ( \ V1 ) / K( X . . ) is obtained by taking the ratio of the relative detection efficiency at the two wavelengths. The determination of this relative detection efficiency is described in the following section. Calibration of the Optical Detection System The relative detection efficiency is determined by the express ion A' r A x ; I(\i) I (X 2 ) K(\ 2 ) I(\ 2 ) T o (\ 1 ) (111-31) where I(\±)/I(\ z ) is the relative intensity of two spectral features measured with the optical detection system and I Q (X\)/I q (X 2 ) is the known relative intensity of the same two spectral features. o For wavelengths greater than 2800 A the relative detection efficiency was determined using a calibrated tungsten ribbon lamp (Eppley model No. EPS-1055) as a light source. Plots of the relative detection efficiency of the vacuum mono chromator system and of the Ebert mount system, both using

    PAGE 58

    a) o 01 o > x: TO D. 2 4CO O LA o — D (U >1o o

    PAGE 59

    k8 / / I / ? I I ; f iJLU_-L_l_J X. O q O O to fO .JLUa-.L_J._i l_ O m r'i 6 6 o

    PAGE 60

    TO

    PAGE 61

    50 O 7rrTTTT~ i j ) ,! i o m to UJULUL-LJ L s.O ro o c o o o o o o AGN310JJJ3 M0U0312Q 3A ; lvn3H

    PAGE 62

    Figure 13 Relative detection efficiency as a function of wavelength for the vacuum monochroma tor and the EMR phototube .

    PAGE 63

    52 s O ?4 L?J -4(LsJ o ?, H O Q > < UJ \ 1200 !400 WAVELENGTH SCO (A) 1800

    PAGE 64

    a) s:

    PAGE 65

    5h do d A0N3I0UJ3 N0!i02i3Q 3AUV"13d

    PAGE 66

    55 the EMI 9558 Q tube, are shown in Figs. II and 12, respectively, for this spectral region. Here the error in determining the relative detection efficiency is estimated at less than 5%. Because there are no standard sources for the vacuum ultraviolet region of the spectrum, the relative detection efficiency in this region must be determined by branching ratio techniques. In the region between 1200 and 1750 A the relative emission rates of two pairs of Nl lines (1493, 1744; 1243, 1412 A) obtained from ion. beam collisions are compared with tabulated transition probabilities 10 to obtain the variation in detection efficiency of the system. A plot of the relative detection efficiency of the vacuum monoc.i roma tor with the EMR tube is shown in Fig. 13 for this spectral region. The results for these two sets of points are connected by assuming that the variation in detection sensitivity is linear between pairs of points when plotted on a s em i 1 oga r i th mic scale. There is some freedom allowed in determining the intersection point of the two linear segments. The particular choice made here results in a curve which is very similar to the quantum efficiency curve for the EMR tube alone. It should be pointed out that the quantum efficiency of the EMR tube falls off very sharply below 1200 A, so that the detection efficiency plotted in Fig. 13 cannot be extrapolated to lower wavelengths. Although the absolute transition probabilities of the Nl lines may be in error by as much as 50%, the ratios should be much less uncertain. However, the assumption that the response curve is linear between pairs of calibration points

    PAGE 67

    56 when plotted on a semi logarithmic scale, and the freedom allowed in fitting the two linear segments of this curve lead to an estimated overall uncertainty in the determination of relative cross sections of approximately 50% for the entire spectral range from 1200 to 1750 A. The uncertainty in obtaining relative cross sections for the spectral range from 1200 to 1A00 A, however, is expected to be much less than 50% In Fig. \k a plot of the relative detection efficiency of the vacuum monoch roma to r with the MEM is shown for the spectral region between 600 and 1200 A. For the region between 1000 and 1200 A the molecular branching ratio method was utilized. 11 Here, the relative detection efficiency has been obtained by comparing the relative emission rates of the Q\ lines of the 2-v" progression of the Werner system of H ? produced in a microwave light source to the transition probabilities given by Allison and Dalgarno. 12 The light intensity was sufficient to achieve 0.30 A resolution. To obtain the relative detection efficiency below 1000 A, the relative emission rates of two pairs of ON lines (796,718; 673,616 A) have been compared with tabulated transition probabilities. This was done for ON emissions resulting both from He + ions bombarding 0, and from a microwave light source. The detection sensitivity curve was obtained as before by assuming a linear variation of sensitivity between pairs of points on a semi logar i thmi c scale. Again, using this technique some freedom is allowed in determining the intersection points of the various linear segments. Since the results differ somewhat

    PAGE 68

    57 depending upon the source of the Oil emissions and upon the choice of intersection points, a smooth response curve was constructed by averaging different possible curves. This average curve is what is presented in Fig. ] k . The slope o of the relative response curve between 6 5 and 750 A is seen to agree well with the slope of the relative quantum efficien cy of the MEM in this region (represented by x in Fig. \k) . The relative quantum efficiency of the MEM was obtained by simultaneously comparing the response of the MEM at various wavelengths to that of a pho tomu 1 t i p 1 i e r tube coated with sodium salicylate under the assumption that the response of the sodium salicylate does not vary with wavelength over this region. The errors in calculating the absolute transition probabilities of the V/erner system are quoted as less than 6%. Again, the ratio of transition probabilities is expected to be even more accurate. Thus, within the spectral region from o 1000 to 1200 A the uncertainty in determining the relative spectral response is expected to be less than 5%. Assuming that it does not fall off too rapidly below 1000 A, the relative detection efficiency is expected to be in error o by less than 20% down to 900 A. The quoted error in the transition probabilities given for the Oil lines is greater than 50% so that below 900 A the uncertainties increase and O are probably as high as 70 100% at 700 A.

    PAGE 69

    58 Dependence of the Emission Cross Section on Polarization In any practical experiment only a portion of the photons emitted from a length l of the ion beam are detected. If the emission of these photons is anisotropic, the number of photons entering the detection system per unit time will depend not only upon the solid angle n subtended by the detection system, but also upon the angle of observation, 6, measured relative to the beam direction. It can be shown 13 that the rate of photon emission from a length £ of the ion beam per unit solid angle in a direction 6 is given by tj 3-Pcos z Q I . . ( 9 ) = — 1>3 4n 3-P (I I I -32) where P is the polarization fraction defined by P = I . . T . I . . + I . . ^o id I I 1-33 In this last equation I and I \~ are the number of photons emitted per unit solid angle per unit time in the direction 6 = 90° with planes of polarization respectively parallel and perpendicular to the beam direction. The number of photons S.. actually entering the detection apparatus, then, is given by (I I I-3V If observations are made at right angles to the beam direction, and if e varies only slightly over the solid angle fi, then

    PAGE 70

    59 S . . is given by 9.1 . .f90°j ai. ^3 t, (I I 1-35; In order to relate the output signal of the detection system to the photons entering the system, the detection sensitivity of the optical system must be known for polarized light. It should be obvious that the count rate S. ^3 is given by = n[K 1 . . + k 1 (1 1 1-36) ^J I'd %3 where K , K is the detection sensitivity for light polarized respectively parallel and perpendicular to the beam direction. Since the total number of photons entering the detection apparatus I., is qiven by I. . + I . . = I . AC + 1; , 2-J t-3 13 (I I 1-37) where C = I^./i and the detection sensitivity for unpolar' ized light is given by K + K K(\) = K (o. + l) 2 2 (|| I-38) where a = K /K , then equation (III-36) can be written (Co. + 1) 13 = n 2K(X) I (a+1) (C+l) (I I 1-39: Using equation (111-32), with 6 = 90°, this equation becomes a 3 2 (C+l) K(X) , J 4v 3-P ( a + l) (C+l) ( I I |-4o) S • = J . . 1-3 1*3

    PAGE 71

    60 and the emission cross section becomes 4v ^J N 1,1 a b S,./K(\) N I % a b where r = (a+l) (C+l 2(C+1) 3-P r , (Mi-41 (III -42) is the correction due to the effect of polarization. This correction term can also be written l-P/3 1 + P(a-l) (a + l) (I I 1-43) It is clear from this last expression that i f P = 0> Y = 1, and if a = l t V = l-P/3. Therefore, in order to actually determine the emission cross section, the polarization fraction must be determined. From equations (111-33) and (111-35) it is clear that the polarization fraction can be written P = S . . S . . *T> *"Z~ S . . + S . . (I I 1-44) As discussed previously the output signal S.. is determined 2* d by the detection efficiency of the optical system. This detection efficiency depends upon the polarization, so that equation (111-44) becomes it n j_ ±_ s j/ k s j/ k n n z Z S../K + S../K II JL II X. o -o (K /K ) I' JL II J_ a +a (K /K ) 111-45:

    PAGE 73

    62

    PAGE 74

    Figure 16 Instrumental polarization of the Ebert mount monochromator as a function of wavelength.

    PAGE 75

    Gk e.o , — o H
    PAGE 76

    65 where a and a are the relati ve emission rates for light polarized respectively parallel and perpendicular to the beam direction, and where the ratio K /K is called the instrumental polarization for the detection system, a. The arrangement for determining the instrumental polarization is shown in Fig. 15. Light from an Eppley tungsten ribbon lamp was depolarized by a diffuser and focused by a quartz lens through a polarization analyzer onto the entrance slit of the monochromator . The. analyzer was mounted so that the polarization axis could be fixed either parallel or perpendicular to the beam direction. The output signal of the photomul t i pi ier was then measured at each wavelength with the polarizer first parallel, then perpendicular. When the incident light is unpolarized, the ratio of the output signals measured with the polarizer first parallel and then perpendicular to the beam direction, s"/,^ is clearly equal to the instrumentation polarization k"/K~. A plot of the instrumentation polarization as a function of wavelength is shown in Fig. 16 for wavelengths between A000 and 7500 A. Therefore, to determine the polarization of a given spectral feature as a function of beam energy, the relative emission rates for the two orientations of the analyzer are computed for each potential applied to the ion chamber, and equation (111-1*5) is evaluated using the instrumental polarization plotted in Fig. 16.

    PAGE 77

    IV. RESULTS Identification of Observed Spectral Features Spectral scans arising from N 2 + collisions are shown in Figs. 17-22 for the wavelength region between 700 and 6200 A. These scans have not been corrected for variations in the sensitivity of the optical detection system as a function of wavelength. o Spectral Features Above 2500 A In Figs. 17, 18, and 19 a spectral scan from 2500 to 5050 A taken with 5 A resolution is shown for a collision energy of A keV. The most prominent features in this spectral region are the vibrational bands of the second positive system of N, (C 3 n -* B 3 II ) and of the first negative sys* u g hi tern of N 2 + (3 2 1 + + X Z l + ), the (0,0) band of this latter system being off scale in Fig. 18. The locations of many of the band heads of these systems are indicated although not o all of those indicated are clearly resolved. With 5 A resolution both of these systems have the appearance of singleheaded bands which are degraded toward shorter wavelengths. -Also present in this spectral region (most prominent at the shorter wavelengths) is the second negative system of 0* ( A n u '^ x 1 ^ a ' ) ' Tnis is an extensive system of doubleheaded bands which are degraded to the red. Below 3000 A other spectral features also appear to be present, but because 66

    PAGE 78

    o — tJ — m c — 0)

    PAGE 79

    IF r/ =>f sc -.i«sr J"

    PAGE 80

    -C 0) 4-J > — + — d) CNJTO — cn 0) H— in O m — o in 0) c c _c l/l T3 4-1 — c — TO l/l O » E <-n o O o 1l/l o i/i -a i-a ro 03 c 2 > < -Q c O O ai cn< -O a) iTO to c > iO 4-J 4J •— l_ O in O QJ — -C Q. — in i/i . — O 4-1 c O in l/l 4J — TO E

    PAGE 81

    7 -^; 2& •P"i. :>r if Z> J.r -•"? D3S/'£N010HJ JO H.^B^nN 3A!lV"ljd

    PAGE 82

    c

    PAGE 83

    72 )3S/SN0±0Hd JO ti39WriN 3AI1V13M

    PAGE 84

    in "O

    PAGE 85

    Ih 03S/SN010Hd --<0 UdGWON 3AliV13a

    PAGE 86

    o

    PAGE 87

    76 33S/SN0±0Hd ^0 H38WnN 3AI1VT3U

    PAGE 88

    — ro 2 C o *-• —ex;

    PAGE 89

    IS/SNOiOMd JO bJSWflN 3AllV'Oy

    PAGE 90

    79 of the relatively low signals and extensive nature of the * second negative emissions, these could not be unambiguously identified. 14 o In Fig. 20 a scan from 5000 to 6200 A is shown taken with a resolution of 8.5 A. This scan was also taken at a collision energy of 4 keV. The width of the rotational structure and the consequent overlapping of the different bands of the first negative system of 0„ + (b h l~ + a h II ) toqether 2 g u a with the relatively low signal make it impossible to identify the individual bands. For this reason only the band sequences (Ad = 0, -1, -2) have been identified. The atomic lines observed in the spectral region above o 2500 A arise, except for four 01 lines, from transitions of the atomic ions of oxygen and nitrogen. These lines appear to be relatively weak compared to the molecular bands of N„ and N 2 , but this is due in part to the decrease in detection sensitivity at the higher wavelengths. o Above 6200 A no additional features were identifiable. o Spectral Features Below 1500 A Figures 21 and 22 show a spectral scan from 1500 to 700 A o taken with 5 A resolution, the collision energy being respectively 2.5 and k keV. The most prominent features in this spectral region are the resonance lines of both Nl and 01. Both of these features (the 1200 A line of Nl and the 130 3.5 A line of 01) are off scale in Fig. 21. Other atomic lines arising from excited dissociation fragments are also identified. 15

    PAGE 91

    8 Below 700 A a spectral feature was observed at approximately 673 A. This feature appeared to be broad enough to be two unresolved lines and probably arises from the 2s3s 2 P° -* 2p 2 3 P transition of Nil and the 2p 2 3s 2 P + 2p 3 2 P° transition of Oil. The only spectral features observed in the wavelength region between 1500 and 2500 A (not shown) were the I7A3.6 A line of N I , which arises from the same upper state as the o 1^93-3 A line, and, at wavelengths greater than 2200 A, the second negative system of 0„ . Emission Cross Sections of the Molecula r Features of H/ and N ? The emission cross sections for the (0,0), (0,1), (1,2), and (2,3) bands of the first negative system of N „ are plotted in Fig. 23 and listed in Table I as a function of ion beam energy, while emission cross sections for the (0,0), (1,0),, and (2,1) bands of the second positive systems of N„ are presented in Fig. 2^ and Table II. The relative emission rates for the individual features were determined at a much larger number of impact energies than indicated in these figures, and a smooth curve was visually fit to these original data points. Within experimental error there appears to be no structure in the relative emission rates as a function of energy for any of these spectral features so that the values for the emission cross sections derived from this smooth curve are averaged values and may well be more accurate than individual data points. The error bars in Figs.

    PAGE 92

    o

    PAGE 93

    82 ( 3 wo 8l _0l)-0

    PAGE 94

    Table 1. Absolute emission cross sections for the (0,0), (0,1), (1,2), and (2,3) bands of the first negative system of N2 + arising from collisions of N 2 + with O2. Energy (keV) Cross Section (10' 18 cm 2 ) (0,0) (0,1) (1 ,2. (2,3 25 30 35 40 50 60 0.70 0.80 0.90 1 .00 1 .25 1 .50 1 .75 2.00 2.-50 3.00 3-50 4.00 5.00 6.00 7.00 0.07

    PAGE 95

    c 3 O O O in U i/i (L) E XI

    PAGE 96

    i — ~T~ o o to o Q. •o c Cvl OJ ..X. o OJ © < © <3 ~ e < x © < x raxC3x6v -0 t o

    PAGE 97

    8 6 Table II. Absolute emission cross sections the (0,0), (1,0), and (2.1) bands of the second positive system of N2 arising from collisions of N£ + with 0£. for 0. 30 0.35 0.40 0.50 0.60 0.70 80 90 00 25 50 75 00 50 3.0 3.50 00 00 00 00 0.02

    PAGE 98

    23 and Ik indicate the estimated error in determining the relative cross section of a particular band as a function of energy. As can be seen in Figs. 23 and 2k, the relative emission rates of the N„ first negative and of the N ? second positive bands increase mono ton i ca 1 1 y above an ion-beam energy of about 0.20 keV . Below this energy the relative emission rate levels off, and, within experimental error, becomes constant as far down as 80 eV . The emission rate of the (0,0) band of the Nfirst negative system remained constant as far down as 33 eV . It was impossible to determine whether this constant signal resulted from emissions of the feature under observation or from the background continuum which was observed at o all wavelengths above 2500 A. Therefore, the energy threshold for the emission cross section could not be determined. The observed background above 2500 A may be due in part to unresolved molecular emissions of the second negative system of 0„ . In addition, no emissions from the 0„ molecule were identified, so that some of this apparent background may result from unresolved 2 emissions. However, this seems unlikely since the relative emission rate of the background, measured at 3200, 3^00, 4 1 5 , ^300, and 4900 A, was found to be fairly constant with both wavelength and collision energy, although there was a slight increase in the observed backo ground at ^ 3 and 4900 A for energies above k keV . The emission rates for all spectral features above 2500 A have been corrected for this observed background.

    PAGE 99

    In order to determine the variation of the emission cross section for a particular molecular band as a function of energy, the relative emission rate of the band head was measured with a 5 A band width for various ion beam energies. The relative emission rates obtained in this way should be free of significant error unless there is considerable overlap of the head of one band by the rotational structure of an adjacent band and unless the rotational-energy distribution in the upper state varies significantly with projectile velocity. To determine the amount of overlap of the head of one band by the rotational structure of an adjacent band for the AD = -1 band sequence of the first negative system of N + , a high resolution scan was taken with a beam energy of 3 keV and a target pressure of 4 X 10" 4 torr. This scan indicated that the rotational structure was relatively compact, extending only over about kO A for the (0,1) band, 30 A for the (1,2) band, and 20 A for the (2,3) band. The error in the relative emission rate due to overlap was estimated at less than 3% for this system. A high resolution scan of the Ay = +1 band sequence of the second positive system of N_ was also taken at a beam energy of 3 keV. Again the rotational structure of the bands appeared relatively compact and the error in the relative emission rates due to overlap was estimated to be no greater than i>% . In experiments conducted by B r egma n -Re i s 1 e r and Doering 16 on the excitation of N 2 in collisions with He and Ne,

    PAGE 100

    83 the energy distribution among the rotational levels of the first negative (0,0) band of Nwas found to be velocity dependent below about 1.2 X 10 7 cm/sec (an ion-beam energy of approximately 2 keV). The excitation of high rotational states was found to increase with decreasing ion velocities and the intensity maximum of the band contour became broader and moved toward higher values. Such a shift in the intensity maximum of the band contour would tend to make the relative emission rate of a particular band measured in the manner described above appear to decrease more rapidly than it actually does at lower energies. However, the magnitude of the error resulting from such a shift could not b precisely determined in all cases due to poor resolution, and no attempt has been made to correct for it. Because of a limited observation length I, emission cross sections arising from excited states of the projectile must be corrected for both the projectile velocity and the lifetime of the excited states according to equation (111-23). The cross sections presented in Figs. 23 and 2k as well as in Tables I and II have been corrected using 66 nsec 17 as the lifetime of all vibrational levels of the + n J. N 2 B z l u state and 38. ^ nsec 18 as the lifetime of all vibrational levels of the N C 3 II state. This correction amounts to less than 3 % below 1 keV, but as much as 30% at 7 keV for the N 2 first negative system, while for the N. second positive system it amounts to less than 1% below 3 keV and only as much as 10% at 7 keV.

    PAGE 101

    9 As pointed out in the discussion of projectile excitation, the effect of cascades was neglected in deriving equation (lM-23). However, since there have been no reported cascades from upper states to the NB state, 19 ' 20 and since decay to the ground state {X 2 Z ) is the only radiative decay mechanism, the corrected emission cross sections a., for the vibrational bands of the N „ first neqativ 1-3 e sys tern should be proportional to the excitation cross sections of the v' = 0,1, and 2 vibrational levels of the N B state. The N. C 3 tt state which gives rise to the N 2 second positive system, however, can be populated by cascades from the E 3 l + 9 state, but there is no way to determine the contrioution of this cascade to the N. second positive emissions since the emissions lie outside the detection range of the apparatus. The relative emission cross sections for the bands of the N„ first negative system were obtained at a collision energy of 4 k e V by assuming that the relative intensities of the various bands were proportional to the relative intensities of the band heads measured with a 5 A bandpass. This assumption should be quite good since each band head contains about the same number of lines (about 50 for the bandpass used here) at least within a given band sequence. To check the validity of this procedure, the ratio of the relative cror. s section of the (0,0) band to the (0,1) band was evaluated at different collision energies. Theoretically, the transition probability for spontaneous emission A v t v ti 's given by 21

    PAGE 102

    91 v',v" K Re l (v' ,v") a(v' ,v") v',v" (IV-1) where Re (v',v") is the average electronic transition moment, q(v',v") is the Fra nek-Condon factor, A , ,, is the v ' , v " band head wavelength, and K is a constant. The ratio of transition probabilities with common upper levels is given by V,t>" Re 2 (V ,v")' \\, jy „, q(v',v") V,y'" Re 2 (v',v<") ^\, )V „ q(v' 3 v"') C I V-2 the so-called branching ratio which is independent of the population of the upper state, and thus constant for any type of excitation process. Since the average electronic transition moment Re is nearly constant for the first nega t i ve system of N„ , 22 the branching ratio reduces to A v',v» X \> 3 v>" l(»'>» n > A v' ,v"' X\, iV „ q(V>,V«>) (IV-3 Using the F ra nekCondon factors tabulated by Nicholls, 23 the theoretical branching ratio Aq o/^o 1 ' s equal to . 3 5 . As shown in Fig. 25, the experimentally determined branching ratio was found to be relatively constant between 2 and 7 keV and to have a value of 0.30 ± 0.01 in good agreement with the theoretical branching ratio and with previous experiments. 4 The increase of the branching ratio as the energy

    PAGE 103


    PAGE 104

    93 oi ivy 9N ONVda

    PAGE 105

    3k is decreased from 2 to 1 keV is probably a result of the increase in the statistical uncertainty of the relative emission rate of the (0,1) band as well as the variation in rotational excitation at these low beam velocities as mentioned above. In this same way, the relative emission cross sections for the bands of the N 2 second positive system were obtained at a collision energy of k keV. These relative emission cross sections were made absolute by normalizing the emission rate of the entire (0,0) band of the N 2 second positive system, and the emission rate of the entire (0,1) band of the N 2 first negative system arising from N 2 + 2 collisions to that of the 4278 A line of Ar II Up' 2 P° * 4s' 2 D) arising from He + + Ar collisions at A keV. The absolute emission cross section for this latter process is given by Jaeck's et at. 25 as 2.hG X 10" 18 cm 2 with an estimated error of less than 30% . Table III gives the absolute emission cross sections obtained in this way for those vibrational bands of the first negative system of hL and of the second positive system of N which could be resolved. Also given in this table are the band-head wavelengths and the estimated error in determining the relative emission cross sections within a given electronic transition. It should be pointed out that the emission rate of the entire (0,1) band of the first negative system of N „ had to be corrected for the overlap of this band by the (1,5) band of the N 2 second positive system.

    PAGE 106

    95 Emission cross sections for the molecular bands of the first negative system of N and the second positive system of ^ which could not be adequately resolved were obtained by calculating the appropriate branching ratios and using the cross sections given in Table III. The branching ratios for the N„ first negative system were calculated using the. F ranck-Condon factors tabulated by Nicholls, 23 (assuming that Re(v), the electronic transition moment for an internuclear separation r, is constant for this system) while those for the N 2 second positive system were calculated using the "smoothed" relative band strengths (defined by the expression { } 2 , where v' and v" represent the upper and lower vibrational state, respectively, and Re (r) is the electronic transition moment) tabulated by Jain and Sahni. 26 The emission cross sections obtained in this way are tabulated in Tables IV and V for a collision energy of 4 keV. The total emission cross section for both the N _ first negative system and the N« second positive system were obtained by simply adding together the total emission cross sections of each v" progression for v' = 0,1,2, and 3. Any contribution due to the v' = k progressions was neglected since no {h,v") band was actually distinguishable, although the possible locations of some of these bands are indicated in Figs. 17 and 18. The errors indicated in Tables IV and V are the estimated errors in determining the relative emission cross sections. In order to determine the total emission cross section for the entire N first negative system as a function of

    PAGE 107

    96 Table III. Absolute emission cross sections for various N2 + first negative and N2 second positive vibrational bands arising from collisions of N2 + with 2 at a collision energy of 4.0 keV. The estimated error in determining the relative emission cross section for a given electronic transition is also indicated. Designation Band -head Wave 1 eng t h o (A) Cross Section (1018 cm 2 ) 1st. Neg (0,0) (0,1) (1,2) (2,3) (3,M 3914.4 4278. 1 4236. 5 41991 4166.8 12.38 ± 3.66 ± 3.08 ± 1 .40 ± 0.47 ± 1% 1% 8% 1 5% 34% N 2 2nd Pos (0,0) (1,0) (2,1) (3,2) 3371 .3 3159.3 3136.0 31 16.7 3-57 ± 7% 2 .92 ± 1% 1.88 ± }}% 0.95 ± 21%

    PAGE 108

    97 Table IV. Absolute emission cross sections for the N* first negative system at a beam energy of k keV. The indicated error is the uncertainty in the relative cross section. Band 10" 18 cm 2 ) Band odO" 18 cm 2 ) (0,0) (0,1) (0,2) (0,3) (0,M 2.20 3-72 0.75 0.13 0.02 ,0) J) ,2) ,3) ,M ,5) 5-37 3.11 3.08 1 .08 0.26 0.05 (0,y") 16.82 ± (1 ,v") 12.95 ± 3% (2,0) (2,1) (2,2) (2,3) (2,M (2,5) (2,6) 57 06 11 25 06 (3,0) (3,1) (3,2) (3,3) (3,M (3,5) (3,6) (3,7) 64 02 01 0.47 0.39 16 05 (2,v") 7-51 ± 15* (3,y") 3-74 ± }h% o(N. 1st. neg. ) = 41.02 X 1 0" 1 i 2 ± \0%

    PAGE 109

    Table V. Absolute emission cross sections for the No second positive system at a collision energy of 4 keV. The indicated error is the uncertainty in the relative cross section. Band a(]Q 1 cm') Band (10 1 8 cm 2 ) (0,0) (0,1) (0,2) (0,3) (o,4) 57 29 86 25 06 ,0) J) ,2) ,3) ,4) ,5) ,6) 2 .92 0.11 1.16 0.98 0.45 0.15 0.04 (o.v"! 7.03 d,u") 5.81 (2,0) (2,1) (2,2) (2,3) (2, A) (2,5) (2,6( (2,7) 0.79 1 .88 0. 16 0.27 0.63 0.46 0.21 0.08 (3,0) (3,D (3,2) (3,3) (3,M (3,5) (3,6) (3,7) (3,8) (3,9) 0.10 1 .29 0.95 0.50 0.01 33 40 0.25 0.11 0.04 (2,v") 4.48 2% (3,i>") 3.98 ± 21% a (N 2nd . pos = 21 .30 X 10 -18 cr 0%

    PAGE 111

    f-

    PAGE 112

    Table VI. Absolute emission cross section of the entire N2 first negative system as a function of collision energy. Collision Energy (keV) Cross Section (10 18, ) 3 5 J»0 50 60 70 80 90 1 .00 1.25 1 .50 1 .75 2 .00 2.50 3.00 3.50 4.00 5,00 6.00 7.00 84 52 95 71 63 8.42 9.96 1 1 .59 15.10 18.29 21.31 23.93 28.95 33. 48 37.38 41.02 W-71 53-97 59.38

    PAGE 113

    02 Table VII. Absolute emission cross section of the entire N£ 2nd. positive system as a function of collision energy. Collision Energy (keV) Cross Section (10 18, 0.50 0. 60 70 80 90 00 25 50 75 00 5 3.00 3-50 00 00 00 00 51 95 1 .30 1 .85 l.kk 3.06 if. 83 6.77 8.49 10.22 13.25 16.30 18.79 21 .30 25.00 28.32 31 -53

    PAGE 114

    03 energy, the variations of the {0,v"), (l,y"), and (2,v") progressions as given in Table I were used along with the emission cross sections at k keV for these progressions given in Table IV. The variation in the (3,u") progression as a function of energy was assumed to be approximately the same as in the (2,v") progression. The results of this procedure are shown in Fig. 26 and in Table VI. The absolute emission cross section of 9-96 X 10" 18 cm 2 ± }Q% at 0.9 keV obtained in this way compares quite favorably with the value of 15-0 X 10 -18 cm 2 ± 50% as determined by Liu and Broida for the N 2 + 2 system. This same procedure was also used to determine the emission cross section for the ntire Nsecond positive system as a function of energy and is presented in Fig. 26 and Table VII. Emission Cross Sections of the Molecu lar Features of + 2The absolute emission cross section at k keV for the + 2 first negative system was determined simply by summing the measured emission rates for the entire Ay = 0,-1,-2 sequences arising from N 2 + + C> 2 collisions and normalizing, O as above, to that of the 42 78 A line of Ar II arising from He + Ar collisions. The emission cross section for the different band sequences and the total emission cross section for the 2 first negative system are tabulated in Table VIM. The 20% uncertainty in the relative emission cross sections is due primarily to the poor resolution and the difficulty in determining the contribution due to the background continuum.

    PAGE 115

    1 *t Table VIM. Absolute emission cross sections for the observed band sequences of the 0i + first negative system at k keV. The indicated error is the estimated uncertainty in the relative cross section. Band Sequence Cross Section (1018 cm 2 ) A V = -2 A V -1 A V = A. 96 ± 20% 12.95 ± 20% 20.57 ± 20% Tota 1 38.48 ± 13%

    PAGE 116

    JO — l/l z>

    PAGE 117

    c p. 3 in C .7 */ o -1 o •/ V

    PAGE 118

    0/ The variation in the relative emission rate as a function of beam energy was measured by observing the central portions of both the Ay = -1 and the Ay = band sequences o at 5570 and 5980 A with a 65 and a 50 A bandpass, respectively. Since the variation in the relative emission rate as a function of energy was essentially identical for both band sequences, only the curve for the Ay = -1 sequence is presented in Fig. 27 . As stated above, there i s cons i de ra b 1 e uncertainty in these measurements due to the background. However, the general shape of the curve is believed to be accurate. Unlike the excitation of the N 2 first negative and N b econd positive systems, there appears an increase in the relative emission rate of the 2 first negative system as the N„ + ion energy is reduced below 0.30 keV. The large cross section at low energies may be due to the n ea r r esona n t charge exchange process: H 2 +U 2 V + °2 (X 3 + N ^ A ' ll ~) + °S (b **0 9 9 9 iv-M The minimum energy defect for this process is approximately 0.4 eV. For such a near-resonance charge exchange process, the form of the cross section is expected to be 27 a 1 1 1 [a-b log w] , ( I V 5 ) where a and b are constants, w is the collision energy, and a is the excitation cross section. The solid curve in Fig. 27 has been calculated from this formula with b/a = 0.35, and fits the relative data very well below 0.2 keV. At the

    PAGE 119

    8 higher energies, excitation of the o + b state is probabl >2 '2 v state is proDaDly due to the ionization of the 0, molecule by removal of the 3o electron. 9 Because the 0,, second negative system was so extensive and ill resolved, no cross section measurements for this system were attempted. Emission Cross Sections of Atomic Features The relative emission cross sections of all atomic features were obtained at k keV as described in Section III (p. k ; j) . Those features observed at wavelengths below 1750 A and listed in Table IX were made absolute by normalizing the emission rate of these features to that of the O Lymann a (1215.6 A) line arising from He + + H ? collisions. The absolute cross section for this latter process is given by Young et at. 28 as 3-83 X 10" 17 cm 2 with an estimated error of 35-^0%. Those atomic features observed at waveO lengths greater than 3000 A and listed in Table X were made absolute by normalizing to the emission rate of the A 2 7 8 A line of Ar II arising from He + Ar collisions, just as for the molecular features. Energy level diagrams for Nl, Nil, 01, and ON are shown in Figs. 28, 29, 30, and 31, respectively, where many of the observed transitions are noted. The production of these excited dissociation fragments is assumed to proceed via an excitation of the parent molecule to an upper state which corresponds to a repulsive potential. For homonuclear diatomic molecules the kinetic energy of each dissociation fragment relative to the center

    PAGE 120

    Table IX. Absolute emission cross sections for lines below 1750 A arising from excited dissociation fragments resulting from collisions of N2 + with O2 at A keV. The indicated errors are the estimated uncertainties in the cross sections relative to that at 1200 A. I on Wa ve 1 eng t h o (A) Upper State C ross Section (IO-I 7 cm 2 ) Nl 1 200 1 1 3 ^ Nl I 01 963.0 953.5 U93.3 I2A3

    PAGE 121

    1 1 Table X. Absolute emission cross sections for lines above 3000 A arising from excited dissociation fragments resulting from collisions of N 2 + with 2 at k keV. The indicated errors are the estimated uncertainties in the relative cross sections. Transition Wa ve 1 eng t h o (A) Cross Section (10" 17 cm 2 ) Nl I 3p 3 D -> 3s 3p l D -y 3s lpO r3 P 5 P" + 3S 5p { 3d 3 F° -> 3p 3 D } 5679. A 3995.0 5005.0 0.28 ± 10% 0.10 ± 15% 0.22 ± 10% kp 3 P -v 3s 3 S° 4 P 5 P -> 3s 5 s° 4d 5 D° -> 3p 5 P 5d 5 D° -> 3 P 5 P ^368.3 3947.3 61573 5330.0 0.09 ± 10% 0.08 ± 15% 0.37 ± 10% 0.11 ± 10% 3 P 2 D° -> 3s 2 P U18.1 0.05 ± 10%

    PAGE 122

    4-1 X) to I) en +J c o < c C 0)

    PAGE 123

    1 1 2 CO ro csT' a. CO CO <\5

    PAGE 124

    E O i_ . +-" x> i/> (U CT> *-> C O < c C 0)

    PAGE 125

    \k o rO ex.
    PAGE 126

    E

    PAGE 127

    1 6

    PAGE 128

    3 c a)
    PAGE 130

    1 19 of mass of the parent molecule is one-half the released kinetic energy, which is not expected to be greater than several hundred eV . For such cases the correction term for the observed emission cross sections arising from the dissociation of the Nprojectile [equation (111-23)] is unity since the lifetimes of the observed atomic states are so short (approximately 10" 9 sec for the Nl and Nil states observed). In addition, the lifetimes of the excited 01 and ON states which were observed are short enough that even an appreciable kinetic energy resulting from the dissociation of 2 would not affect the observed cross sections. The cross section for the 01 3s 5 S° state was not determined, however, because of uncertainties due to the long lifetime of this metastable state. In addition, the cross sections for several other atomic features which are identified in Figs. 18, 19, 21, and 22 were not determined because o of poor resolution. This was also true of the 672 A line of Nil and the 673 A line of ON; however, the cross section for these two features could well be as large as that for the O o 1085 A line of Nil and the 83A A line of ON, respectively. The absolute emission cross sections of several excited dissociation fragments are plotted in Fig. 32 as a function of ion beam energy, and are tabulated in Table XI, where the designation of the upper level of the transition and the observed energy thresholds for emission are also given. Just as for the molecular features of N the relative emission rates for the different spectral features shown in

    PAGE 131

    cxl Ln ltv o en — lt> oo o +

    PAGE 132

    1 2 1 mi ll i — r — i rriTT-n i r i — i — r o •qcJ < o < o o -1 >o g:: L'J UJ I I I I I I | L. __ JLULJ_i -I LU..LJ I 1-i — O 3° C_ — o — o H < K <4 X **3 o < G_ O x < X < O b . | M l I I I 1 Lii.U-.i_J.__ I L IJ-LLJL.J. o o o 5 b b (-UiO) _C

    PAGE 133

    ;22 c

    PAGE 134

    23 laoo inmo — lt\ -^in lt\ —• .— cr> OOOOOOO' — — ^ N CM n -T Lnr-^oo cno-— cn co ro r«~\ m . — NCMCMNCMMNtM o-\ r^i ltvvo r~1~^ o~\ — crvrooooo-oMmj-iAvDr-vcnxio OOOOOOO — — — CNCMf-i — r~-CNi-3-cNicx)CNjr^.OrM-a-r^>rocN — VO f~^CO 01(710 O. — — . — — — — ooooo — — — — — — — — OO JOOOOOOOOOO vO — O O Nmo-J lA^fl^O WM v£>r--.cocncr>o — — . — — • — — — ooooo. ^_„__._ f"ar^-r~~or~-ocNoooooor^r^ r-o~\^r co o cm -3ltv in c-\ cn ooo foooj--r iAinu\ LnmuimLn^r oou"»oi-noooooooo mO N1ANO WOlflOOOO O — — — ' — CM CM «*"* o~\ -3 1A\0 N

    PAGE 135

    \2k Fig. 32 were determined at a much larger number of impact energies than indicated here, and a smooth curve was visually fit to these original data points. The statistical uncertainty in each of the original data points was less o than 5% for the Nl 1200 A line at impact energies above 0.2 keV, for the Nl 1 1*93.3 A line above 0.3 keV , for the Nl U12 A line above O.k keV, for the Nl 955 A line above 0.5 keV, and for the Nil 1 8 5 A line above 1.0 keV. For the O 01 1303.3 A line the statistical uncertainty was less than 5% above 2.0 keV. The uncertainties increase at the lower energies as the signals decrease. The observed energy thresh olds for the features listed in Table XI were ta^en to be that energy below which the net signal becomes zero. In the spectral region below 1 500 A there were no observed background emissions, so that the net signal was taken as the output signal obtained less the dark count of the detector. The uncertainties in the energy thresholds are due to statistical fluctuations in both the signal and the dark count. Just as in the case of the molecular emissions, these cross sections rise monotonically from threshold. However, for the atomic transitions of both nitrogen and oxygen the emission cross sections peak between 3 and 6 keV and then begin to decrease. In order to determine the excitation cross section of the states listed in Table IX, the contribution to these emissions due to cascade must be determined. Very few of the transitions which would populate these states could be

    PAGE 136

    12: distinguished within the spectral range of the detection system. The only well resolved transition was the kp 3 P -* 3s 2 S° transition of 01 resulting in the A 3 6 8 . 3 A line (see Table X). Other transitions which would populate the 3s 2 S° state were either indistinguishable or beyond the spectral range of the system. If the latter are assumed negligible, then the cascade contributes less than h% to the population of the 3s 2 S° state of 01. No other cascades which would contribute to the observed ultraviolet lines of 01 and Oil were distinguishable. To determine the contribution from cascades to the observed ultraviolet emissions of N I and Nil, an attempt was made to estimate the emission cross sections of those transitions resulting from cascades which fall within the spectral range of the detection system, even though they were often not clearly resolved from other spectral features. In addition these estimated cross sections had to be corrected because-of their longer lifetimes and because of the finite observation length. This correction was made using equation (111-23), assuming that x. = 1/A-. for the cascade transition and that the atomic fragments had the same velocity as the parent molecule. In this way, it was estimated that cascades contribute no more than 5% to the population of the 3s h P state of Nl and no more than 10% to the population of the 3s 2 P state of Nl and the 3p J P state of Nil. No other cascades which would contribute to the observed ultraviolet lines of Nl and Nil were distinguishable.

    PAGE 137

    126 Polarization Measurements Since all observations have been made at 90° to the direction of the beam, any anisotropics in the patterns of radiation may affect the magnitudes of the cross sections. Although emissions arising from molecular transitions are generally not expected to be polarized, Cahill et at. 29 have reported polarization of molecular emissions in electron impact experiments. For this reason, the polarization of the N 2 first negative (0,0) band was measured as described in Section III. Within experimental error, the emissions were found not to be polarized over the range of beam energies 0.3 8.0 keV. However, because of uncertaintie in the instrumental polarization as well as the reduction in signal due to the polarization analyzer, the errors were fairly large, often being as large as 50%. Measurements of the polarization of the observed atomic O emissions above 3000 A were not feasible since these emissions were relatively weak and often poorly resolved. For the vacuum ultraviolet lines, we have no way of measuring the polarization, nor can the optical axis be rotated relative to beam direction in order to determine the anisotropics directly. However, measurements of the polarization of the Lyman a, H a ' and H p ^' nes °f hydrogen resulting from dissociative collisions have been made by Gaily et al., 30 Isler and Nathan, 31 and Isler, 32 respectively, and may give some indication of the percentage polarization to be expected. Gaily has found that the Lyman a emissions arising from H_ + + He

    PAGE 138

    2 7 collisions were not polarized, whereas Isler and Nathan have observed a maximum polarization of approximately 1 2% for H a + emissions in He + H 2 collisions at an ion energy of k 5 eV , and Isler has observed a maximum polarization of approximately 12% for the H emissions in H. + He collisions at 1 keV, 6% for H emissions in H + Ar collisions at about 30 eV, and 2.5% for H. emissions in H„ + + Kr at 30 eV . p 2 It is obvious that the polarization will depend upon the interacting species as well as the transition observed, but if the maximum polarization fraction is only of the order of 10%, and since the instrumentation polarization varies from 1/2 to 2 (see Fig. 16), then the emission c oss sections presented here will be high at most by 10% according to equation (III -k2) . It should also be pointed out that when many different molecular states contribute to dissociation into a given atomic state (as may be the case for both N ? and especially at energies as high as several hundred electron volts) preferential population of the magnetic sublevels of the excited fragments is diminished, the anisotropics in the angular distribution of these fragments tend to become smoothed out, and the extent of any polarization arising from dissociation is, therefore, reduced. 33

    PAGE 139

    V . D I SCUSS ION Ion Beam Excited State Population There is considerable evidence that processes such as stripping, charge transfer, and dissociation of both the projectile ion and the target are affected by the state of the incident ion entering the collision chamber. 31 *" 37 Although in most experiments it is difficult precisely to determine the distribution over internal states of the incident ions, it is often possible to estimate th: approximate composition of the ion beam from a knowledge of the cross sections for producing the various excited states as well as the lifetimes of these states. According to Shemansky and Broadfoot, j8 experiments conducted of electron bombardment of N 2 indicate that for an electron energy of 20 eV approximately 56% of the ions are produced in the X 2 l + state G kQ% in the A 2 n state, and k% in the B 2 l + state. For hiqher bombardment energies it is energetically possible to populate additional excited states of N, + , for example the C i + state as well as several metastable quartet states. Since the lifetimes of the B 2 L^ and C 2 Y, + states are 6.6 X 10" 8 sec. 17 and 1 X 10" 7 sec., 39 respectively, whereas the time for the ions to reach the collision chamber is generally greater than 5 psec, ions formed in these states will undergo spontaneous radiative decay to the ground state before reaching the collision chamber. In addition investigations of the 128

    PAGE 140

    129 metastable quartet states by Maier and Holland 40 indicate that the fraction of the ion beam existing in these longlived states is only of the order of 10~ 4 . It would, therefore, appear that the N 2 ions entering the collision chamber are almost exclusively in the X 2 l + and A 2 n states. For electron impact energies from 20 to 100 eV , Shemansky and Broadfoot 38 indicate that approximately k0% of the N 2 ions are formed in the A state. Holland and Maier 41 found that only 30% of the ions were formed in the A state for an electron energy of 46.5 eV, while the percentage initially formed in photo i on i za t i on experiments is reported to be between 45 and 60%. 42 Although the effect upon the excitation and lifetime of the A state by the magnetic and electric fields present within the ion source is unknown, it is assumed that approximately 35% of the N„ + ions are initially formed in the A state. Since the lifetime of this state is reported to be approximately 10 usee, 41 approximately 20% of the N 2 ions are in the A state at the collision chamber when the beam energy is 7 keV. The explanation of the low energy peak in the emission cross section of the _ + first negative system (Fig. 26) lends further evidence for the presence of the A state in significant quantitites. The excitation of the vibrational and rotational levels of both the 7. z l and the A 2 n states of N + might also be expected to depend upon electron bombardment energy. However, the emission cross sections of the resonance lines of o both Nl and 01 (1200 and 1303-3 A, respectively) as well as

    PAGE 141

    30 the (0,0) band of the first negative system of N + were found, within experimental error, to be independent of electron bombardment energy above 20 eV. This is understandable for the atomic lines arising from excited dissociation fragments, since it is not expected that an electronic transition to an upper repulsive potential curve would be significantly affected by the vibrational or rotational state of the lower potential curve. The fact that the (0,0) band of the first negative system of N 2 + is also independent of bombardment energy would seem to indicate that the vibrational state of the projectile ions entering the collision chamber are not dependent upon the electron bombardment energy at least for bombardment energies above 20 eV . Therefore, unless the excitation by electron bombardment is appreciably affected by the magnetic and electric fields present within the ion source, the N + X 2 l+ state should be produced 9 predominantly in the v" = vibrational level, while the relative populations of the vibrational levels of the A 2 n u state are expected from the F ra nekCondon principle to be given by U A (v' = 0): H A (v' = }): H A (v' = 2): W (v' = l): UJv' = k): WJv'S) = 100: 127:92: 51 :23 : 1 . These values have been calculated using F r a n c k Co ndon factors tabulated by Nichols, 43 assuming, since the operating temperature within the ion source is not expected to be greater than 1000° K, that the N 2 molecules are in the X 1 l + v" = state.

    PAGE 142

    In transit from the ion source to the collision chamber kO-SQZ of the ions originally produced in the A 2 n state will spontaneously decay to the X 2 l + state at the higher ion energies, populating the upper vibrational levels of this state. Using the relative populations of the vibrational levels of the A and X states given above and transition probabilities from the A to the X state calculated with Nichol's Franck-Condon factors, the relative population of the vibrational levels of both electronic states at the collision chamber were determined, assuming that only ] 5% of the ions remained in the A state. These are presented in Table XII with the population of the X 2 i + v = level normal ized to 100. Only those levels with v < 5 were considered. Table XII. Relative population of the vibrational energy levels of the X and A states of N + at the collision chamber. The population of the y = level of the X state is normalized to 100. Relative Popu 1 a t i on 2v + X Z E •U 100 7 3 1

    PAGE 143

    32 Exc i tat io n of the N„ B 2 l + State — — / u In the case of electron excitation, the vibrational energy distribution of excited electronic states of a molecule can be well described by the F ra nek-Condon principle for electron impact energies of about 100 eV. 4 ^ The simplicity of the Franck-Condon principle for explaining molecular transitions is very attractive and recent studies of the relative band intensities of the Ay = -1 sequence of the N 2 first negative system arising from collisions of H + , H + , He , N , and Ne on N 2 , and from collisions of N 2 + on He and Ne, conducted by Moore and Doering 45 and by B regma n -Re i s 1 e r and Doering, 16 respectively, indicate that, for sufficiently large ion velocities, the relative band intensities excited by heavy particle collisions can also be adequately described by the Franck-Condon principle. To determine if this might also be the case for collisions of N 2 + on the relative populations of the vibrational levels of the N„ + B 2 l + state 2 u were determined as a function of b earn energy. The population of the v' vibrational level, N D (v'), can B be related to t h t i on N D (v') = K a e emission cross section a , „ by the equa v ' jV » A V,iX Re 2(v '> v ") q(V ,v") (v-i) where v" is tne vibrational level of the ground electronic state of N 2 , A y , y „ is the wavelength of the emission band head, Re(v' t v") is the average electronic transition moment for the transition, q(v',v") is the Franck-Condon factor, and

    PAGE 144

    133 A' is a constant. For the N 2 first negative system, R*e is nearly constant within a band sequence. 22 Therefore, the population of the v' vibrational level relative to the v' = vibrational level is given by N B (v' ) \ 3 v' ,v' + ] v ' , V ' + ' q(0,\) A'„ro; O 0,1 X 0,1 q(v',v> + \) (V-2) for the hv = 1 band sequence. The relative populations calculated from this equation are shown in Fig. 33 for energies above 0.6 keV. Above h keV (a velocity of 1.7 X 10 7 cm/sec) the relative population of the vibrational levels of the upper state appear to be velocity independent. While the relative population of the v' = 1 level appears constant for energies even as low as 0.6 keV (6.4 X 10 6 cm/sec), that of the v' = 2 level increases mono to n i ca 1 1 y as the energy of the N 2 ion decreases below k keV. Bregman -Re i s 1 e r and Doering 16 observed a similar velocity dependence for exciting the vibration levels of the N 2 state in collisions of N* ions with Ne and He. In their experiments the relative population of all states with v' > increased mono ton i ca 1 1 y as the projectile velocity was decreased below 1.2 X 10 7 cm/sec (a collision energy of 2.1 keV), but was velocity independent above this. They also found that the relative population of the v' = 2 level increased more rapidly than that of the v' = 1 level as the velocity was decreased; the increase in the relative population of the v' = 1 level as the collision energy was reduced from 2.1 to 0.6 keV , however, was only 8%, and

    PAGE 145

    Figure 3 3 Relatjve populations of the vibrational levels of the N 2 B l u state as a function of ion beam energy. The arrows iiark the relative populations expected from the Franck-Condon principle.

    PAGE 146

    3 5 2^ O < ..J CL O a. f 5, < ijj IT LABORATORY ENERGY (keV

    PAGE 147

    36 such a small increase could fall within the error bars of our mea surements . This same type behavior has been observed in charge exchange excitation of the N. B state by Moore and Doering, 45 where the excitation of the higher vibrational levels becomes + important at He ion velocities as high as 7 X 10 7 cm/sec (71 keV) and increases more rapidly with decreasing velocity than for the direct excitation process. Lipeles 46 has attempted to explain similar observations by a simple model based upon the distortion of the ground vibrational state of a neutral molecule in the presence of a projectile ion. The distortion of the ground state was calculated by assuming a ha.monic potential with the addition of a polarizability energy dependent upon the internuclear distance. Distorted Franck-Condon factors calculated from the resulting perturbed harmonic oscillator wave functions were found to agree quite well with the observed enhancement of upper level excitation for 1 keV Ar + ions on CO and N 2 . One would also expect from Lipeles' model that the perturbation of an N 2 ion caused by neutral atomic and molecular targets should be less than that of a neutral N. target caused by an approaching ion, in agreement with the observed results. The simplest model, therefore, which would explain both the direct and the charge exchange excitation of the N* B state at high energies appears to be that of a grazing collision of the projectile and target accompanied by an abrupt conversion of translational to internal energy. Because of the short duration of the collision at high energies, the inter-

    PAGE 148

    137 nuclear distance of the N £ or N 2 + molecule would remain constant, and the relative population of the vibrational levels could be found using tabulated F ranckCondon factors. At the lower energies, however, the molecule is being perturbed during the collision, and the relative population of the upper vibrational levels is no longer adequately predicted using undistorted F ranck-Condon factors. This simple model does appear to adequately explain the excitation process for the charge transfer collisions observed by Moore and Doering 45 as well as those by Haugh and Bayes U7 for Ar collisions with CS 2 and N 2 0, where the relative population of the various vibrational levels appears to agree very well with those calculated from undistorted Franck-Condon factors within the region where the relative population is constant with ion energy. However, for the direct excitation of N 2 in both our experiments (N 2 + + 2 ) and those conducted by Bregman-Reisler and Doering 16 (N 2 + + He and N + + Ne), the observed relative populations of the vibrational levels of the B state at high velocities, although apparently velocity independent, do not agree with those expected for excitation of the N 2 B state from the ground electronic and vibrational state. According to tabulated Franck-Condon factors 23 for the excitation process N , + [X 2 l* (v=0)] + M -> N + [B 2 Y + (v=v')} + M } 2 ~g " " < 2 where M is any target, the relative populations in the upper state should be N o (0)iN„(]):N 1t (2) = 1 : A 6 : 7 a B B

    PAGE 149

    138 The experimental results obtained in these experiments, however, were N B (0) :N B (]) :N B (2) = 10 0:73:^0 for N 2 + , and the results obtained by and Doering for N + He were may easily result from one or both of two processes: (i) population of the upper vibrational levels of the N + X state by spontaneous decay of the A state in transit from the ion sourci to the collision chamber and subsequent excitation of the + N 2 B state via F ranck-Condon type transitions, or (ii) col 1 i s iona 1 1 y induced transitions from the A to the B state. If it is assumed that 35% of the N* ions produ ced in the

    PAGE 150

    3 3 collision chamber are in the A state and that approximately 60% of these ions decay to populate the N + X state. The resulting relative population of the N„ B state due to FranckCondon type transitions is given by N B (0) :A r s (D :N B {2) = 100:^9: 12, whereas, if all the ions in the A state decay into the X state before reaching the collision chamber, the relative population N B (0) :N B (\ ) :N B (2) = 100:50: 15To obtain the relative population of the N B state observed experimentally would require an initial A state population of 10 %. Since it is not expected that this number of ions are originally produced in the A state, co 1 1 i s i ona 1 1 y induced excitation from the A to the B state must contribute to the enhanced excitation of the upper vibrational levels if the Franck-Condon principle is indeed valid for these collisions. Although there are no tabulated Franck-Condon factors for the optically forbidden A -* B transition, an examination of the potential energy curves of Gilmore 19 (see Fig. 3*0 indicates that an enhancement of the upper vibrational levels of the B state would be expected for such a transition. The fact that B regma n -Re i s 1 e r and Doering also expect the same composition of the primary N_ ion beam in the collision chamber may well explain the similarity in the relative population of the vibrational levels of the N* B state at high energies, although it seems somewhat surprising that the excited state population of the primary ion beam is so nearly the same for two different types of ion source operated under different conditions.

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    Figure Ik Selected potential energy curves (reproduced from ref. 19) of N 2 and N

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    U ! i"i X ,,, /'»' •. ', I ) ) + i , , I ; 26, c\\ -7 V; * Wi., or :,"-/'*'"',.•'..v I , ' MI
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    142 As has already been pointed out, the velocity v above which the relative population of the vibrational levels becomes independent of the primary ion velocity differs considerably depending upon whether the excitation proceeds via a charge-transfer or a d i r ec t -exc i ta t i on channel, this velocity being 1.7 X 10 7 cm/sec for N 2 + + 2 * N 2 + B + [0-]; 6.k X 10 6 cm/sec for N 2 + + He (Ne) * N 2 + B + [He(Ne)]; 16 and approximately 1 X 10 8 cm/sec for X + + N 2 -> N+ B + [X], where X is He, H, H,, N, Ne. 45 This would seem to imply that the perturbations of the neutral N molecule by an approaching ion in the charge-transfer channel are much stronger than those of the N. ion by neutral targets in the a i r ec t -exc i ta tion channel. At velocities lower than v , the perturbation o influences the molecule or molecular ion long enough for the internuclear distance to change significantly during the collision. Because of the long range of the force exerted by the -ion upon the neutral molecule in the charge-transfer channel, enhanced excitation of the upper vibrational levels is observed at higner velocities. This is in qualitative agreement with Lipeles' simple model. Certain other experiments, however, indicate that this trend is not generally valid. Studies of d i rec t -co 1 1 i s i ona 1 excitation of N« and CO by H , H. , and N ions in an inelasti scattering experiment, conducted by J. H . Moore, Jr. 48 indicated that there was no significant enhancement of the upper vibrational levels in the ion velocity range 2-7 X 10 7 cm/sec, and that the relative intensities of the vibrational bands

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    k3 agreed well with those predicted by F ra nck-Condon factors. In addition, in charge-transfer reactions with tri atomic molecules studied by Haugh and Bayes 47 the populations of the vibrational levels in the product excited CS + and N + ions agree with predictions based on F ra nck-Condon factors at Ar ion velocities as low as 1 X 10 7 cm/sec. It seems clear, therefore, that the deviation of the relative population of the vibrational levels in a molecular transition from that expected by the F ranck-Condon principle must depend not only upon the effective range of the force causing the perturbation, but also upon the i n t e rmo 1 ecu 1 a r distance at which the transition occurs. If the transition occurs at relatively large inter molecular distances (as expected for near-resonance charge transfer collisions, for example) neither the projectile nor the target molecule will be significantly perturbed by the other, and the Franck-Condon principle should adequately describe the transitions even at moderate relative velocities. If, however, a rather intimate collision is required before a given transition occurs, one would expect the wave functions of both the target and the projectile to be perturbed. In fact, if the collision is very intimate, the identity of the individual molecules may become somewhat vague the description of the collision process being best described by a complex quas i mo 1 ecu 1 a r model consisting of four nuclei. Thus, the i n te rmo 1 ecu 1 a r distance f?_ at which the interaction potential begins to significantly perturb the molecular energy levels of the projectile or the target and the

    PAGE 155

    u distance R c at which the transition occurs (the crossing point between the average potential energy curves of the initial and final states) will determine whether or not the transition can be adequately described by the FranckCondon principle. If R > r it should be possible to describe the transition by the F ranck-Condon principle at nearly all collision energies. In the region where R„ R the "interaction time" will be the determining factor, whereas, when Rg < R the transitions can probably be adequately described only by a complex qua s i mo 1 ecu 1 a r model. Comparison with Charge Transfer Data Shown in Fig. 35 are the cross section for C> + production (x) and the total cross section for slow ion production (,) in N 2 + 2 collisions as a function of ion beam energy. Although an exact determination of the cross section for the production of the 0„ second negative system was not attempted, our measurements indicate that the total cross section for the production of both the 0* first and second negative systems can hardly be greater than 5 X 10" 17 cm 2 ± k0% below 1.0 keV , and will be much less than this at energies as low as 200 eV. Thus, the majority of the + molecules produced in charge exchange, at least at the lower energies must either be in the ground electronic state (^ 2jl Q ^ or in a m etastable state which cannot be detected using optical techniques, for example the a 4 IT state (see Fig. 36), since this could arise from the charge exchange p roces s

    PAGE 156

    o — E + + U CMCM 0) o z: o. c

    PAGE 157

    \kf> CTT1 — ! — ! i 1 — h ... CJ O tt O 2 JLL1.JLJ L ! TTTT _ rT -_ r -. 1 r . CO DC ; ijJ o ir o _ h2 < 1 m J < 1 O 6 q 6 o NO! o o 3S SS080 3SNVH0X3 39WH0 "1V101

    PAGE 158

    Figure 36 Selected potential energy curves of C, (reproduced from ref. 1 9 ). ' and 0,

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    20 •-'•! u L. U8 0( v ! 3 ) i 0'f ? D") orij)1 ots b ) \A ? n„
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    \kS N + (x 2 Y.^) + c, ( 1 :. ) N-tf l I + ) + 9 + (a H, ) , 2 v " "#' "2 v " " ' g' ' "2 ~g' where the energy defect is only 0.5 eV . The total cross section for slow ion production in the N 2 + °2 s Y stem must include not only the production of 0_ , but also the production of from dissociative collisions. In addition, reactive processes resulting in slow ions {e.g., NO ) might also be detected, although one would expect the cross section for such processes to be small for energies greater than 100 eV. Furthermore, at the lower energies dissociation fragments of N« may also be counted, depending upon the geometry of the slow-ion collector used in these experiments; this is not clearly specified in the original paper. If it is assumed that N ions arising from the dissociation of the N_ projectile, and ions resulting from reactive processes do not contribute greatly to the total cross section for slow ion production at energies greater than 100 eV, then the cross section for the production of + ions in this energy region is of the order of k X 10~ 16 cm 2 ± 70%. The emission cross sections, however, for the features which were observed can hardly be greater than 5 X 10 _li cm 2 ± k0% in this energy region. Thus, the majority of the ions produced in N_ + collisions at low energies must be in the ground state, or in metastable states. Also, since the total emission cross section of all the 01 transitions observed cannot be greater than 5 X 10" 17 cm 2 ± k0% at these energies, it appears that the majority of 01 atoms resulting from dissociative collisions are also in the ground state, or in metastable states.

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    5 Production of Excited Dissociation Fragments There are a large number of possible interaction channels which would produce the resonance emissions of Nl, Nil, 01, and Oil. However, only those with the smallest energy defect for direct and charge exchange excitation are listed in Table XIII. No reactive channels, {e.g. N_ + -> NO + [NO]} have been considered since no evidence for such was observed and since the cross section for such channels generally become large only at very low energies. The observed thresholds for the production of these states are considerably higher than the minimum energy defects, especially for the production of the ion emissions. This is in contrast to the otservations made by Holland and Maier 6 of Nl emissions arising from collisions of He with N^ where the energy threshold for emission agrees quite well with the energy defect for charge exchange reactions He + + N 2 -v N + + N + He, where N denotes an excited nitrogen atom. Based on the discussion above, this might indicate, as far as Nl emissions are concerned that the i n t e rmo 1 ecu 1 a r distance R _ at which the transition occurs is fairly large for He + N 2 charge exchange collisions, whereas for N* + Q collisions, the distance R is comparable to /?_ , the distance at which distortion of the parent molecule becomes appreciable There is little information on the upper states of the N 2 molecule whose dissociation limits correspond to the excited states of Nl and Nil. However, recent measurements of

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    151 c

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    »52 the released kinetic energy as a function of electron collision energy in studies of dissociative ionization of N, by electron impact conducted by Deleanu and Stockdale 51 and by Smyth, Schiavone, and Freund 52 indicate that the bulk of N + ions whose released kinetic energy peaks near 3 to k eV results from a molecular state whose dissociation limit is approximately 35 eV that is the N + ( 3 P) + N(3s) limit. This indicates that the upper molecular potential for the production of the 1200 A line is probably repulsive and is only 3 to k eV higher than the dissociation limit at the equilibrium internuclear distance of the N 2 X state. Thus, the emission thresholds observed in He + + Ncollisions resulting in the O 1200 A line would appear to correspond to those expected from a Franck-Condon type transition, while in N„ + + collisions the N 2 molecule is apparently strongly perturbed during this collisional process at least near the threshold energy and when a transition occurs it is to the strongly repulsive part of the upper potential curve, if indeed the collision pro cess is not so intimate that the individual molecules lose their identity. In fact, since a perturbation of the parent molecule is expected to reduce the "spring constant" of the molecule, a transition to the strongly repulsive part of an upper potential seems unlikely. Thus, it is expected that the correct treatment of the transitions resulting in dissociation fragments near threshold will require a knowledge of the potential surfaces of a complex qua s i mo 1 ecu 1 a r model consisting of four nuclei.

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    53 One might expect, however, that at higher collision energies the transitions would again become Fra nc kCondon like, much as was the case for the excitation of the N„ + B state. The only way to determine this would be to measure the released kinetic energy in dissociative collisions as a function of collision energy, and these measurements cannot be made with the present system. However, measurements of released kinetic energy from dissociative collisions of N„ on N^ at ion energies of 2 keV conducted by Moran et aZ-. 53 indicate that the dissociation can be explained quite well by F ra nek-Condon type transitions to the repulsive energy states. The measurements, however, are for dissociative transitions via the N 2 D state resulting in N + ( 3 P) andN( l+ S°) From a study of the dissociation of CH. , CH + , and CH* ions of 1.3 3.0 keV energy in collisions with He, Ar, H 2 , air, and CH, Kupriyanov found that the relative yields of dissociation fragments are insensitive to the neutral target gas, which would imply that the post co 1 1 i s i on s ta te population of the projectiles in states which lead to dissociation is not greatly influenced by the gas giving rise to the excitation. 51 * To see if this were true for the dissociation of the N„ projectile at higher energies, the absolute emission cross sections of several N I and Nil lines were determined at k keV for N„ collisions with Ar. These are presented in Table XIV along with the corresponding cross sections for N collisions with 0^ at the same energy and the relative cross sections of o the two systems, normalized to the 1200 A line. Since a

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    Sh Table XIV. Emission cross sections of several Nl and lines arising from dissociative collisions of N2 + with 02 and with Ar at a collision energy of k keV. The ratio is the emission rate for a particular line relative to the emission rate for the 1 200 A line. A(A) (10 1 7 Rat io + 0, Nl Nl I 1 200 1135 1085 916 5.37 1 .31 1 -73 1.27 1 .00 0.3k ± 02 0.A8 ± 0.02 0.28 ± 0.01 + Ar Nl N I 1 200 1135 1085 916 3.09 0.79 1 .22 1.11 1 .00 0.36 ± 0.02 0.59 ± 0.03 0.43 ± 0.02

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    55 comparison of the signal from the 1135 A line to that of the 1200 A line, etc. is all that is actually desired, all errors due to the spectral response of the system can be ignored. The errors of the relative magnitudes, then, are approximately 5%, and this is what is presented in Table XIII. Here it can be seen that not only are the magnitudes of the cross sections different, but the relative magnitudes for the two systems are also quite different. Thus, the post collisionstate population of (N £ ) at least in those states which lead to the 1085 and 91b A lines are seen to be significantly influenced by the target gas giving rise to the excitation at least at an ion energy of k keV . It is clear from Fig. 26 that the variation of the emission cross sections as a function of energy has the same functional form for the atomic transitions of both oxygen and nitrogen. The cross sections rise mono ton i ca 1 1 y from threshold, peak between 3 and 6 keV and then begin to decrease. This same functional form of excitation has been noted in ion-atom collisions also performed in this laboratory. 55 For ion-atom collisions, the two state s em i -c 1 a s s i ca 1 approximation yields an expression for the total excitation cross section, when integrated over all impact parameters, given by 56 a(T c ) = p 4vR 2 H-V c /T ] [i^fnJ E s (2n)] (V-3) where T Q is the initial kinetic energy of the colliding system (center of mass), V is the threshold energy, R is the internuclear distance of the pseudo-crossing, E is the

    PAGE 167

    156 exponential integral of order 5 and p is the probability that the particles approach along the specified potential energy curve. The parameter n is given by n = l' LZ [M/2T Q (]-V c /T o )]l/2 f ( V _i,j where M is the reduced mass and the Landau-Zener velocity, V LZ' ' S related to the potentials of the qua s i -mo 1 ecu 1 e by LL 'on 1 'oo nn 1 v ? ' Here ' e on is the matrix element coupling the two collision channels, and e^' , e^' are the slopes of the incoming and outgoing potential curves, respectively, which would exist if e Qn were zero. All matrix elements are evaluated at the crossing point. In deriving this expression the assumption is made that for slow collisions the atomic nuclei move as classical particles under the influence of the total potential energy of the system. This potential energy is given as a function of internuclear distance by the potential energy curve for the quas i-mol ecul e created during the collision process. Different curves correspond to the different excited states of the atoms and correspondingly of the quas i -niolecul e. There will be a finite probability of a transition when a p s eudo c ro s s ing of two quasi-molecular potential curves occur (i.e., when e „„ " £ _ I is a minimum. Since the variation with collision energy of the e mission cross sections of excited dissociation fraqments in N + + 2 2 collisions appear similar to that observed for ion-atom collisions, an attempt was made to fit the experimental cross

    PAGE 168

    57 sections to equation (V~3) using R' 2 = pR 2 and V _ as variable parameters. Values of V were obtained from a twopoint fit of equation ( V 3 ) to the rising portion of the cross section, while values of R 1 were chosen to give the correct magnitude of the cross section. Figure 37 shows a surprisingly good fit of the Landa u-Zene r curve to the experimental results for the Nl 1200 A line, using V = 6.9 X 10 6 Li L O cm/sec and R 1 = 0.62 A. Also shown in this figure is the best fit to the Nil 1085 A line, using V Tr> = 32.0 X 10 6 cm/sec L 6 o and R 1 = 0.71 A. Although several defects in the LandauZener formula have been pointed out by Bates 57 in regard to ion-atom collisions, the good agreement between tr.is theory and our results at least points out that ion-molecule collisions resulting in excited dissociation fragments may be described sem i -c 1 a s s i ca 1 1 y by a pseudoc ros s i ng of averaged potential energy surfaces.

    PAGE 169

    — c — c

    PAGE 170

    59 ( s ujo ai _oi)jD

    PAGE 171

    V I . CONCLUS ION Since cascades appear to contribute less than 5% to the resonance lines of Nl and 01, the emission cross sections for these features should be approximately equal to the excitation cross sections for the production of the N I ( 3 s k P ) and 01 (3s 3 S ) states due to collis.ion induced dissociation. The contribution of cascades to the other atomic and ionic O lines below 1750 A also appears small so that the emission cross sections of these features are proportional to the excitation cross sections. In addition the emission cross sections of the N £ first negative system are also proportional to the cross sections for populating the various vibrational levels of the N 2 B state, since there are no known transitions -to this state from upper states. The cross sections for the production of these states, however, are of necessity composite cross sections due to the presence of both N 2 + X and A states in the primary ion beam. Although 80% of the ions are believed to be in the X state at the collision chamber there is no way of determining the relative magnitudes of the individual cross sections arising from N 2 X collisions with 0X and from N + A collisions with 2 X. That the presence of the A state ions can make a significant contribution is indicated by the emissions arising from the 2 + first negative system at low projectile energies, as well as the enhanced population of the 160

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    upper vibrational levels of the N 2 + B state for ion energies above k keV. The vibrational population of the X and A states are also somewhat uncertain, although, since variations in the electron bombardment energy from 20 100 eV produced no significant effect upon emission cross sections, we have assumed here that the vibrational state population is as spec i f i ed in Tabl e XII. The fact that the primary ion beam is composed of more than one well-defined state often makes comparison with theory somewhat difficult. However, recent developments in laserinduced fluorescence techniques promise to make this an ideal tool to determine precisely the distribution over internal states of the incident ions in future experiments of this type . 58 At the present time, however, there appears to be no theoretical treatment which can be satisfactorily applied to thed i ssoc i a t ion processes measured in this experiment. The apparently good fit of the experimental data to a LandauZener type expression for the cross section perhaps indicates that the process can be treated as a pseudoc ros s i ng of averaged potential energy surfaces. The determination of such potential surfaces, however, does not appear likely in the foreseeable future, as ab initio calculations of even the upper molecular potential energy curves of N N + , and 2 which lead to excited dissociation fragments are not yet available. Some experimental work, however, is now being done to study the kinetic energy released from these upper

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    62 states, and should be able to give a rough indication of the shape of the upper potentials within a limited range of internuclear distances. 51 ' 52 The determination of the potential surfaces for the lower energy states, however, may be possible in the near future. Considerable work has been done in recent years on linear atom-diatom collisions, and some work has also begun on collisions involving four atom complexes, most involving complexes with two or three hydrogen atoms. 59 Most of this work has been applied to low energy reactive collisions such as N ? + -» N0 + + 0. The greatest need for precise potential energy surfaces is at low energies, near threshold. However, our results on the vibrational excitation of the N + B state, along with those of B regma n -Re i s 1 e r and Doering, 16 indicate that a simpler model may be adequate at higher energies. Such a model might extend the simple kinematic model for atom-diatom reaction collisions used by Suplinskas in recent years. 60 With this model he has been very succesful in describing angular and velocity distributions, differential cross sections, and internal energy distributions which agree remarkably well with experiment. Such a model, extended to diatom-diatom collisions and incorporating Lipeles 1 model 46 for distortion of the molecules by longrange forces might well show close agreement with our measurements, at least at the higher energies.

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    7. 1 1 1 2 13 14 REFERENCES C. Liu and H. P. Broida, Phys. Rev. A2_ , 1 8 2 ^ (1970) A tabulation and critical assessment of many of the measurements made of the formation of specific excited states of both atomic and molecular systems between 1945 and 1971 can be found in E. W. Thomas, Excitation in Heavy Particle Col 1 isions (Wiley I n te r sc i ence , New York, 1972). J. P. Doering, Phys. Rev. 133 , A I 5 3 7 ( 1 9 6 i+ ) . S. H. Neff, Astrophys. J. 1 40 , 348 (1964). M. Hollstein, A. Salop, J. R. Peterson, and D. C. Lorents, Phys. Letters 324, 327 (1970). R. F . Hoi 1 and and W. 1299 (1971 ) R. H. Huqhes and D. K. W. Ng, Phys (1964). Ma i er II, J . Chem . Phy s . 5_5 , 36 , Al 222 Rev R. C. Isler, Rev. Sci. Instrum. 4 5, 30i 974) . E . W . Thomas, Excitation in Heavy Particle Collisions (Wiley Interscience, New York, Y^JlY, pp^ 12-24. W. L. Wiese, M . W , Smith, am Glennon, Atomic Transition P t obab i 1 i t i es , NBS Ref. Data Ser. 4(U.S. GPO, Washington, D. C, 1966), Vol. 1. For a discussion of this technique and necessary precautions see M. J. Mumma, J. Opt. Soc. Am. 62, 14 5 9(1972). A. C. Allison and A. Dalgarno, Atomic Data J_, 289 (1970) J . A. Sm it, Physica 2, 1 04 (1935). The various molecular features were identified with the aid of R. W. B. Pearse and A. G. Gay don, The Identification of Molecular Spectra (John Wiley and Sons, Inc., New York, 1 963 ) , 3~rd edition. 163

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    64 15All atomic emission lines have been identified with the aid of We i s e ejt_ aj_. (ref. 10), R. L. Kelly, Atomic Emis si on Lines Below 200u Angstroms, Hydrogen Through A r gon ~TNa va 1 Research Lab., Washington, D . C . , 19 68), N R L Report 6648 , and Charlotte E. Moore, A Multiplet Table of Astrophysical In terest ( N a t i ona 1 Bureau of Standards, Washington, D.C., 1959), PB 151 395. 16. H. Bregman-Reisler and J. P. Doering, Phys. Rev. A 9 , 1 152 (197M . — 17JDesesquelles, M . D u f a y , and M . C. Poulizac, Phys. Lett. A2 2 9 6 (1968), and R. G. Bennett and F. W. Dal by, J. Chein. Phys. 3J_, 4 3 4 (1959). 18. A. W. Johnson and R. G. Fowler, J. Chem Phys 5 3 65 (1970). — ' 19F. R. Gilmore, J. Quant. Spectr. Radiat. Transfer 5, 369 (1965). 20 L. Wallace, Astrophys. J. Suppl. Ser. 62, 6, 445 (1962). — 21 G. Herzberg, Spectra of D i a torn i c Molecules (Van Nostrand, New York, 19 5 0), p . 200. 22. R. N. Zare, E. 0. Larson, and R. A. Berg, J. Mol. Spect rose. J_5_, 117 (1 965) . 23. R . W. Nicholls, J. Res. Natl. Bur. Std. (U. S.) 65A , 451 ( 1961 ) . 24. (a) J. P. Doering, Phys. Rev. 1_3J_, A 1537 (1964), (b) E. W. Thomas, G. D . Bent, and J. L. Edwards, Phys. Rev. J_65_, 32 (1968), and (c) J. H. Moore, Jr. and J. P. Doering, Phys. Rev. 1 77 , 218 (1969). 25. D. Jaecks, F. J. de Heer, and A. Salop, Physica 36, 606 (1967). 26. D. C. Jain and R. C. Sahni, J. Quant, Spect rose. Radiat. Transfer ]_, 475 (1967). 27. D. Rapp and W. E. Francis, J. Chem. Phys. 3_7> 2631 (1962) 28. R. A. Youna, R. F. Stebbings, and J. W. McGowan, Phys. Rev. 171, 85 (1 968) . 29. P. Cahill, R. Schwartz, and A. N . Jette, Phys. Rev. Letters J_9, 283 (1967); See also A. N. Jette and P. Cahill, Phys. Rev. W_6, 186 (1968); Phys. Rev. A], 558 (1970) .

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    165 30 31 32. 33 34. 35. 36 37 38. 39. A . 41 . 42. 43. 44, 45. 46. T. D. Gaily, D. H. Jaecks, and R. Geballe, Phys. Rev. 167 , 81 (1968). R. C. Isler and R. D. Nathan, Phys. Rev. A6_, 10 3 6 (1972). R. C. Isler, Phys. Rev. A9, 1 8 6 5 (1974). R. J. Van Brunt and R. N. Zare, J. Cbem. Phys. 48, 4304 (1968). C. F. Barnett and H. B. Gilbody, "Measurements of Atomic Cross Sections in Static Gases," Sec. 4.2, p. 390 in Atomic and Electronic Physics: Atomic Interactions , Vol. VIM, Part A ( B . Bederson and W. L. Fete, Eds.) of series Methods of Experimental Physics , ( L . M a r t a n , Ed.) Academic Press, New York, 1968. J. W. McGowan and L. Kerwin, Can. J. Phys. 41, 316 (1963). ~~ J. W. McGowan and L. Kerwin, Can. J. Phys., 42, 2086 (1964). E. Lindholm, Proc. Phys. Doc. A66, 1061 '53). D. E. Shemansky and A. L. Broadfoot, J. Quant. Spectrosc. Radiat. Transfer JJ_, 1 4 1 (1971). P. G. Fournier, C. A. van de Runstraat, J. R. Grovers J. Schopman, F. J. deHeer, and J. Los, Chem. Phys. Lett . 9.426 (1 971 ) . W. B. Maier II and R. F. Holland, J. Chem. Phys. 51, 2997 (1970). R. F. Holland and W . B. Maier II, J. Chem. Phys. 56, 5229 (1972). R. I . Schoen, Can. J. Chem. 4 7 , 18 7' 969 R. W. Nicholls, J. Quant, Spectrosc. Radiat. Transfer 2, 433 (1962). C. Y. Fan, Phys. Rev. 1 03 , 1740 (1956); D. E. Shemansky and A. L. Broadfoot, J. Quant. Spectrosc. Radiat. Transfer 11, 1401 (1971). J. H. Moore, Jr., and J 218 (1968) . Doer i ng , Phys. Rev. 177, M. Lipeles, J. Chem. Phys. 51, 1252 (1969).

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    6 6 *» 7 • M . J. Haugh and K . D. Bayes, Phys. Rev. A2_ , I778 (1970. 48. Unpublished results discussed in reference 16. **9. R. F. Stebbings, B. R. Turner, and J. A. Rutherford, J. Geophys. Res. 7J_, 771 (1966). 50. R. F. Stebbinqs, B. R. Turner, and A. C. H. Smith, J. Chem. Phys. 3_8, 2277(1963). 51. L . Deleanu and J. A. D. Stockdale, J. Chem. Phys. 63, 3898 (1975). 52. K. C. Smyth, J. A. Schiavone, and R. S. Freund, J. Chem. Phys . 5_9, 5223 ( 1 973) . 53T. F. Mo ran, F. C. Petty, and A. F. Hedrick, J. Chem. Phys . 51, 2112 (1969) . 54. S. E. Kupriyanov, Kinetika i Kataliz 3_, 13 (1962). [English translation: Kinetics and Catalysis 3, 9 (1962)]. 55R. C. Isler and L. E. Murray, Phys. Rev. A 1 3 , 2087 (1976). 56. N. F. Mott and H. S. W. Massey, T he Theory of Atomic Col 1 i s i on s , 3rd. edition (Oxford University, London, 1 9 65) , Chap. XIII. 57D. R. Bates, Proc. Roy. Soc. A, 2 57 , 22 (i960). 58. R. N. Zare and P. J. Dagdigian, Science 1 8 5 , 7 3 9 (1974) 59. JW. McGowan, The Excited State in Chemical Phy sics, Vol. XXVIII of Ad v ane es in Chemical P h y s i c s , e d . by I. Prigogine and S. Rise (New York: J. l/TTey and Sons, I n ter sc i ence , 1975), pp. 114-169. 60. R. J. Suplinskas, J. Chem. Phys. 4j_, 5046 (1968); T. F. George and R. J. Suplinskas, J. Chem. Phys. 51, 3666 (1969); J. Chem. Phys. 54_, 1037 (1971); J. ChiTn". Phys. 54, 1046 (19 71).

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    BIOGRAPHICAL SKETCH Lambert Edward Murray was born on January 19, 19^9, at Greenwood, Mississippi. In May, 1967, he was graduated from Marks High School and entered the University of Mississippi in the fall of the same year. After two years he transferred to Harding College, and received a Bachelor of Science Degree in Physics in May, 1972. In September of that year, he enrolled in the Graduate School of the University of Florida and has worked as a graduate assistant in the Department of Physics while pursuing the degree of Doctor of Philosophy. Lambert Edward Murray is married to the former Alice McKay Shields. He is the 1976 recipient of the Graduate Student Teaching Award from the University of Florida Graduate school. He is also a member of Alpha Chi, Phi Kappa Phi, and the American Association of Physics Teachers. 167

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    \ certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Ml Ralph C . I s I e'r Associate Professor of Physics I certify that 1 have read this study and that in my opinion it conforms to acceptable standards of s;holarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy! ~)V-rX1 *kL\/ Thoma s L . Ba i 1 ey Professor of Physi cs> \ certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertaticn for the degree of Doctor of Philosophy! i UJCharles F . Hooper Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy! ^cZ J o^li R . S a b i n Professor of Physics and Cherni stry

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    I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. j^M.M. <*PDav i|d YA . M i cha Professor of Chemistry and Physics This dissertation was submitted to the Graduate Faculty of the Department of Physics and Astronomy in the College of Arts and Sciences and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. August , 1 977 . Dean, Graduate School

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