Title: Crossed molecular beam studies of sensitized fluorescence
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00098917/00001
 Material Information
Title: Crossed molecular beam studies of sensitized fluorescence
Physical Description: iv, 78 leaves : ill. ; 28 cm.
Language: English
Creator: Cutshall, Euel Ray, 1950-
Copyright Date: 1977
Subject: Fluorescence   ( lcsh )
Molecular beams   ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Statement of Responsibility: by Euel Ray Cutshall.
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 73-77.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00098917
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000063266
oclc - 04205542
notis - AAG8464


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The author wishes to thank many people for their contri-

butions to this study. Of course, the main person that is to

be thanked is Professor E. E. Muschlitz, Jr., whose guiding

hand helped in so many ways. Professor Muschlitz was always

willing to sit down and discuss any questions or problems

that arose.

Dr. A. N. Schweid is the person responsible for design

and construction of the majority of the apparatus. Without

his initial help these studies would have taken much longer.

A special thank you goes to the men who work in the

Electronics Shop of the Chemistry Department. Mr. R. J.

Dugan is responsible for the design of several circuits unique

to this experiment. Mr. J. W. Miller, Mr. J. B. Chamblee and

Mr. W. Y. Axson were invaluable in keeping the electronic in-

strumentation operative. Mr. Axson and Mr. Chamblee have

even worked on their own time on occasion to repair electronic

components. Without their help the data for this study could

never have been gathered.

To truly express my thanks to my wife would be impossible.

She has been my constant companion and friend throughout the

years of graduate work, and for this I am so very grateful.






A. Historical Perspective 1
B. Use of Nozzle Beams to Study Electronic
Energy Transfer Processes 3
C. Purpose and Scope of Present Study 4

A. Introduction 5
B. Gas Inlet Manifolds and Vacuum Chambers 10
C. Metastable Beam Production and Analysis 14
D. Target Beam Production and Analysis 21
E. Photon Collection and Detection 31
F. Data Output 35
G. Cryopump Assembly 36


A. Metastable Beam 46
B. Target Beam 49

A. Band Profile Measurements 54
B. Branching Ratio Measurements 62

A. Band Profile Measurements 64
B. Branching Ratio Measurements 67



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



Euel Ray Cutshall

June 1977

Chairman: E. E. Muschlitz, Jr.
Major Department: Chemistry

Measurements have been made of the vibrational branching

ratio (v'=0)/(v'=l) in N2 (C 3 ) formed in the following


Ar(3P2,0) + N2(X1 ) -. Ar( S) + N2(C 3 )

by observation of the fluorescence N2 (C B). The measure-

ments were made in the relative energy range 0.053 to 0.408

eV using crossed supersonic molecular beams. Measurements

have also been made of the N2 (C, v'=0) to (B, v"=0) band

profile at relative energies of 0.074 eV, 0.089 eV and 0.161

eV. Rotational temperatures of 10900K and 1280K were cal-

culated from the 0.089 eV and 0.161 eV profile, respectively.

The vibrational branching ratio measurements have been

compared to a theoretical "Golden Rule" model. The agree-

ment is good in the low energy region from 0.053 eV to 0.15 eV.


A. Historical Perspective

The first evidence for molecular beam formation was ob-

served in 1883 by Fleming. Using an incandescent lamp, he

discovered that there was a shadow of the filament on the

inside surface of the lamp apparently due to copper vaporized

from the filament supports. From this he concluded that the

copper molecules shot off the filament supports in straight

lines. This agreed with the kinetic theory prediction that

molecules have straight trajectories in the absence of molec-

ular collisions or applied fields.

In 1911 Dunoyer designed the first molecular beam appa-
ratus. He used a glass tube under vacuum divided into three

separate chambers by collimating holes. Heated sodium in the

source chamber formed a deposit on the wall of the third

chamber. The shape of the deposit indicated that a molecular

beam of sodium had been formed. In 1921 the famous Stern-

Gerlach experiment was conducted. In this experiment a

beam of silver atoms was deflected in an inhomogeneous magnet-

ic field. These results verified the existence of space

quantization and electron spin. Also, the magnetic moment

of the electron was calculated. This experiment showed that

molecular beams would be of great value in investigating

physical phenomena previously inaccessible to experimental


By 1928 using source pressures much greater than were

previously thought possible, Johnson obtained molecular beams

of much greater intensity than previous beams. The Knudsen

number, the ratio of the mean free path to the orifice diam-

eter, of Johnson's source was 0.001 and thus was well into

the range of continuum flow and could be classified as a

nozzle beam source.

Johnson's work was for the most part ignored until

Kantrowitz and Grey revived the idea in 1951.5 They proposed

the use of a molecular beam source in which continuum flow

dominated rather than free molecular flow as in the previous

effusive type sources. In this type of source they stated

that beam intensities several orders of magnitude greater

than effusive sources might be attained. Also, they believed

that in this type of source the velocity distribution would

be much narrower than in the effusive source.

These ideas were quickly implemented by Kistiakowsky

and Slichter.6 Although they showed that higher beam inten-

sities were possible, their apparatus lacked sufficient pump-

ing speed to show how effective the new design was.

In 1954 Becker ani- Bier designed a similar apparatus with

a higher pumping speed and obtained beam intensities approach-

ing that predicted by Kantrowitz and Grey. Two years later

Becker and Henkes measured the velocity distribution of argon

atoms from a nozzle beam source.8 They found a narrowed

velocity distribution as was again predicted by Kantrowitz

and Grey. In these experiments the advantages of nozzle beam

sources over effusive sources were conclusively demonstrated.

B. Use of Nozzle Beams to Study Electronic
Energy Transfer Processes

The transfer of electronic energy from one species to

another plays a very important role in many phenomena. These

processes occur, for example, in electrical discharges, com-

bustion, high temperature shocks, secondary processes in

radiation chemistry, upper atmosphere reactions and laser
action, with the main emphasis today in this last area.

The operation of laser systems such as Ar-02 and He-Ne is

due to electronic energy transfer which serves as the exci-

tation mechanism.10

The molecular beam technique has recently proved to be

a valuable tool in the study of electronic energy transfer

processes. Using molecular beams, it is possible to measure,

for certain excited states, the velocity distribution of

reaction cross sections, the angular distribution of reaction

products, and the internal and kinetic energy distributions

of these products.9'11-14 In addition, by using molecular

beams from nozzle sources, greater intensities with wider

ranges of relative velocities and narrower velocity distri-

butions are possible.

C. Purpose and Scope of Present Study

In this investigation a crossed nozzle beam study of

electronic energy transfer has been conducted for the follow-

ing reaction:

Ar( P2,0) + N2(X1 ) + Ar(1S) + N2(C3 u)

in the relative energy range 0.053 0.408 eV by observing

the light emitted in the transition from the N2 C state to

the B state. This process is known as sensitized fluores-


It has been shown previously by Fishburne that the meta-

stable argon states 3P0 (11.72 eV) and 3P2 (11.54 eV) upon

collision with ground state N2 molecules give N2(C3 u) which

subsequently fluoresce to yield N2(B311 ).16 The lifetime of

the N2 C state has been reported as 28 nsec; therefore, all

of the sensitized fluorescence occurs at the intersection of

the two beams.17

The purpose of this study is to repeat the measurements

made by Schweid on product vibrational energy distributions

in this system using a much greater metastable intensity and

over a wider relative energy range, and to extend the work
to include measurements of rotational energy distributions.


A. Introduction

The molecular beam apparatus used in this study is shown

in Figure 1. The sections which have not been modified since

the work of Sanders are described in more detail in that refer-

ence.18 The modifications include the following: A mono-

chromator has been added to the optical system, the low voltage

D. C. discharge cell for the production of metastable atoms

has been replaced by an electron gun and the effusive source

and velocity selector have been replaced by a supersonic nozzle


A schematic drawing of the apparatus is shown in Figure 2.

It consists of three differentially pumped vacuum chambers,

gas inlet manifolds for the two nozzle beams and the electronic

instrumentation required for time-of-flight studies and for

measuring low level fluorescent light intensities.

The target beam is a supersonic nozzle beam of N2 which

is formed by maintaining a high pressure behind a very small

circular orifice in the nozzle cap. The beam is collimated

by a skimmer mounted on the wall of the target gas chamber and

also by a collimating hole located in the main chamber. A

mechanical chopper modulates the target beam which then inter-

Figure 1

Main Vacuum Chamber







0-- 1-45*/ "

0 O d O
.n0 C3= /


. (w LA 0 ^ :

us 4 O
U 0 u
cc ac

sects the metastable beam at right angles. Finally, the

beam enters a quadrupole mass spectrometer and is velocity

analyzed by determining its flight time.

The metastable beam is also a supersonic nozzle beam.

Metastable argon is produced by an electron gun which sets

up a glow discharge between the nozzle and skimmer. After

exiting the metastable chamber, the metastable atoms pass

between a pair of deflector plates which sweep out any ions

or electrons. The beam then passes through a collimating

hole in the main chamber and a mechanical chopper which is

used only during time-of-flight measurements. After inter-

secting the target beam, the metastable beam may be inter-

cepted by a movable beam flag or allowed to pass on to the

metastable atom detector, a magnetic electron multiplier.

Fluorescent light produced in the interaction zone, the

region where the metastable and target beams collide, is

detected by photon counting techniques. After being collected

and focused, the photons pass through a monochromator which

only transmits those photons in a selected wavelength range.

Finally, the photons reach the cathode of a photomultiplier;

the pulses from which are amplified and then counted by a

dual channel photon counter. Signal averaging is accomplished

by synchronizing the counter gates with the target beam

modulation frequency.

The various components of the apparatus are described in

detail in the following sections.

B. Gas Inlet Manifolds and Vacuum Chambers

A schematic drawing of the gas inlet manifold used for

delivering gas to the nozzle in the metastable chamber is

shown in Figure 3. Prior to its use in an experiment the

metastable gas inlet manifold is evacuated by a roughing pump

to a pressure of 50 microns or lower as read on a Pirani


The argon used is manufactured by Airco Industrial Gases

of Murray Hill, New Jersey, and is rated at better than 99.995

% purity. After leaving the storage cylinder, the argon passes

through valve 1, the argon regulator shutoff valve, and valve

2, a solenoid valve used to mechanically stop the argon flow
into the metastable chamber in case of power failure. The

argon then passes through a coiled copper tubing trap cooled

to dry ice acetone temperature. This trap removes any con-

densable impurities from the argon which might contaminate

the filament or attenuate the metastable beam. After passing

through shutoff valve 4, the argon goes through a leak valve

which serves both to regulate the amount of gas flowing through

the nozzle and to reduce the pressure of the gas coming from

the argon tank.22 The pressure behind the orifice in the
nozzle cap is then read off an absolute pressure gauge.

Finally, the argon passes through shutoff valve 7 and a 7

micron mesh filter before going into the nozzle.24 The filter

removes any small particles which might clog the small nozzle

opening. During normal operation valves 3, 5 and 6, a pump-

out valve, are closed.


Wallace and
Tiernan Guage


Pirani Guage



Figure 3. Metastable Chamber Gas Inlet Manifold

A schematic drawing of the target gas manifold is shown

in Figure 4. Features of this manifold assembly such as the

filter, the leak valves and the gas cylinders are identical

to that of the metastable gas manifold. Again, the initial

pumpout procedure involves evacuating the gas lines by a

roughing pump to a pressure of 50 microns or lower as read on

a thermocouple gauge. 2526a All of the numbered valves ex-

cept 2 and 5, the solenoid valves designed to stop the gas

flows in case of power failure, are shutoff valves. During

normal operation with a seeded beam valves 1, 2, 5, 6, 7, 8

and 10 are open. The leak valves are adjusted to give the

desired backing pressure, as read on an absolute pressure

gauge, behind the nozzle orifice and also to give the desired
flow rates of seeded (N2) and seeding (He or Ar) gases.

The flow rates are monitored with mass flowmeters located

just before each leak valve.27 Seeding conditions from day

to day can be reproduced by reproducing mass flowmeter read-


All three differentially pumped chambers are evacuated

by oil diffusion pumps backed by roughing pumps. Six-inch

oil diffusion pumps with Mexican hat cold caps are used in both

the target gas and metastable chambers.28a Additionally,

there is a water-cooled baffle between the diffusion pump and

the metastable chamber to prevent diffusion pump oil from

getting inside and contaminating the filament used for meta-

stable atom production.28b The voltage to both six-inch

diffusion pump heaters can be varied between 0 and 240 volts

Wallace and Tiernan

Figure 4. Target Chamber Gas Inlet Manifold


using adjustable A. C. autotransformers. 29 These were in-

stalled to prolong heater lifetime by reducing the A. C.

voltage input and thereby the heater current. It was found

experimentally that the heater voltage could be reduced to

200 volts without any loss of pumping speed by the diffusion

pumps. The main chamber has a ten-inch oil diffusion pump

and a freon-refrigerated baffle.26b,30 Because of the high

pumping speed requirement for nozzle beams, sizable roughing
pumps are used on all three chambers. The foreline pres-

sures of all three chambers are monitored by thermocouple

gauges, and the chamber pressures are monitored by ionization

gauges. 3233 Typical static chamber pressures are given


Metastable chamber: 1 x 10-6 torr

Target gas chamber: 1 x 10-7 torr

Main chamber: 1 x 10-6 torr

C. Metastable Beam Production and Analysis

In this study metastable argon atoms are produced in

a glow discharge which is initiated and sustained by an elec-

tron gun between the nozzle and the skimmer. This configu-

ration is shown in Figure 5.

The nozzle used here is made in two pieces, the body

and the cap. The body is a brass cylinder 3 inches long and

0.625 inches in diameter with a 0.0625 inch hole drilled

through its center to accommodate the argon flow. Also, the

i ,,-I



body is made in such a way that there is a cylindrical cooling

channel between the outside wall and the inside flow tube.

In certain experiments when it is necessary to cool the nozzle,

cold air is forced through the cooling channel. The air is

cooled by passage through a coil of copper tubing immersed in

a dry ice acetone bath. The nozzle cap is a truncated cone

made of Inconel. Inserted in the end of the cap is a 3 mm

0. D. molybdenum wafer with a 0.002 inch diameter hole in its

center. An Iron-Constantan thermocouple used for measuring

nozzle temperature is inserted into a small hole drilled in

the side of the nozzle cap. The thermocouple output is fed

to a temperature controller which gives a direct readout of

nozzle temperature.35a

The skimmer, a hollow brass cone with a 0.040 inch

diameter opening in the tip, is screw mounted to the meta-

stable chamber wall. It removes unused gas from the axis of

the beam and also defines the beam path.

A stainless steel rod attached to the rear of the nozzle

is coupled through the vacuum chamber wall to a micrometer

screw mechanism on the outside of the apparatus which gives

a direct reading of the nozzle cap to skimmer distance. The

nozzle is connected to the argon inlet line by a flexible

stainless steel tube. Likewise, flexible stainless steel

tubes are used to connect the inlet and outlet of the cooling

channel to the inlet and outlet for the cold air flow. By

using this type of tubing as connectors, the nozzle skimmer

distance can be adjusted. It was determined experimentally

that a nozzle skimmer distance of 0.420 inches gave the

greatest mecastable intensity as measured by the magnetic

electron multiplier.

The electron gun used in these experiments for metastable

atom production is shown in more detail in Figure 6. It is

a very simple design consisting basically of only a heated

filament and a grid. The filament is heated by a low voltage,

high current power supply.36 The electrons "boiled off" are

repelled from the filament due to its -10 V potential, supplied

by a separate power supply, and attracted toward the grid due

to its +65 V potential, supplied by still another power

supply.37'38 The path of the electrons crosses the path of

the argon beam at an angle of 900. These electrons initiate

and sustain a glow discharge directly across the path of the

argon. Metastable argon atoms are formed in the glow dis-

charge and exit the metastable chamber through the skimmer.

The filament and its supports are spot welded together.

Nickel tabs bent at a 90 angle are spot welded directly to

high current headers in the filament block assembly. The

filament,.a piece of iridium ribbon about one inch long, is

then sandwiched between and spot welded to the nickel tabs.

The shield, a small rectangular piece of nickel sheet, pro-

tects the high current headers from the heat generated by

the filament. After the filament assembly is spot welded

together, the filament is cataphoretically coated with thoria.

The grid consists of a 0.050 inch nickel wire frame to

Nozzle Cap

Figure 6. Electron Gun

+65 V

-10 V

-10 V


which 0.003 inch nickel wires have been spot welded.

After the metastable argon beam leaves the metastable

chamber through the skimmer, it passes directly between a

pair of deflector plates, one of which is at ground potential

and the other at +300 V. This effectively removes any ions

or electrons from the metastable argon beam. The beam is

further defined by passing through a 0.079 inch diameter col-

limating hole in the main chamber.

The beam then arrives at a mechanical chopper assembly.

During the photon counting portion of an experiment the chopper

is open and not in use. It is rotated at a speed of 50 hertz

and is used only when a time-of-flight velocity analysis is

carried out on the beam. A schematic drawing of the chopper

is given in Figure 7. It is similar to the target gas chopper;

and a detailed description of the circuitry, instrumentation

and procedure used for measuring the velocity distribution

is given in the next chapter. The two analyses are identical

except for the fact that the metastable atom detector is

a magnetic electron multiplier, while the target gas detector

is a quadrupole mass spectrometer.

Each revolution of the chopper allows two sets of two

beam pulses to pass, one short set and one long set. Also,

simultaneously with each beam pulse that is passed an elec-

trical signal is produced by a photocell located 180* away

from the beam position. The short beam pulses, produced by

the narrow 0.010 inch slot, are used in the time-of-flight

analysis of the beam. The long beam pulses (5.0 msec wide)

are not used.








After passing through the intersection zone, the meta-

stable beam arrives at a magnetic electron multiplier shown

in Figure 8. This electron multiplier serves two purposes;

First, when the chopper is rotating, a velocity analysis

can be carried out on the metastable beam; and second, when

the chopper is open and not rotating during the photon count-

ing portion of an experiment, it allows the metastable beam

intensity to be monitored. The output current from the elec-

tron multiplier is measured by an electrometer using a 1 meg-

ohm input resistor.40 This current is proportional to the

metastable atom flux and is monitored continuously on a

digital voltmeter and chart recorder during an experiment.41,42

D. Target Beam Production and Analysis

A schematic drawing of the components which form the

target beam nozzle is shown in Figure 9. The nozzle is made

entirely of Inconel and is screw mounted together. The center

of the nozzle has a 0.002 inch hole drilled in it which serves

as the nozzle opening. As in the metastable chamber, the

rear end of the nozzle has an Inconel rod attached to it which

is coupled through the chamber wall to a micrometer dial out-

side the apparatus. The distance read on the micrometer dial

is the distance between the nozzle cap and the tip of the

skimmer. The skimmer used here is identical to the one used

in the metastable chamber. The oven is connected to the

target gas inlet by a flexible copper tube. This allows the






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nozzle skimmer distance to be changed for optimization of

target beam intensity, and it was determined experimentally

that a nozzle skimmer distance of 0.400 inches gave the

greatest fluorescent light intensity.

The heater is a long strand of tantalum wire strung

back and forth from one end to the other of the oven through

three alumina insulators. The alumina insulators are mounted

in the oven 1200 away from one another. The power supply

used to heat the tantalum wire is an A. C. autotransformer

coupled to a high current filament transformer. With this

supply the nozzle can easily be heated to 400C. The tem-

perature is measured by a Chromel-Alumel thermocouple and

read directly from a temperature controller.5b

By heating, the velocity of the target beam can be greatly

increased from its room temperature value. The relationship

between beam energy and oven temperature in the limit of com-
plete expansion is given below:43

Ez = C T (1)

Here Ez is the translational energy directed along the beam

axis, Cp is the specific heat of the beam gas at constant

pressure, and T is the oven temperature.

The velocity of the target gas can also be increased by

seeding; that is, mixing the target gas with a lighter one.

The light gas, He, accelerates the heavy N2 gas molecules to

higher velocities.44 For high gas densities the velocity of

both components of the gas will be the same; however, the

two components have different masses and therefore different

translational energies. The energy of a molecule of compo-

nent i is given by

E. C T (2)

where Mi is the molecular weight of component i, M is the

average molecular weight and C is the average molar heat

capacity. It should be noted that the seeding technique can

also be used with a gas heavier than the target gas, i.e.,

reverse seeding. Reverse seeding using argon reduces the

translational energy of the target gas.

The following expression has been derived by Anderson

and Fenn for relative beam density as a function of relative

flight time:45

S -= exp{-I M2[( 1)2 (b 1)2]} (3)
max T

b = [11 + (1 + 16 )-

where S/Smax is the ratio of the beam density at a particular

flight time to the maximum beam density, T is the ratio of the

time-of-flight to the time-of-flight for which S is a maximum,

y is the specific heat ratio C p/C and Ms is the Mach number

at the skimmer entrance. The Mach number is defined as the

ratio of the stream velocity u along the beam axis to the local

speed of sound in the gas: M = u/&kT/m)2. Using equation

(3) the Mach number which best characterizes the nozzle beam

may be estimated by comparison with the experimentally deter-

mined velocity distribution. In previous work it was found

that a Mach number of 10 best described the nozzle velocity

distribution.18 The same result should hold true for the

metastable nozzle because of its similar design.

The target beam enters the main chamber through the

skimmer and is further defined by a 0.079 inch diameter col-

limating hole. The beam then encounters the same type of

chopper assembly (Figure 7) as the one used with the metastable

beam. The chopper is powered by a synchronous hysteresis

motor which is driven by an amplified oscillator signal.46,47

During an experiment the chopper rotates at a speed of 50

hertz and therefore modulates the target beam at a frequency

of 100 hertz. The beam modulation permits both a velocity

analysis to be carried out on the target beam and signal

averaging to be conducted with the photon flux.

As with the metastable beam each revolution of the

chopper produces 2 long and 2 short pulses. The photocell

produces an accompanying electrical pulse for each beam pulse.

The short beam pulses travel across the main chamber to the

target beam detector where they are velocity analyzed. The

long beam pulses contain the molecules that produce the pho-

ton signal. After traveling through the interaction zone,

the target beam molecules reach the target beam detector, a

quadrupole mass spectrometer, which is shown schematically

in Figure 10.48a- A 0.070 inch slit further collimates the

beam before it enters the ionizer. Ionization of the beam

is accomplished by electron impact. The ions are then swept

into the quadrupole and mass analyzed to separate the target






(.D -4



M 0
a H

and seeding gases. The quadrupole is set at mass 28 (N2)

for these studies. An electron multiplier provides the cur-

rent output signal from the quadrupole.48b This current

signal is converted to a voltage signal by the beam pulse

amplifier, a specially designed 2 stage amplifier.49

The pulses from the photocell provide both a trigger

signal for the photon counter and a zero-time reference signal

for the beam velocity analysis. The alternating long and

short photocell pulses are first shaped into square waves by

a Schnitt trigger circuit and then separated into separate

trains of long and short pulses by a pulse separator.50,51

The time relationship between the photocell pulses and the

beam pulses is shown in Figure 11.

The output of the first stage of the beam pulse amplifier

is fed into a lock-in amplifier whose reference signal is

the train of long optical pulses. 52a The output of the lock-

in amplifier is read directly from a digital voltmeter and

is proportional to the target beam intensity. The output

of the second stage of the beam pulse amplifier is fed into

a waveform eductor which is triggered by the short optical

signal, the zero-time signal.52b The eductor scans and

signal averages an adjustable time segment of the beam signal,

that segment which corresponds to the short beam pulse. Both

the short optical signal and the waveform eductor output are
displayed on a dual beam oscilloscope. The time between

the rise of the short optical signal and the maximum of the

time-of-flight peak from the eductor gives the flight time


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of the target beam. It was determined experimentally that

each beam pulse was delayed 6 psec in traveling through the

beam pulse amplifier; therefore, 6 psec was subtracted from

each flight time measured before a velocity calculation was

carried out.

The short optical signal may also be fed into a crystal

clock timer which provides an output pulse at a known adjust-

able delay time after the rise of the short optical signal.55

This timer pulse, which rises at a known preset time after

zero-time, can then be fed into the oscilloscope instead of

the short optical pulse. The time between the timer pulse

and the maximum of the time-of-flight peak can then be meas-

ured on the scope on a faster time scale. This yields a more

accurate flight time determination.

E. Photon Collection and Detection

The fluorescent light emitted in the interaction zone

is collected and focused by a concave mirror lens system

onto the entrance slit of a monochromator. Light exiting the

monochromator is focused by another lens onto the cathode of

a photomultiplier. This arrangement is shown in Figure 12.

In order to double light collection efficiency a concave

mirror is located below the plane of the molecular beams at

a distance equal to its radius of curvature (20.0 mm).

A biconvex lens, lens 1, is located above the plane of the

molecular beams at a distance equal to its focal length (25










Figure 12. Photon Collection and Analysis

mm).56b Photons collected by this lens are directed upward

with parallel paths. The photons are focused by another bi-

convex lens, lens 2, through a quartz window onto the entrance

slit of a monochromator which selects the desired wavelength

of light to be studied.56c,57 The concave mirror and lenses

1 and 2 are mounted inside an aluminum tube (3 inches in

diameter) which is fastened to the lid of the main chamber.

The monochromator utilizes a 1200 groove/mm grating with

a 5000 A blaze. The entrance and exit slits are removable

and come in a variety of 5 different sizes corresponding to

bandpasses of 10, 20, 50, 100 and 200 A. The wavelength

range of the monochromator is 1750 to 10000 A with wavelength

readings accurate to 10 A.

Light leaving the exit slit of the monochromator strikes

the cathode of a photomultiplier.58 The monochromator and

photomultiplier are located under the black plastic covering

on the lid of the main chamber in Figure 1. The photomulti-

plier is cooled to -25C by a thermoelectric refrigerator to

reduce the dark noise.59 Under these conditions with a bias

potential of 1250 V on the photomultiplier the dark noise is

reduced to about 12 counts sec When photon measurements

are not being made, a manual shutter just below the photomulti-

plier can be closed sealing it off from incoming radiation.

The wavelength response of the photon detection system

has been discussed previously by Sanders.18

Pulses from the photomultiplier provide input to a linear

amplifier and are counted by a digital synchronous computer.61

This photon counter operates in the "chop" mode and stores

counts in two different channels, A and B. A gating signal

derived from the long optical pulses from the target beam

chopper is used to determine which channel receives counts at

any particular time. The long optical pulse is fed into a

pulse generator operated in the pulse delay mode.54b The

pulse generator produces a 5 msec square wave just exactly

like the long optical pulse except that it is delayed by

200 psec. This is more than sufficient time for the N2 to

travel from the chopper to the interaction zone, about 2.2

inches, and fluorescence to begin. The delayed pulse is used

as the gating signal for the photon counter. The rise of

this pulse opens channel A of the counter, and counts are fed

into this channel for a time preset on the rear of the counter

- 4 msec in these experiments. These counts correspond to

fluorescent emission counts plus background counts, since

during the 4 msec interval the 5 msec target beam pulse is in

the interaction zone. Channel A is then closed, and the next

1 msec is dead time. The fall of the delayed pulse opens

channel B, and for the same preset time, counts are stored

in this channel. These counts correspond to background counts

only, for channel B is opened 200 Vsec after the target beam

chopper closes, and all of the N2 target beam pulse has already

left the interaction zone. The only fluorescence that is

taking place is that due to the N2 background gas, and this

is constant whether the N2 pulse is present or absent. Channel

B is then closed after the same preset time of 4 msec, and

the next 1 msec is again dead time. This long dead time was

chosen because it makes timing errors (such as slight varia-

tions in the chopper frequency) insignificant. The cycle

starts all over again with the rise of the next delayed pulse,

and the process is repeated for the number of cycles preset

on a front panel control. The difference between the number

of counts in channels A and B is the number of counts due to

fluorescent emission from beam molecules only.

F. Data Output

The outputs of the electrometer used to monitor the meta-

stable beam intensity and the lock-in amplifier used in time-

of-flight determinations are displayed on two digital volt-

meters.62a Also, the outputs of the two mass flowmeters which

give the flow rates of the target and seeding gases are dis-

played on digital voltmeters.63 The contents of these four

voltmeters are fed to a teletype through a special inter-


When the number of cycles preset on the photon counter

has been reached, the contents of channels A and B, their sum

and their difference is printed on the teletype. On the next

line the values of the four voltmeters are printed. The

whole process automatically starts again, unless the inter-

face is in the manual mode. In this case data collection

stops until manually restarted.

G. Cryopump Assembly

Preliminary experiments were conducted to determine what

the background count rates were at the wavelengths to be

studied in this work. In these experiments the target beam

was not used; only the metastable argon beam passed through

the interaction zone. The wavelengths corresponding to two

vibrational bands in the C B transition of N2 were observed.

These were the v' = 0 to v" = 0 band the the v' = 1 to v" = 0

band corresponding to wavelengths of 3346 A and 3135 A, re-

spectively. In order to measure the intensity of the entire

band, slits allowing a 100 A bandpass were used in the mono-

chromator. With no nitrogen flowing through the interaction
zone, the normal background count rate of about 12 counts sec

should be observed if no other reactions were producing any

fluorescent light at these wavelengths. At 3346 A the back-
ground was measured to be the expected value of 12 counts sec

However, at 3135 A the background count rate was approximately

350 counts sec-1, nearly 30 times higher than expected.

From this it was concluded that some other reaction pro-

ducing fluorescent light at or near this wavelength must be

occurring. Using the quadrupole mass spectrometer, it was

observed that the only other gas in the main chamber besides

argon was water vapor, mass 18, which adsorbs strongly to the

chamber walls. Therefore, the metastable argon must be react-

ing with water vapor to produce the light,


The spectrum of the light radiation from a pulsed dis-

charge in argon with a small water vapor impurity has been

investigated by Bertschinger et al.65 A long lived band spec-

trum around 3090 A was found which could not be attributed to

known transitions in argon or Ar2. It was concluded that the

following reactions were taking place:

Ar(3P2) + H20 Ar + H + OH(A2 +)

OH(A2+) + OH(X2H) + hv(3090 A)

Metastable argon transfers electronic energy to an H20 mole-

cule, dissociating it and forming an electronically excited

OH radical. The OH radical decays radiatively to its ground

state producing light around 3090 A. This same process sees

to be occurring in the interaction zone.

A background intensity this high would reduce the signal-

to-noise ratio and give less accurate experimental data. To

reduce the background intensity at this wavelength a cryopump

was installed. It is shown in Figure 13. Basically, it is

a sealed stainless steel can, 5 5/8 inches in diameter and

5 inches long. Four-inch copper fins were strapped around

the body of the can to increase the cooled surface area. A

sidearm going into the can is welded to a stainless steel

flange on the outside of the apparatus. The can is filled

with liquid nitrogen through the sidearm which also serves

as a vent for gaseous nitrogen. The cryopump filled with

liquid nitrogen effectively reduces the partial pressure of

water vapor in the main chamber. The background counts at

3135 A are reduced from 350 to 50 counts sec-I which is an

acceptable value for the experiments done in this work.


Prior to the start of any experiment the three vacuum

chambers and both gas inlet manifolds are evacuated to pres-

sures at least as low as those mentioned in Chapter II B.

This can be done overnight. Also, all electronic equipment

to be used in an experiment is turned on during the initial

pumpdown and allowed to warm up overnight.

After pumpdown, the gas flows into both the metastable

and target gas chambers can be started. The regulators on

the gas cylinders to be used in the experiment are adjusted

to a value of 20 PSIG.

The argon flow rate into the metastable chamber is ad-

justed using the leak valve shown in Figure 3 so that the

metastable chamber pressure as read on the ionization gauge

is in the range 4 6 x 104 torr. This pressure range gives

a glow discharge with the greatest stability. Once started

the argon flow takes about 4 hours to come to equilibrium.

After pumpdown, the target gas flow should also be started.

For an unseeded beam, only N2 is fed into the target gas man-

ifold. For a seeded beam, N2 and the seeding gas, either He

or Ar, are used. Flow rates for the N2 and seeding gas are

adjusted individually using the leak valves shown in Figure

4 to values which give the appropriate gas mixture for the

desired N2 velocity. It should be mentioned that at times

these valves are very sensitive, and small changes in their

settings can lead to large changes in the gas flow rates.

Each time a valve setting is changed, the gas flows and there-

fore, the N2 velocity may take up to 8 hours to equilibrate.

In any event, an experiment should not be started for at

least 8 hours after the gas flows have been set. A typical

backing pressure behind either nozzle opening is about 20


During some experiments the target beam nozzle is heated.

If so, the A. C. heater is turned on after the gas flows are

started; and the temperature of the nozzle is allowed to

come to equilibrium during the same 8 hour period as for the

gas flow. The nozzle temperature desired is set by applying

the appropriate potential difference across the heater ter-

minals and is monitored by a thermocouple connected to a

temperature controller. These voltage values were determined

experimentally and are listed in Table 1. These values depend

to some extent on the gas mixture used in the nozzle. The

values listed in Table 1 are for pure N2.

At the beginning of each experiment the cryopump is filled

with liquid nitrogen, and the probe of the liquid nitrogen

indicator is inserted into the cryopump. This indicator is

connected to a buzzer which is energized whenever the liquid

nitrogen in the cryopump falls below a certain level. Usually,

the cryopump has to be refilled every 3 hours.

With the argon flow equilibrated, the glow discharge is


Table 1

Heater Voltage Values
For Certain Target Nozzle Temperatures

Heater Voltage (V) Nozzle Temperature (OC)

2 100

9 200

17 292

23 350

30 400

started by gradually increasing the current going through the

filament in the electron gun. The filament current is slowly

increased in 1 amp steps with a 2 minute waiting period be-

tween each increase. The filament is biased at -10 V (anode

voltage) with respect to ground, and the grid at +65 V with

respect to ground. However, it was found that the glow dis-

charge started much more easily if the anode voltage were

initially set at -50 V. After the glow discharge starts, the

anode voltage is then reduced to the -10 V value. The fila-

ment current is increased to a value which gives an emission

current of about 75 milliamps and a corresponding grid current

of about 70 milliamps. These currents are monitored on analog

type milliammeters.67 The above current values were chosen

because they gave very adequate metastable intensities which

were much more stable than with higher emission current values.

The metastables are detected by a magnetic electron

multiplier; the current output of which is measured by an

electrometer and recorded on a chart recorder. The metastable

intensity takes 3 4 hours after start up to settle down to

a constant value. After the metastable intensity has stabi-

lized, the photon counting part of the experiment can begin.

For the lower relative energy measurements between meta-

stable argon and N2 it was necessary to cool the metastable

nozzle. This was accomplished by forcing cold air through a

hollow cylindrical jacket surrounding the nozzle (see Figure

5). The air used for cooling contains water vapor which has

to be trapped out prior to entering the copper cooling coil

which is immersed in a dry-ice acetone bath. Otherwise, the

cooling coil would soon become blocked by ice. The water

vapor is condensed out before it enters the cooling coil by

running the air through two glass traps in series which are

also immersed in dry ice acetone baths. From the cooling

coil the air goes directly to the nozzle jacket and back out

of the metastable chamber through a vent. The temperature

to which the nozzle is cooled can be adjusted by changing

the flow rate. The nozzle temperature is monitored using

a thermocouple connected to a temperature controller. Although

the controller was set up to read temperatures only in the

range 0 200C, by reversing the thermocouple input leads

and recalibrating the instrument, temperatures to -100C

could be measured. It was found that the metastable nozzle

could be cooled as low as -36C. After the cool air flow is

started, it takes about 2 hours for the nozzle temperature

to come to equilibrium.

Just prior to the photon counting portion of the experi-

ment time-of-flight measurements are carried out on the meta-

stable argon and the N2 beams as described in Chapter II C

and II D. The shutter between the monochromator and the photo-

multiplier is then opened, and photon counting begins. Only

2 bands of C state to B state emission from N2 were studied,

the v' = 0 to v" = 0 band and the v' = 1 to v" = 0 band.

In one series of experiments slits allowing a 10 A band-

pass were placed in the monochromator, and band profile meas-

urements were carried out on the (0 0) band at different

relative energies of N2 and metastable argon. The wavelength

range for the profile measurements was from 3310 A to 3375 A.

Intensity limitations prevented a profile study of the

(1 0) band.

In the other series of experiments conducted, slits

allowing a 100 A bandpass were used in the monochromator to

measure total photon intensities from the (0 0) and (1 0)

bands. In these experiments light from the entire band had

to be collected. Therefore, the monochromator was not set

at the band heads which are 3370 A for the (0 0) band and

3158 A for the (1 0) band; but rather at lower wavelengths

in each band which were determined experimentally to give

the largest photon signal.68 The experimental wavelength

settings are 3346 A for the (0 0) band and 3135 A for the

(1 0) band. Data points were taken alternately in sets of

3 for each wavelength until at least 15 data points for each

wavelength were obtained.

The photomultiplier shutter is then closed, and time-of-

flight measurements are again taken for both beams. This is

done as a check to make sure relative energy conditions of

the two beams have not changed. No changes greater than 1%

were ever noticed.

At the end of each experiment the remaining liquid nitro-

gen in the cryopump is blown out using compressed air, and

the cryopump is evacuated overnight using a roughing pump to

remove any water remaining inside.25 If this were not done,

water in the bottom of the cryopump would seep in between the


bottom and side of the stainless steel can and might crack

the bottom weld of the cryopump when frozen by liquid nitro-

gen in the next experiment.


A. Metastable Beam

The dimensions associated with the metastable argon beam

are listed in Table 2.

A preliminary experiment was done in this study to deter-

mine the metastable atom intensity. In this experiment a

Faraday cup was placed in the beam path at a distance of 10.25

inches from the skimmer orifice. Metastable argon atoms collide

with a gold plated surface on the inside of the Faraday cup,

ejecting electrons. The current produced is measured by an

electrometer and is proportional to the metastable argon atom


The metastable beam intensity can be estimated from

calculations using the following quantities: the secondary

electron current, the secondary electron ejection coefficient

and the beam dimensions. The secondary electron ejection co-

efficient for Ar(3P2,0) on a gold surface is 0.66 electrons/

metastable atom.69

The electrometer signal was measured to be 0.975 V with

a 10 ohm input resistor; therefore, the measured secondary

electron current was 9.75 x 10-10 amp. The number of atoms

detected per second is given by (9.75 x 10-10 amp)(1.6 x 10-19

"Table 2

Metastable Beam Dimensions

A. Orifice diameters and slit dimensions (in.)

Nozzle orifice 0.002
Skimmer orifice 0.040
Collimator orifice 0.079
Magnetic electron multiplier entrance
slit (width) 0.010
Magnetic electron multiplier entrance
slit (height) 0.250

B. Distances (in.)

Nozzle to skimmer 0.42
Skimmer orifice to collimator 3.10
Collimator to chopper 0.10
Chopper to multiplier entrance slit 18.31

coulomb/electron)- (0.66 electron/atom)-1 = 9.2 x 109 atoms

sec-1. The solid angle subtended by the slit of the Faraday

cup is calculated by dividing the slit area by the square

of the skimmer-to-Faraday cup distance, i.e., (0.01 inch )

(10.25 inch)-2 = 9.5 x 10-5 steradians. Therefore, the meta-

stable argon beam intensity is 9.7 x 1013 metastables ste-

radian- sec .-l This intensity is over 100 times greater

than the value obtained by Sanders, 6 x 1011 metastables

steradian-1 sec-1, using an effusive type, D. C. discharge

source with mechanical velocity selection in the same appa-


In another series of preliminary experiments the velocity

of ground state argon atoms was compared to the velocity of

metastable argon atoms in the beam. The velocity of the ground

state argon was measured with the quadrupole mass spectrom-

eter, while the velocity of the metastable argon was measured

with the magnetic electron multiplier. The velocity distribu-

tions of the two turned out to be significantly different,

although both experiments were carried out under the same

beam conditions and at the same temperature. The peak in the

velocity distribution of ground state argon came at 576 meters

sec-1, and the peak of the metastable argon at 637 meters

sec-1, a faster value. No explanation of this difference is

proposed at this time.

Under normal operation the glow discharge heats the meta-

stable nozzle from its room temperature value, about 28C

with the diffusion pumps on, to a value of 43oC. This gives

a metastable argon velocity of 640 meters sec-1. With the

cooling system operating at full capacity under the same beam

conditions the nozzle can be cooled to a value of -360C which

corresponds to a metastable argon velocity of 535 meters sec -

Therefore, by cooling the metastable argon velocity can be

varied from 535 meters sec-1 to 640 meters sec-1. The tem-

perature, and thereby the velocity, is adjusted by changing

the flow rate of cooled air through the nozzle jacket.

B. Target Beam

A characterization of the target beam has been conducted

in detail previously by Sanders.18 Since those studies were

conducted, the only modification of the target nozzle has been

the addition of a heater in the nozzle body. The heater is

described in Chapter II D. Therefore, the only characteriza-

tion studies described in this work have to do with the heat-

ing of the target beam.

The dimensions associated with the target beam are listed

in Table 3.

Using the heater, the nozzle could easily be heated to

4000C. Equation (1) in Chapter II D predicts that the beam

energy, and therefore the beam (velocity) 2, is directly pro-

portional to the nozzle temperature. An experiment was con-

ducted by measuring the N2 beam energy as a function of tem-

perature. The results are shown in Figure 14. The behavior

is linear as predicted.

Table 3

Target Beam Dimensions

A. Orifice diameters and slit dimensions (in.)

Nozzle orifice 0.002
Skimmer orifice 0.040
Collimator orifice 0.079
Ionizer entrance slit (width) 0.070
Ionizer entrance slit (height) 0.250

B. Distances (in.)

Nozzle to skimmer 0.45
Skimmer orifice to collimator 2.80
Collimator to chopper 0.40
Chopper to ionizer slit 21.20












Q 0 0 0 0 0 Oro
(D _t" CJ 0 CO ;f

9- eO


By a combination seeding and heating technique the range

of the N2 beam velocity could be varied from 579 meters

sec- to 2095 meters sec The lowest velocity value for

N2 corresponds to "reverse" seeding the N2 with argon at room

temperature, and the highest velocity corresponds to seeding

the N2 with helium at 4000C.


A. Band Profile Measurements

Band profiles of the N2 C3 u (v' = 0) to B3 v = 0)

band, the (0 0) band, were measured at Ar* N2 relative

energies of 0.074, 0.089 and 0.161 eV. These profiles are

shown in Figures 15 through 17. Slits allowing a 10 A band-

pass were used in the monochromator for these measurements.

The three measurements above were made with an unseeded N2

beam. Higher relative energy measurements with seeded N2

were not possible due to lack of intensity. Also, the N2

C3 u (v' = 1) to B3H1 (v" = 0 ) band, the (1 0) band, was

not intense enough for profile studies.

The emission intensities of the lines of a rotational-

vibrational band, assuming a thermal distribution of rotational

levels, is given by the following:70

2 C 4
em em Sj exp [-BvJ'(J' + 1)hc/kT] (4)

where Cem is a constant depending on the change of dipole

moment and the total number of molecules in the initial vibra-

tional level, Qr is the rotational partition function, v is

the frequency of the emitted light, J' is a rotational level

0 0

C.) J
Z <


Ai!S u-jUl

0 0
0 0
















I I If I






00 (

0 0 0
0 1

C) i
* II 0 > I I

t r00
S o d r o


0 0 0 0 0 0
0 CO C\J 0
- 0 d d d 0
/AjiSU@.ui Ai^DIad



0 0 0
00 -4
o o



0 ro -

0 O >

On 0 O z
1 -4

o o
00 t (D i


0 CO o\j 0
b 0 06

0 0 0 0 0 0
0 co co CoJ 0
- 0 d 0 0 0
4iXsu~u[ OA!i.tDld

in the upper state, B v is the rotational constant of the

upper state vibrational level, Sj is the "line strength,' and

the remaining variables have their standard meaning.

The "line strengths" of a symmetric top molecule have

been derived by Honl and London.71 For the R branch of a

rotational vibrational band in an electronic transition

with AA = 0, Sj is given by the following:

S -R (J' + A')(J' A') (5)

In the case under consideration here, a C311 + B3 transition,

A' = 1. Therefore, SR is given by the following:

SR (J' 1)2 (6)
J J,

Equation (4) can be transformed into the equivalent form:

I B ,J'(J' + l)hc
In( 'm) = A kT(7)

where A = In (2 Cem v4/Qr ) may be' considered a constant since

for a given band v covers only a very small range of values.

Again, assuming a thermal distribution of rotational levels,

a plot of-ln (Iem/SJ) against J'(J' + 1) should give a straight

line of slope -Bv ,hc/kT. Therefore, the "rotational" tem-

perature of the transition can be calculated.
The above calculation was carried out for the three line

profiles measured in this work, and plots of In (Iem/Sj) vs.

J'(J' + 1) are shown in Figures 18 through 20. A least squares

procedure was used to calculate the slope. Rotational tem-

peratures of 1090 and 12800K were calculated for the relative

m 0

I C T)
0 0
0 o

CD 0
0 *

Z 1-'-

0 LO
0 r,-
i I

0 LO

(PSl/) Uj


> 0
0 -0

Oo O -3
o d 0

S0 -0 >
0 z-- Q0


z 0

0 O




0 0 N 00

C~l o '-- 0
LO d y 0
('/ 0d 0

0 0
in to


c 0
~ 0
m 0 co
0 0
S0 >

0 0
C 0 < W* 0

o a
0 .

0 0

o r

0 Lo 0 Lo 00
0 -- Lo Cj 0

energies of 0.089 and 0.161 eV, respectively. At 0.074 eV

the plot was not linear, and therefore a rotational tempera-

ture could not be calculated.

For these calculations the wavelength of rotational-

vibrational transitions of a particular J value in the R

branch were determined from high resolution work done on this

transition by Setser et al.72 Relative intensities at these

wavelengths were then determined using the low resolution

band profiles, and these values were substituted into equation

(7) for Im

B. Branching Ratio Measurements

Data were collected for the (0 0) and (1 0) bands

as described in Chapter III. The signal-averaged photon count

rates were recorded once every 100 sec of counting time.

Typical photon count rates for the (0 0) and (1 0) bands

were about 1000 and 250 counts sec- respectively. These

values were somewhat smaller at the higher relative energies

where a large amount of seeding gas had to be used in the

target gas flow. Measurements were made in the energy range

0.053 0.408 eV.

For a particular relative energy the average photon count

rate for each band was calculated by a minicomputer.73 A

special program was written for the minicomputer for this

purpose. In this program the mean count rate and the standard

deviation of the mean (S. D.//-n, where S. D. is the standard

deviation of the data and n is the number of data) are cal-

culated. The minicomputer rejects any data greater or less

than two standard deviations of the mean from the mean and

recalculates the mean count rate. The mean count rate for

each band is then divided by its appropriate Franck-Condon

factor to give a photon count rate which is proportional to

the vibrational population of either the v' = 1 or v' = 0

level of the N2 C state.74 For example, the (0 0) band

count rate is divided by the v' = 0 to v" = 0 Franck-Condon

factor (0.4527) to give a number which would be the photon

count rate for all transitions from the zeroth vibrational

level of the C state to any vibrational level in the B state,

i.e., a number proportional to the population of the zeroth

vibrational level of the C state. For the (1 0) band a

Franck-Condon factor of 0.3949 was used. Calculation of the

branching ratio (v' = 0)/(v' = 1) follows directly from the

two Franck-Condon corrected photon count rates. The experi-

mental results obtained are shown in Figure 22 (Chapter VI B).

It should be mentioned that the error bars on these

points are no larger than the circles drawn around each point.

This is due to the fact that the Aphoton count rates were 3 -

4 times as great as the background count rates in each meas-



A. Band Profile Measurements

A comparison of the low wavelength tail of the three

band profiles is shown in Figure 21. All three profiles are

normalized to their peak height. As is expected, the higher

relative translational energy measurements show more rotation-

al excitation at the higher J values. The rotational tem-

peratures calculated and their respective relative transla-

tional energies are the following: 0.089 eV 10800K and

0.161 eV 12800K.

If a thermal distribution of rotational levels were

present in all three measurements, the plots of ln (I/S ) vs.

J(J + 1) should all be linear. Looking at the plots of In

(I/Sj) for the three profiles in Figures 18 through 20, it can

be seen that the plots for relative translational energies of

0.089 and 0.161 eV are linear, and a thermal distribution of

rotational levels exists. However, the plot at 0.074 eV is

not linear; therefore, the rotational levels are not distrib-

uted thermally. This may be due to the fact that the threshold

energy for the reaction Ar* + N2(X) Ar + N2(C) is approxi-
mately 0.05 eV as measured by Sanders. Further supportive

evidence for this threshold was found in this work. At the






00 (9 Q \J N
o5 0 0 ci 0

lower relative energy branching ratio measurements a gradual

decrease in photon intensity was observed. The lowest rel-

ative energy line profile (0.074 eV) could be near enough to

the threshold that the rotational distribution of levels is

affected in some way.

B. Branching Ratio Measurements

A reaction dynamics model which predicts product vibronic

state distributions in collision-induced electronic-to-vi-

brational energy transfer processes has been proposed by

Berry.75 In this model the interaction which leads to elec-

tronic energy transfer is treated by perturbation theory.76,77

For a perturbation V which is independent of time the relative

transition probabilities Wif for formation of final product

states can be calculated directly by a first order treatment

of the Fermi Golden Rule:75

Wif = (27/h)112pf(E) (8)

where pf(E) is the density-of-final-states function and e is

the mean available energy for the vibrational state in question.

In these studies i refers to the zeroth vibrational level of

the N2 X state, and f refers to either the zeroth or first

vibrational level in the N2 C state. Assuming the energy

transfer from metastable argon to the N2 molecule occurs very

suddenly, the matrix elements in equation (8) become Franck-

Condon factors for the initial and final oscillator states:75

Ii2 a il2 (9)

The density-of-final-states function pf(E) used by Berry

assumes a vibrating rotator model for N2 and was derived by

Ben-Shaul et al. for the atom + diatom case to be the follow-


p (E) a (1 f ,)3/2 / (1 fv,)3/2 (10)
where f is the fraction of mean available energy E channeled

into vibration in a particular product vibrational state


The present study is only concerned with the N2 C state

population ratio (v' = 0)/(v' = 1). This ratio can be cal-

culated from the ratio of the relative transition probabil-


Wo l<0c0x>I po(
W = <0c i 2 ) (11)

71 clOx> >I pl(e)

Since f0 in p0 (E) is zero, the above expression reduces to

the following:

1W = 1.792 (1 f 3 (12)

where the Franck-Condon factors used are those calculated by

Benesch et al. and f1 is the fraction of mean available energy

going into vibrational state 1.79 f1 is calculated from the


f E(C,v' = 1) E(C,v' = 0) (13)
R.K.E. + EAr* E(X,v" = 0 C,v' = 0)

where R.K.E. represents the relative kinetic energy of the

Ar* N2 and the electronic and vibrational spacings were

obtained from Benesch et al.80 The statistical average meta-

stable energy EAr. was calculated from 3P2,0 energy values

given by Setser et al. assuming both metastable components are

equally reactive and present in a statistical distribution.72

The transition probability ratio W /W1 was calculated

over the R.K.E. range 0 0.40 eV and is plotted against R.K.E.

along with the experimentally determined branching ratio in

Figure 22. The Golden Rule model fits the data reasonably

well at the lower energy values; however, the fit is poor at

the higher energy values. Also, the two curves do not have

the same shape. The curves suggest that the standard Franck-

Condon controlled excitation process from the N2 X state to

the N2 C state does not play a major role in the energy trans-

fer at the higher energy values. These findings agree with

the work of Stedman and Setser concerning the dynamics of
reactions of metastable rare gas atoms. Their generaliza-

tion that "neutral excitation is not expected to follow Franck-

Condon excitation" is correct for the Ar* N2 system at the

higher relative energy values.81

As a qualitative explanation of the branching ratio vs.

R.K.E. curve, consider the following model. During the Ar* -

N2 collision the wavefunction of the N2 X state is perturbed.

The perturbed wavefunction describes an N2 molecule with a

weakened N N bond; the amount of weakening depending on the

turning point in the collision and hence on the R.K.E. There-

fore, the higher the R.K.E. the larger re is for the per-

turbed wavefunction.

0 0

o C

-i t

0 0
Q LO -
o 0- 0

0 0
00 4

o 0
0 0 o &
0d --

roto C i

(l=0A/O=IA) 04M
0 0 r

/ 0 I

to 0 t0o 0 t0

Now consider the energy level diagrams given in Figure

23. The shape of the harmonic oscillator wave functions for

the zeroth vibrational level of the X state and the zeroth

and first vibrational levels of the C state are shown. The

minima of both electronic states are shown at their standard

r values, and both are referenced to zero potential energy.

In the above proposed model the re value is assumed to in-

crease with increasing R.K.E. As re starts to increase the

overlap, and therefore the transition probability, between

the C state first vibrational level wave function and the X

state zeroth vibrational level wave function, the (1 0)

overlap, reaches its maximum value, while the (0 0) over-

lap is still slowly increasing. Therefore, the branching

ratio would decrease at first. As re increases further, the

(0 0) overlap reaches its maximum value, and the (1 0)

overlap its minimum value causing the branching ratio to in-

crease. And finally, the (0 0) overlap begins decreasing

again, and the (1 0) overlap begins increasing to its

maximum value again causing the branching ratio to go back

down. Although this is only a qualitative explanation for

the change in the branching ratio, it does seem to explain

the general shape of the curve.


5000 -N2(C,( )


c 0


0.90 1.00 1.10 1.20 1.30 1.40

re (A)
Figure 23. N2 Potential Energy Diagram


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Euel Ray Cutshall was born March 31, 1950, in Sheffield,

Alabama. He graduated from Coffee High School in Florence,

Alabama,in 1967. He entered the University of North Alabama

in 1967 and graduated with a Bachelor of Arts degree in both

Chemistry and Mathematics in 1972. After serving a three

month tour of duty for training purposes in the U. S. Army,

he entered the Graduate School at the University of Florida.

From 1973 to present he has pursued studies in Chemistry

leading to the degree of Doctor of Philosophy.

He is married to the former Linda Washburn, who received

her Bachelor of Arts degree in Early Childhood Education from

the University of Florida in 1976, and has a young son,


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.

E. E. Muscle itz, Jr. Ch Trman
Professor!/f Chemistry

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.

7 E C / C it u_-
Charles P. Luehr
Associate Professor of Mathematics

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.

Willis B. Person
Professor of Chemistry

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.

Thcmas L. Bailey
Professor of Physiis

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.

Samuel 0. Colgate/
Associate Professor of Chemistry

This dissertation was submitted to the Graduate Faculty of
the Department of Chemistry in the College of Arts and Sciences
and to the Graduate Council, and was accepted as partial ful-
fillment of the requirements for the degree of Doctor of

June 1977

Dean, Graduate School

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