• TABLE OF CONTENTS
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 Title Page
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Introduction
 Theory
 Description of apparatus
 Experimental results
 Discussion
 Reference
 Appendix
 Biographical sketch
 Copyright














Title: Angular dependence of the scattering of metastable helium atoms in helium and neon.
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Title: Angular dependence of the scattering of metastable helium atoms in helium and neon.
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Table of Contents
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
    List of Tables
        Page iv
        Page v
        Page vi
    List of Figures
        Page vii
    Introduction
        Page 1
        Page 2
        Page 3
    Theory
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
    Description of apparatus
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
    Experimental results
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
    Discussion
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
    Reference
        Page 57
        Page 58
        Page 59
    Appendix
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
    Biographical sketch
        Page 79
        Page 80
    Copyright
        Copyright
Full Text











ANGULAR DEPENDENCE OF THE

SCATTERING OF METASTABLE HELIUM

ATOMS IN HELIUM AND NEON










By
HUBERT LYLE RICHARDS


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
June, 1963















ACKNOWLEDGMENT


The author wishes to express his appreciation to t

members of his supervisory committee and especially to

Dr. E. E. Muschlitz, Jr., chairman of his supervisory committee,

for directing this investigation and for his many helpful

suggestions.

He also wishes to express his appreciation to the

National Science Foundation for the financial assistance that

made this work possible.














TABLE OF CONTENTS


Page


ACKNOWLEDGMENT
LIST OF TABLES
LIST OF FIGURES

Chapter

I INTRODUCTION


II THEORY

III DESCRIPTION OF APPARATUS


EXPERIMENTAL RESULTS


V DISCUSSION

VI SUMMARY

REFERENCES
APPENDIX I ORIGINAL BEAM COMPOSITION DATA
APPENDIX II ORIGINAL SCATTERING DATA
VITA















LIST OF TABLES


DIMENSIONS OF SCATTERING ELEMENTS

SUMMARY OF ANGULAR RESOLUTIONS

SUMMARY FOR HELIUM IN HELIUM

SUMMARY FOR HELIUM IN NEON

CROSS SECTIONS

BEAM COMPOSITION AS A FUNCTION OF SOURCE PRESSURE

BEAM COMPOSITION AS A FUNCTION OF ELECTRON ENERGY
AT 100 x 10-3 mm SOURCE PRESSURE


8. METASTABLE
ANGULAR

9. METASTABLE
ANGULAR

10. METASTABLE
ANGULAR

11. METASTABLE
ANGULAR

12. METASTABLE
ANGULAR

13. METASTABLE
ANGULAR

14. METASTABLE
ANGULAR

15. METASTABLE
ANGULAR


HELIUM IN HELIUM,
RESOLUTION 8053'

HELIUM IN HELIUM,
RESOLUTION 8053'

HELIUM IN HELIUM,
RESOLUTION 8053.'

HELIUM IN HELIUM,
RESOLUTION -6021'

HELIUM IN HELIUM,
RESOLUTION -6021'

HELIUM IN HELIUM,
RESOLUTION -6021'

HELIUM IN HELIUM,
RESOLUTION 50 Ps


30 VOLT ELECTRONS
Ps = 34 x 10-3 mm

35 VOLT ELECTRONS
Ps = 34 x 10-3 mm

45 VOLT ELECTRONS
Ps = 34 x 10-3 mm

30 VOLT ELECTRONS
Ps = 40 x 10-3 mm

35 VOLT ELECTRONS
Ps = 40 x 10-3 mm

45 VOLT ELECTRONS
Ps = 40 x 10-3 mm

30 VOLT ELECTRONS
= 42 x 10-3 mm


HELIUM IN HELIUM, 35 VOLT ELECTRONS
RESOLUTION -50 Ps = 42 x 10-3 mm


16. METASTABLE HELIUM IN HELIUM, 45 VOLT ELECTRONS
ANGULAR RESOLUTION o5 Ps = 42 x 10-3 mm

iv


Table

1.

2.

3.

4.

5.

6.

,7.


Page

18

12

38

39

47

61


62








LIST OF TABLES--Continued


Page


Table


HELIUM IN HELIUM, 30 VOLT ELECTRONS
RESOLUTION 30 Ps = 36 x 10-3 mm

HELIUM IN HELIUM, 35 VOLT ELECTRONS
RESOLUTION -30 Ps = 36 x 10-3 mm

HELIUM IN HELIUM, 45 VOLT ELECTRONS
RESOLUTION -30 Ps = 36 x 10-3 mm


17. METASTABLE
ANGULAR

18. METASTABLE
ANGULAR

19. METASTABLE
ANGULAR

20. METASTABLE
ANGULAR

21. METASTABLE
ANGULAR

22. METASTABLE
ANGULAR

23. METASTABLE
ANGULAR

24. METASTABLE
ANGULAR

25. METASTABLE
ANGULAR

26. -METASTABLE
ANGULAR

27. METASTABLE
ANGULAR

28. METASTABLE
ANGULAR

29. METASTABLE
ANGULAR

30. METASTABLE
ANGULAR

31. METASTABLE
ANGULAR

32. METASTABLE
ANGULAR


30 VOLT ELECTRONS
Pg = 35 x 10-3 mm

35 VOLT ELECTRONS
Ps = 34 x 10-3 mm

45 VOLT ELECTRONS
Ps = 34 x 10-3 mm

VOLT ELECTRONS
Ps = 31 x 10-3 mm

5 VOLT ELECTRONS
Ps = 31 x 10-3 mm

5 VOLT ELECTRONS
Ps = 31 x 10-3 mm

SVOLT ELECTRONS
Ps = 38 x 10-3 mm

5 VOLT ELECTRONS
P, = 38 x 10-3 mm

5 VOLT ELECTRONS
Ps = 38 x 10-3 mm

)VOLT ELECTRONS
s = 37 x 10-3 mm

5 VOLT ELECTRONS
s = 37 x 10-3 mm

5 VOLT ELECTRONS
s = 37 x 10-3 mm


HELIUM IN NEON, 30 VOLT ELECTRONS
RESOLUTION 30 Ps = 44 x 10-3 mm


HELIUM IN HELIUM,
RESOLUTION -1022'

HELIUM IN HELIUM,
RESOLUTION -1022'

HELIUM IN HELIUM,
RESOLUTION 1022'

HELIUM IN NEON, 3C
RESOLUTION -8053'

HELIUM IN NEON, 35
RESOLUTION 8053'

HELIUM IN NEON, 45
RESOLUTION -8053'

HELIUM IN NEON, 3(
RESOLUTION -6021'

HELIUM IN NEON, 3.
RESOLUTION -6021'

HELIUM IN NEON, 4!
RESOLUTION -6021'

HELIUM IN NEON, 3(
RESOLUTION -50 P,

HELIUM IN NEON, 3,
RESOLUTION -50 PE

HELIUM IN NEON, 4!
RESOLUTION -50 PE








LIST OF TABLES--Continued


Table Page

33. METASTABLE HELIUM IN NEON, 35 VOLT ELECTRONb
ANGULAR RESOLUTION 30 Ps = 44 x 10-3 mm 76

34. METASTABLE HELIUM IN NEON, 45 VOLT ELECTRONS
ANGULAR RESOLUTION -30 Ps = 44 x 10-3 mm 76

35. METASTABLE HELIUM IN NEON, 30 VOLT ELECTRONS
ANGULAR RESOLUTION 1022' Ps = 32 x 10-3 mm 77

36. METASTABLE HELIUM IN NEON, 35 VOLT ELECTRONS
ANGULAR RESOLUTION 1022' Ps = 32 x 10-3 mm 77

37. METASTABLE HELIUM IN NEON, 45 VOLT ELECTRONS
ANGULAR RESOLUTION 1022' Ps = 32 x 10-3 mm 78














LIST OF FIGURES


Figure Page

1. Cross Section of Apparatus 15

2. Inhomogeneous Field Magnet 17

3. Schematic Diagram of Apparatus 19

4. Auxiliary Vacuum System 21

5. Experimental Appearance Potential Curves at Two
Source Pressures 24

6. Metastable Beam Intensity Versus Source Pressure. 25

7. Beam Intensity at 30 Volts Versus Magnet Current 28

8. 71101/73103 Versus Electron Energy 29

9. 71101/73103 Versus Source Pressure at Three
Electron Energies 30

10. Log io/iT+ in Helium Versus Pressure for Three
Electron Energies 33

11. Log i0/iT in Neon Versus Pressure for Three
ElectrTn Energies 34

12. 2.303 Slope/L Versus 1/(1 + R) for Metastable
Helium in Helium 35

13. 2.303 Slope/l Versus 1/(1 + R) for Metastable
Helium in Neon 36

14. Corrected Cross Sections Versus Angular Resolution
for Metastable Helium in Helium 40

15. Cross Sections Versus Angular Resolution of
Metastable Helium in Neon 41


vii














CHAPTER I

INTRODUCTION


Experimental procedures in which the generation and

observation of an atomic or molecular beam is an important part

have been applied to a large range of problems. Much of the

work includes studies of gas kinetics, molecular scattering

cross sections in gases, the interaction of molecules with

surfaces, and diffraction of molecular beams. Of particular

interest are the scattering experiments which have proved to be

a much more satisfactory tool for the study of the interactions

of individual particles than experiments in which averaged

properties, such as viscosity and diffusion are measured.

Through the observation of single collisions it is possible

to determine the magnitude and variation with distance of the

intermolecular forces (1,2) that exist between uncharged particles

without relating to bulk property measurements.

Collisions between atoms under gas-kinetic conditions can

be classified as elastic or inelastic depending,whether or not

energy is exchanged between the relative translational motion and

internal motion of either or both colliding systems. If it is

not, then the collision is elastic, otherwise inelastic. For each

type of collision process a collision cross section may be defined

as a measure of the probability of occurrence of the process

1









concerned, and the magnitude of the cross section is governed

by the nature of the forces between the colliding particles.

Collision cross sections have been investigated by

many workers using molecular beam methods. For example, Mais (3)

and others (4,5) studied the scattering of a beam of alkali

metal atoms in mercury and various gases. Knauer (6) studied

the collision cross sections of helium, hydrogen, oxygen, and

water in their parent gases. He also determined the cross

sections of helium and hydrogen in mercury vapor as a function

of temperature, and therefore of the energy of the beam particles

from which the interaction potentials were evaluated. Amdur (7)

and co-workers have used the molecular beam technique to determine

the force law between relatively high velocity atoms and molecules

in the past few years. Quite recently, Amdur, Jordan, and

Colgate (8) have done experiments on the scattering of a helium

beam in helium in the energy range from 150 to 1500 ev from which

intermolecular potentials were determined. In 1958 Smith and

Muschlitz (9) determined total cross sections for collisions of

thermal energy metastable helium atoms in various gases which

included helium and neon. Up to the present there has been no

experimental work on the determination of the energy of interaction

between metastable helium and normal helium. However, Buckingham

and Dalgarno (10) have calculated the interaction potentials of

normal and metastable helium atoms, and found both a maximum and

a minimum in the potential curve.

This dissertation concerns the measurement of collision

cross sections for the scattering of excited helium atoms in








helium and neon as a function of the minimum angular resolution

of the beam apparatus. Some of the helium atoms in gaseous

helium are excited to both the 21S and 23S metastable states.

An atomic beam of the helium atoms is then produced and allowed

to enter a collision chamber in which a gas is introduced at

low pressure (ca. 10-3 mm). The scattering of the metastable

helium atoms in the beam is observed by measuring the electron

current ejected by the excited atoms when they arrive at metal

detector surfaces. Both elastic and inelastic collisions of

the excited atoms take place. Since the method of detection is

insensitive to particles in the ground state, there is no inter-

ference from the normal atoms in the beam. Because of the two

metastable atoms formed, a knowledge of the beam composition is

necessary if one is to determine the individual cross sections.

The beam composition has been determined by passing the beam

Through an inhomogeneous magnetic field.















CHAPTER II

THEORY


Several general references are available on scattering

theory (11,12,13) and on molecular beams (14-17). The first

experimental production of a molecular beam was carried out by

Dunoyer (18) to verify one of the fundamental postulates of

kinetic theory, namely, the rectilinear motion of gas molecules

between collisions. The precise development of the technique

was carried out by Stern and his collaborators (19,20). The

source of an atomic or molecular beam is an enclosure filled

with gas or vapor and provided with a slit through which a

beam of particles effuses. For collision-free rectilinear motion

of molecules in the beam rather than turbulent flow of a hydro-

dynamic nature, the width of the source aperature must be smaller

than the mean free path of the particles in the source.

Metastable atoms are those in which one of the electrons

has been excited to an upper level for which the transition back

to the ground state by electric dipole radiation is forbidden.

In general, L-S coupling holds for light atoms, in which case the

selection rules are:


I AJ = 0, 1 J = 0-o> J = 0

II aS =0

III A. = +1








where J, the total angular momentum, is the vector sum of the

orbital angular momentum, L, and the spin angular momentum, S,

and I is the angular momentum of the electron making the

transition.

The 21S state of helium is metastable with respect to

the llSo ground state because of rules I and III. The 23S state

is metastable because of rules II and III. However, metastable

atoms do have finite lifetimes because decay to the ground state

is possible by processes such as magnetic dipole radiation and

double photon emission. However, the probabilities for these

processes are quite small compared to those for electric dipole

radiation. Breit and Teller (21) have measured the mean life of

the 21S in the absence of collisions to be about 0.14 sec and

stated the lifetime was much shorter than for the 23S. Phelps (22)

has also stated that the 21S helium lifetime is greater than 0.03 sec

and 23S greater than 0.2 sec. These are quite large compared to the

mean lives of the non-metastable excited states which are on the

order of 10-7 to 10-9 sec. For the lifetimes of the metastable atoms

given, the loss of intensity in traversing the distance of the

apparatus at thermal velocities (--105 cm/sec) would be negligible.

If the excitation energy of a metastable atom exceeds the

work function of a metal surface, it is energetically possible for

a collision of the second kind-to occur in which the atom returns

to the ground state and an electron is liberated from the surface

to take up the excess energy. This process was first established

in 1924 by Webb (23) for metastable mercury atoms impinging on a

metal surface. Further studies by Messenger (24), Coulliette (25),








and Sonkin (26) showed that the ejection efficiency depends

critically on the nature of the surface in a complex fashion.

A detailed study of the ejection efficiency of metastable helium

atoms on a molybdenum surface has been made by Oliphant (27).

The 23S metastable state of helium has an excitation energy of

19.82 ev and the 21S state 20.61 ev, and the ejection efficiency

of these metastable atoms incident on a platinum surface was

measured by Dorrestein (28) to be 0.24 and 0.48, respectively.

Stebbings (29) has obtained a value of 0.29 for the ejection

efficiency of 23S helium atoms on a gold surface.

Electron ejection has been discussed by Cobas and Lamb (30)

and by Lamb and Retherford (31) and quite extensively by Hagstrum (32)

for the similar case of ejection of electrons from metals by ions.

The positions of the energy levels in the atom and metal make it

highly probable that a helium metastable atom will be ionized on

approaching a metal surface and will subsequently be neutralized

by an Auger transition. This would mean that the ejection efficiencies

for both metastable states, as well as for the ion, would be equal.

Earlier work by Molnar (33) showed that this was true within

experimental error.

In general, any method of excitation could be used to

excite atoms or molecules to metastable levels. Electron impact

was chosen primarily because the electronic excitation cross section

is large. The energy of an electron beam can also be controlled

relatively easily thereby allowing the excitation of individual

metastable levels if more than one exist.








The excitation functions (the probability of excitation

as function of electron energy) for metastable helium atoms have

been calculated with some success by Massey and Mohr (34) and

Massey and Moiseiwitsch (35). Early experimental measurements

of the electronic excitation functions of 23S state of helium

were made by Woudenberg and Milatz (36) in which the metastable

atoms were detected by the absorption of light of appropriate

energy to induce transition to a higher energy level, namely,

23S to 23P. Maier-Libnitz (37) passed a beam of electrons

of known energy through helium gas and measured the electron

current as a function of its energy. The relative decrease in

electron current with increasing energy was said to be caused

by inelastic collisions of electrons with the helium atoms

resulting in excitation of the metastable levels. Excitation

functions for both 21S and 23S states of helium were determined;

however, the results were only qualitative.

Dorrestein (28) measured the total excitation function for

helium by electron impact. Essentially the same experiment was

performed by Schultz and Fox (38) using a retarding potential

difference method to obtain an electron beam with an energy

spread of 0.1 ev. Frost and Phelps (39) analyzed these data

and were able to obtain separate excitation functions for the

21S and 23S states. These excitation functions, which include

the metastable atoms that result from transitions from higher

levels, could be used to ascertain the beam composition at a

given electron energy.








In 1921, Stern (40) suggested that the molecular beam

method could be used as a test to decide between the classical

and quantum theoretical predictions for the magnetic properties

of atoms and molecules. If a beam of atoms, each with a magnetic

moment, is passed through an inhomogeneous magnetic field, the

direction of the inhomogeneity being essentially parallel to the

field, the angular momentum vector of each atom will process

about this direction and the atom will be deflected by the

magnetic force. The magnitude of the deflection is proportional

to the projection of the moment on the field direction. From

later experiments (41) he and co-workers confirmed the predictions

of the quantum theory that there are only a few possible orientations

of the moment with respect to the field, and consequently there will

be a splitting of the beam into discrete components.

According to theory, every system which has a single

angular momentum vector J (in units of h/2r) has also a magnetic

moment 4 = gJ, where is measured in units of the Bohr magneton

Po = he/4nmc, and g is the gyromagnetic ratio in units of e/2mc.
Here m is mass of the electron. The quantum number J may have

integral or half-integral values. The projection of the angular

momentum J upon the field direction will have 2J + 1 permissable

values. Thus a beam of atoms having a magnetic moment will be

split in a magnetic field into-2J + 1 parts. The J values for the

21S and 23S states of helium are 0 and 1, respectively. The

singlet (21S) state will be unaffected when passing through a

magnetic field but the triplet (23S) will split into three

components, i.e., Mj = 0, 1l. Of these three components, only








those with Mj = l will be deflected. By making use of this

property of the beam it is possible to determine the ratio

71101/73103 where 71 and 73 are the respective electron ejection
efficiencies for the two metastable states, and I01 and 103 are

the intensities of the respective metastable states.

Assuming that the three states, Mj = 0, 1 are equally

populated it is possible to write the following equations for

the total currents detected in the scattering region with the

magnetic field off and on, respectively:


i0 = 7111 + 73103 [II.1]

r 1
i = 71101 + 7313 [II.2]

the difference is

= 2 =2 1 [11.3]
i0-i 7303 I3I.


By dividing equation [II.1] by equation [II.3] we obtain


i0 3 71101 + 73103
io-id- 2 73103 .4


which,if rearranged, gives



71101 2 10
73103 3 io-i- 1 [II.5]


In order to observe the collision cross section for any

process one must be certain that the beam particles do not undergo

multiple collisions. Thus the pressure must be low enough so that








each beam particle interacts at most with only one scattering

particle.

If I is the beam intensity, the decrease in intensity

-dl, as the beam passes through a distance in the scattering

gas, dx, is directly proportional to the intensity, the density

of scattering particles, a measure of which is the pressure,

p, and the cross section for the process under study, a, or

analytically


-dl = Icpdx [II.6]


Integrating from the initial intensity, 10, at x = 0 to intensity,

I, at x =L one obtains


I = I0 e- 1P [II.7]


Since the energy levels of the two metastable states of helium

are so close together, it was possible only to obtain a beam in

which both metastable species were present. The intensities of

the 21S and 23S metastable states follows the equations:


Ii = I01e-olP [II.8]

and

13 = I03e-3LP [II.9]


respectively. The total beam intensity is then the sum of the

intensities of the two states.

As stated previously, the metastable species eject electrons

with an efficiency 71 or 73. The metastable current measured








corresponding to the beam intensity is then:


i = 71101 + 73103 [II.10]

for the initial intensities, and


iT = 7111 + 7313 [II.11]

for the intensities at any point. Substituting relations [II.8]

and [II.9] into [II.11]:


iT+ = 71l01e-l P + 73103e-C3)P [II.12]

and dividing [II.10] by [II.12] one obtains


io 711 01 + 73103
iT+ 71I0le-1- P + 73103e-3 p [.13]


This equation does not allow the ready evaluation of either al

or a3 unless a1 = a3 in which case:


0 eal P eP 3P [11.14]
iT+

Solving for a,

2.303 -
al 3 .- log i- [II.15]


the cross section may then be obtained from the slope of a plot

of log iO/iT+ versus p. This is the total cross section for all

the atoms in one cm3 of gas at 1 mm pressure. The cross section

in cm2 per atom, a, is equal to a/N where N is the number of atoms

per cm3 at 00C and 1 mm pressure, 3.536 x 1016








Taking the logarithm of equation [II.13] and making

the approximation that e-n = 1-n for small n, one gets

i0
In -- = ln(71101 + 73103)
iT+

-ln[71Iol(l-xlt.p) + 73I03(1-a3Jp)] [II.16]

Simplifying

0 L P(al0 01 + a373,03)
n = -n 1 1101 + 3103 [11.17]
1T+ 71101 + 73103

and making the further approximation that In(l-n) = -n for
small n

io 9P(a17101 + a373103)
In --- = [II.18]
IT+ 71101 + 73103

and now dividing the numerator and denominator of the right

side of this equation by 71101 and setting

73103 R
71101

one obtains

i0 P(al + 03R)
in.---- = [II.19]
oT+ 1 + R


It should be noted that R is just the reciprocal of the

quantity in equation [11.5] and can be determined experimentally

instead of having to use separately determined values for the

ejection efficiencies and beam composition. a1 and a3 are

constants and R is constant for any particular electron energy,








so a plot of log io/iT+ versus p will yield a straight line

with a slope

m (al + a3R)
m 2.303(1 + R) [1


Therefore, if one studies the slope as a function of the electron

energy and hence the composition of the beam, one can obtain

values of m as a function of R. Rearranging equation [II.20] one

obtains


2.303m al-a3
1+R + a3 [II.21]


A plot of 2.303m/l versus 1(1 + R) yields at straight line and

the values of a3 and al are obtained directly from the values of

2.303m/l at 1(1 + R) = 0 and 1, respectively. This method of

plotting the data was suggested by Phelps in a private communication

and is a more convenient way of analyzing the data than the method

used by Smith and Muschlitz (9). Equation [II.20], upon rearrangement,

becomes

(1 + R)m/. = a3R + al [11.22]


These authors then plotted (1 + R)m/fL versus R, which yields a

straight line of slope equal to a3 and an intercept on the

ordinate equal to a1. Finally, correcting for temperature will

give the desired cross sections.















CHAPTER III

DESCRIPTION OF APPARATUS


The molecular beam apparatus used to make the total cross

section and beam composition measurements is essentially the same

as that described by Smith and Muschlitz (9). As shown in Figure 1,

it consists of four vacuum chambers: the atom source, fore chamber,

post chamber, and scattering chamber. When making the beam

composition measurements, an inhomogeneous field magnet is placed

in the post chamber between the fore chamber and scattering chamber.

To provide room for the magnet an auxiliary chamber is used to

lengthen the post chamber. The magnet and auxiliary chamber are

removed while making the total cross section measurements.

An atomic beam is produced by introducing gas through an

adjustable leak valve into the source at room temperature and

allowing it to effuse through the first defining hole, Hl, into

the fore chamber. Some of the atoms are excited by electron

bombardment before leaving the source region. The electron beam

which passes directly behind H1, is produced by thermionic emission

from a thoriated iridium filament, and is confined by a magnetic

field of approximately 200 gauss produced by the magnets, D. A

potential applied cross plates E in the fore chamber deflects any

charged particles from the beam that.are produced in the source.











The beam entering the post chamber through the second

defining hole, H2, is a pencil-shaped, beam, 0.5 mm in diameter,

composed of metastable and normal atoms. It then passes through

the inhomogeneous magnet and into the scattering chamber through

a hole in the cylindrical can, G, which separates the scattering

region from the post chamber, or enters the scattering chamber

directly depending on the type of measurement to be done. A

magnetically operated shutter, S, is located directly behind H2

which allows the beam to be interrupted to obtain zero readings.

Fast mercury diffusion pumps maintain pressures below 10-4 mm

in the fore chamber and 10-5 mm in the post chamber.

The inhomogeneous field magnet, shown in Figure 2, is of

the Stern-Gerlach type (41-42), and patterned after that used by

Bederson (43) and co-workers. The magnet is made of Armco

magnet iron, and is in two sections to facilitate the coil

winding. There is a total of 193 turns of 18 gauge Nylclad copper

wire on the two halves. Cooling is provided by water-cooled copper

tubes which are placed between and around the coils. The magnet

has a field gradient ( H/z), of approximately 3,800i gauss cm-1

where i is the current through the coils.

Cylindrical symmetry is maintained throughout the scattering

region. Dimensions of the scattering elements are given in Table 1.

The angular resolution is varied by changing the diameter of the

hole in the scattering cylinder bottom, SB. The scattering

elements are heavily gold plated so that the electron ejection

efficiency will be uniform.























































Figure 2.--Inhomogeneous Field Magnet









TABLE 1

DIMENSIONS OF SCATTERING ELEMENTS



Length of Scattering Region 2.19 cm

Diameter of Scattering Cylinder 1.91 cm

Diameter of Hole in Scattering
Cylinder Lid 0.13 cm

Diameter of Holes in Scattering
Cylinder Bottom 0.683,0.485,0.381,0.227,0.104 cm





The beam enters the scattering region through the hole in

can G and passes through a larger hole in the scattering cylinder

lid, SL. The metastable atoms are then detected at the scattering

cylinder, SC, the scattering cylinder bottom, SB, or the target, T,

depending on whether the scattered or unscattered fraction of the

beam was to be measured. Current measurements are made simultaneously

by means of Cary Instruments (Model 31MS) vibrating-reed electrometers.

These are supplied in a "master-slave" arrangement in which the

oscillator of one of the instruments is used to drive the reeds in

both electrometers.

Figure 3 shows a schematic diagram of the apparatus

including the electronic circuit. The electronic circuitry used

by Smith and Muschlitz (9) has been completely redesigned. The

electron source emission regulator provides a steady current of

electrons at constant energy through the source chamber, regardless

of variations in the line voltage and in the pressure of the system.








19
















cI I








---
o- --L 0'





-- .; o o 0
i '1 < ) CO



SOQ
0 0 5








-01)
0 i- I
O
*H
















-- .--- -)-


I-)2 *I








Also it supplies all the necessary dc potentials to be supplied

to the source. In this automatic emission regulator, the sum of

the electron currents to the anode and catcher is controlled by

the filament voltage, using a saturable core reactor as the

controlling device. In this circuit the potentials applied to

the source are obtained from two electronically regulated power

supplies. With this design it is possible to operate over a wide

range of electron beam energy with a constant electron current.

One of the electrometers is connected to T and the other

to SL with each of the outputs fed to one channel of Varian

(Model G-22) dual channel recorder.

The electrometer connected to SL drifts when the voltage

applied to SC and SB is changed from a positive to negative

potential with respect to ground. As can be seen from Figure 1,

SL fits down over the scattering cylinder, SC, thus resulting

in a capacitance. By reducing the time constant of the RC circuit,

the drift can be greatly reduced. This was accomplished by

decreasing the input resistance of the voltage supply to the

scattering elements. Also the drift rate can be decreased by

gradually changing the potential applied to SC and SB by adjusting

the potentiometer, P; reversing switch Sl; and then gradually

applying the opposite potential in the same manner so that the

only resistance in the circuit is the internal resistance of the

battery.

The auxiliary vacuum system used for gas manipulation and

pressure measurements is shown in Figure 4. The upper manifold







21










T--o
--8 / -



03



Co











00 1 0
M I0 1w>



U"










Dco






01



















< c ___ n8
y_^ -C--)s<- --
*-;*~C3 ________
^^1
- -- ^) 5
"5~~&0 s-------














_____ ___
i-----------------------------








is used for pressure measurements either with ion gauge, Ii, or

the McLeod Gauge. By using the appropriate stopcocks, the

pressure can be measured in any of the vacuum chambers. The

two lower manifolds are used to introduce gases into the source

and the scattering region. A variable leak valve, L1, is used to

decrease the pressure from bulb B to approximately 0.1 mm, and

also vary the pressure in the source. L2 is a specially constructed

bellows-type needle valve used for the same purpose in the scattering

region but to about 10-4 to 10-3 mm. Scattering and source

pressures are measured with the McLeod Gauge, which has been

previously calibrated (9).

Matheson Company helium (99.99 per cent minimum purity)

is introduced into the system through a trap containing degassed

charcoal at liquid nitrogen temperature. This helium is used

in both the source and scattering regions with estimated impurities

to be less than one part in 104. The neon was taken from flasks

of reagent-grade gas supplied by the Air Reduction Sales Company.

Reported impurities, determined by mass spectrographic analysis,

were less than one part in 104. The apparatus itself was filled

through liquid nitrogen traps with helium (99.99 per cent minimum

purity) at one atmosphere between periods of operation, thus

preventing the adsorption of foreign gases on the walls.














CHAPTER IV

EXPERIMENTAL RESULTS


In all beam work, intensity of the beam is a prime

factor. The metastable beam intensity depends on the number

of electrons in the source, the energy of the exciting electrons,

and the source pressure. The electron beam current to the

catcher, C, shown in Figure 3, is directly proportional to the

electrons in the source. It is evident that the number of

helium atoms excited to metastable states is directly proportional

to the electron beam current. The energy spread of the electron

beam in the source is approximately 3 eV.

The effects of electron energy and source pressure on

the beam intensity are shown in Figure 5. These experimental

appearance potential curves are the sums of the 23S and 21S

appearance potential curves at two different pressures of helium

in the source. These compare favorably with the total metastable

appearance potential curve obtained by Frost and Phelps. As seen

from the figure, the intensity is the greatest above 30 volts,

and thus provides a lower limit on the electron energies to be

used. A plot of the metastable beam intensity, in arbitrary

units, versus the source pressure is shown in Figure 6. The

metastable intensity increases linearly at lower pressures and

begins to fall off at higher pressures. This deviation from

linearity is probably caused by the increase in pressure in the

23




















20





15





10




5




0


Figure 5.--Experimental Appearance Potential Curves
Pressures


at Two Source


25


25 30
POTENTIAL (VOLTS)


20


35






I I I I I


40-


o-
z30-
LJ
F-




< 20




10-




0 20 40 60 80 100 120 140
SOURCE PRESSURE (mm x103)


Figure 6.--Metastable Beam Intensity Versus Source Pressure









fore chamber and subsequent scattering of the beam in that region.

However, the pressure is still low enough that the criterion for

effusive flow is obeyed, which is necessary for the formation of

a molecular beam.

For the beam composition measurements, a fairly large

source pressure (100 x 10-3 mm) is required to obtain sufficient

beam intensity because of the relatively long distance from the

source to the scattering chamber (/20 cm). In this pressure

range the optimum catcher current was found to be 0.75 ma which

was maintained throughout subsequent experimental work. During

the scattering measurements the magnet was removed; thus the beam

length was decreased to approximately 2.5 cm. Over this length

a sufficient intensity could be obtained at lower source pressures

with the same catcher current.

The detection and measurement of the metastable beam

current for the beam composition and scattering experiments are

performed identically. To obtain the total beam intensity entering

the scattering region it was necessary to measure four currents.

The metastable currents, iT+ and iSL+, were measured with a

positive potential of 16 volts on SB and SC. SB and SC were then

made 16 volts negative with respect to ground and the currents

to T and SL measured; i.e., iT and iSL. iTT is a measure of
-T_ +
the unscattered fraction of the beam and the sum of the other

three currents is the scattered fraction. A negative potential

of 16 volts was applied to TC throughout the experiments. The

metastable current corresponding to the total beam intensity

entering the scattering region, i0, was taken as the sum of all

measured currents.








The beam, composed of singlet and triplet metastable

atoms, passes through the inhomogeneous field magnet. The

amount of deflection produced by passage through a magnet with

a gradient of ( H/ z) is given by


SH d12 + 2dd2]
SH 6T) [ 4kT


where pH is the effective magnetic moment, bH/Bz is the gradient,

dl = magnet length, d2 = distance between magnet and entrance to

scattering region (5 cm). For a deflection of 0.375 cm or 10 times

the radius of the hole at G for the Mj = -1 components of the

triplet beam, the calculated gradient necessary was 1.53 x 104 gauss/cm.

Since the calculated gradient was 3800i gauss/cm amp, the current i

through the coils necessary to produce this deflection would then

be 4 amperes. Figure 7 shows the beam intensity in arbitrary units

versus the magnet current in amperes at an electron energy of

30 volts. Saturation of the beam was attained with a magnet current

of approximately 5.5 amps. This value was used throughout the

following experiments requiring magnetic deflection.

The total metastable current, i0, is determined without and with

the magnetic field. The ratio, 71101/73103, which is computed in

the manner discussed previously, is shown as a function of electron

energy and at one source pressure in Figure 8. Figure 9 shows the

dependence of 71101/73103 on the source pressure at three electron

energies. The original data can be found in Appendix I. The

intercepts and slopes of these three lines were determined by the

method of least squares. The intercepts, at zero pressure, agree











8


>-

z 6
w



< 4
L1



2-



O I I I I I 3
0 1 2 3 4 5
MAGNET CURRENT (AMPS)
Figure 7.--Beam Intensity at 30 Volts Versus Magnet Current






2.50


2.00


1.50 -


63103
1.00



0.50


U 1


ELECTRON ENERGY


(VOLTS)


Figure 8.--71I01o/7303 Versus Electron Energy


25


50


0


I


--


O

















! I I --I-I-II I






2.0


1b i-01 30v
1.0

0.8-

0.6 ".

0.4

02-

S -I I I I I !
0 20 40 60 80 100 120 140
PRESSURE (mm x103)
Figure 9.--71101/73103 Versus Source Pressure at Three Electron Energies








well with the values of 101/I03 calculated from data given by

Frost and Phelps (39), whose results are denoted by the squares.

The experimental values obtained for 71101/73103 are applicable

to the composition of the beam at the entrance to the scattering

region while those calculated or extrapolated apply to the

composition of the beam in the source.

The scattering experiments were performed by introducing

a gas into the scattering region at a known pressure and measuring

the beam intensity in the manner described previously. These

measurements were performed with five different angular resolutions.

The resolution is taken as arc tan a/L where a is the radius of

the hole in SB and L is the length of the scattering chamber

which is 2.19 cm. This resolution is actually the minimum angle

for which the particles in the beam axis are counted as scattered.

The average angle through which the beam particles are counted

as scattered can be found by integrating arc ctn x/a from 0 top.



Sarc ctn 2 dx
avg = a
dx



= arc ctn + a [ln(l + 12/a2)]
a 21.


Table 2 summarizes the angular resolutions 8 and eavg-

Figures 10 and 11 are plots of log i0/iT+ in helium and

neon respectively versus pressure for three electron energies at

a minimum resolution of 8053'. The curves are displaced along the









TABLE 2

SUMMARY OF ANGULAR RESOLUTIONS


a 9 eavg


2.19 cm 0.052 cm 1022' 6032'

2.19 cm 0.114 cm 30 .1150'

2.19 cm 0.191 cm 50 17013'

2.19 cm 0.243 cm 6021' 20025'

2.19 cm 0.342 cm 8053' 25038?
1




abscissae for clarity. The best straight line for each of the sets

of points was determined by the method of least squares. The

original data may be found in Appendix II. Also the data for

helium and neon at the other resolutions can be found in

Appendix II, and were treated similarly. A decrease in slope, m,

was found with increasing electron energy indicating a difference

in the cross sections for the two metastable species. Also the

decrease in slope with increasing fraction of 21S helium in the

beam would mean that the cross section for the 23S is larger

than that for the 21S state.

Figures 12 and 13 are the plots of 2.3 slope/I versus

.1/(1 + R) at the electron energy corresponding to each value of

m for helium and neon at the five different angular resolutions.

The value of R is obtained from Figure 9 at the particular source

pressure used. The cross sections a3, for the 23S helium in helium






0.5


0.4



03


log .i


02-



0.1



0-


PRESSURE (mmx104)


Figure 10.--Log io/iT+ in Helium Versus Pressure for Three Electron Energies





























5 10 15 20
0 O PRESSURE (mm x104)


Figure ll.--Log io/iT+ in Neon Versus Pressure for Three Electron Energies


0.5


log io
it.



















300-






D.
Cl!


200-










100-


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 09 1.0
1
1-+R
Figure 12.--2.303 Slope/)L Versus 1/ + R)for Metastable Helium
in Helium





















S230







150







70-


0 0.1 0.2 0.3 04 0.5 0.6 0.7 0.8 0.9 1.0
1

Figure 13.--2.303 Slope/. Versus l/J + R)for Metastable Helium
in Neon









and neon are obtained directly from the values of 2.303 slope/I

at 1/(1 + R) = 0. The singlet cross-sections (1l) are directly

obtained at 1/(1 + R) = 1. Table 3 summarizes the slope, the

2.303 slope/i, the values of 1/(1 + R) used, and the values of

the cross-sections in cm- and (A2) for helium in helium.

Likewise, Table 4 summarizes these data for neon. Figures 14

and 15 are plots of the 23S and 21S total cross-sections of

helium metastables in helium and neon respectively at the five

minimum angular resolutions.









TABLE 3

SUMMARY FOR HELIUM IN HELIUM


Angular Resolution Energy Slope 2.303 Slope 1
_1 +R


30
35
45


276.2
260.9
242.7


= 347 cm-1
0
= 98 A


195.3
185.5
175.1

= 240 cm1-
02O
= 68 A2


157.6
149.8
142.6

=193 cm-1
-0)
55 A2


151.8
145.7
137.8

= 184 cm-1
= 52 A2


127.2
123.1
117.6

= 150 cm-1
= 42 A2


290.5
274.4
255.2

a, = 190
o1 = 54


S 205.5
195.1
184.2

a1 = 145
01 = 41


165.8
157.6
150.0


S= 120
01 = 34


159.6
153.2
145.1

a1 = 117
01 = 33


133.8
129.5
123.7

ai = 105
l = 30


0.371
0.450
0.587


cm-l
A2


0.375
0.456
0.589


cm-1
02
A


0.386
0.465
0.594


cm1
02
A


0.382
0.463
0.592


cm-1
A


0.371
0.450
0.587


cm-1
02
A


1022'


6021'


8053'








TABLE 4

SUMMARY FOR HELIUM IN NEON


Angular Resolution Energy Slope 2.303 Slope 1
L 1 + R


215.5
197.1
179.3

= 288 cm-1
0
= 81 A2


160.5
146.4
128.9

= 226 cm-1
02
= 64 A


136.1
124.7
112.8

-1
= 186 cm-1
= 53 A


127.7
116.2
104.5


=176 cm-1
S0 2
50 A-


8053'


= 155
= 44


226.6
207.3
188.6

0i = 113
oi = 32


168.8
154.0
135.6

ai = 75
o1 = 21


143.2
131.2
118.7


0.367
0.448
0.585


cm-
02
A


0.390
0.469
0.595


cm-1
02
A


0.379
0.456
0.590


al
ri1


134.3
122.2
109.9


al =
al =


114.6
104.9
94.7

-1
cm
02
A2


120.6
110.4
99.6

ai = 58
0l = 16


0.379
0.460
0.590


cm-1
02
A


0.367
0.448
0.585


-1
cm
A2
A2


1022'


6021'









I I I I I I I I



O THIS WORK
( H & M-Q3
OB&D


1601

150

140

130

120

110

100

90O

80

70

60

50

40-

30-


20


I I


0 1 2 3
ANGULAR


4I
4 5


RESOLUTION


6 7 8 9


(DEGREES)


Figure 14.--Corrected Cross Sections Versus Angular Resolution for
Metastable Helium in Helium


o
H-



GO
0
0(


0


' I I


J V T
y^ ^^ -

<^-^-^









I II I I I I I I-


H & M-o-3
This Wortk


150

140

130

120

110

O00

-90
0<
z 80

y 70
GO
60


U 50


03


I-


I I I


I I I I


0 1 2 3 4
ANGULAR


5 6 7
RESOLUTION


8 9 10


(degrees)
Figure 15.--Cross Sections Versus Angular Resolution for Metastable
Helium in Neon


-0


40

30

20

TO


I I I I I I i i















CHAPTER V

DISCUSSION


The determination of the excitation functions for the

singlet and triplet metastable states of helium and hence the

composition of the metastable beam is quite complicated. There

are a number of factors that influence the composition of the

beam regardless of the method of production; be it electron impact

or gaseous discharge. The metastable atoms produced are lost

mainly by diffusion to walls, by de-exciting collisions with gas

atoms resulting in actual transfer from the metastable state to

a radiating state or by collisions which perturb the metastable

atom sufficiently to break the optical selection rule (collision

induced radiation), excitation transfer on collision, and by

the imprisonment of resonance radiation. All of these processes

are a function of the pressure in the source region in which the

excitation occurs.

Figure 9 shows plots of the ratio 71101/73103 against

pressure in the electron bombardment source for 30, 35, and

45 volt electrons, respectively. The slopes and intercepts at

zero pressure are given in Appendix I. The slopes at the three

different energies are nearly the same within experimental error.

The points at zero pressure indicated by the rectangles were

obtained from the Frost and Phelps report (39) and the agreement

42









is quite good, especially at 35 volts. When comparing this

work with Frost and Phelps, one must assume 71 = 73. There

is good experimental and theoretical justification for this

as was shown earlier (p. 6). At first it was thought that the

pressure dependence might be due to a change in composition of

the molecular beam as it passed through the fore chamber. The

results of the scattering cross section measurements given in a

previous chapter show that the cross section for the triplet

metastables on normal helium to be larger than that for singlet

metastables on normal helium; however, calculations show that

the difference in the cross sections would have to be much

larger than was observed in order that the pressure dependence

be so pronounced. It is more reasonable that most of the pressure

effect is due to the imprisonment of resonance radiation. At the

low source pressures normally used the other effects mentioned

above would be negligible because the cross sections for the given

processes are quite small (44,45).

The term resonance is applied to radiation emitted by an

atom in an optically allowed transition from an excited state to

the ground state. The resonance radiation is absorbed by the gas

in its normal state. When a resonance quantum is emitted by an

excited atom, it may be absorbed by another atom, thereby exciting

it to the same state. As the pressure of the gas increases, the

number of atoms in the excited state increases. This phenomenon

is known as imprisonment of resonance radiation. The increased

production of the singlet metastables is due mainly to a larger

number of excited atoms in the 2-1 resonance state as the pressure








in the source is increased. These may then decay not only to the

ground state but also to the 21S metastable state. The excitation

function for the 31P level in helium by electron impact has been

studied by St. John and co-workers (46) by measuring the intensity

of the 5016 A line (31P--> 21S transition) at different pressures

of helium. Above a pressure of --3 x 10-4 mm, an enhanced intensity

was observed and attributed to the imprisonment of resonance

radiation, and should also happen for the 21P -- 21S transition.

Calculations could be made to corroborate this effect in the

present experiments; however, a few drastic assumptions must be

made with regard to the number of photons reflected from the

walls and the effect of the transitions from higher excited states.

Gabriel and Heddle (47) have done an experimental study of the

excitation processes in helium; however, this was done under

controlled electron impact at 108 eV. Their results cannot be

compared to this work done at the lower energies (30 to 45 eV)

because of the quite different behavior of the system in these

two energy ranges.

Another point of interest in connection with the beam

composition is the alignment produced in the 23S metastable state

by electron bombardment which has been suggested by Krotkov and

Holt (48). They suggested that if all the atoms in the 23S

metastable state were produced by transitions from the 23P state,

the relative population of the Mj = 1 sublevels would be 25 per

cent each and the Mj = 0 sublevel 50 per cent. Of course, the

23S metastable atoms made directly by electron bombardment populate

the three magnetic sublevels equally. If one assumes the extreme









situation of 25-50-25 for the relative population of the Mj = 0, -1

sublevels rather than equal population one can calculate the beam

composition in a similar manner as described earlier. The agreement

with Frost and Phelps and this work is then very poor. In Figure 14

the square points are the respective cross sections calculated at

8053' and 1022' using this calculated beam composition. There is

little effect on the cross sections at 8053' but there is a

considerable decrease in the triplet cross section at 1053'.

Figure 8 shows the increase of the ratio 71101/73103 with

increasing electron energy as is expected since the excitation

cross section for the singlet metastable state increases with

increasing energy above 30 volts while the cross section for

triplet decreases (39). The maximum at 70 volts may or may not

be real because the experimental error becomes appreciable at

the higher energies since the triplet fraction of the beam decreases

and therefore results in a smaller part of the total beam being

deflected in the inhomogeneous magnetic field. The intercept

shown at 0 for the ratio is placed at the excitation energy of

the 21S level. This was done in order to see how well it fit

in with the rest of the data. The fit seems to be quite good.

Since the excitation energy of the metastable levels is

large, various inelastic collisions between a metastable helium

atom and another atom are possible, e.g.:


He + X ->He + X [V.1]

He + X ->He + X + hv [V.2]

He* + X ---He + X + K.E. [V.2']

He + X ->He + X+ + e- [V.3]









He* + He ---> He + He+ + e- [V.4]

He* (21S) + X ---He* (23S) + X + K.E. [V.5]


The first of these is the transfer of excitation energy

between particles; the second, a collision-induced radiative

transition where hv represents a photon. Equation [V.2'] represents

the de-excitation of the excited atom by a collision with another

atom with the energy of excitation being transformed into kinetic

energy. The same considerations may be applied to this type of

reaction as those applied to the excitation of atoms by collisions

with other atoms and are fully discussed by Herzberg (49). In

most cases, such processes would have a low probability. Equation

[V.3] is a special case of [V.1] in which the excitation energy of

the metastable atom is large enough to ionize the struck atom.

Equation [V.4] is a collision between two metastable atoms in

which one is ionized while the other is de-excited to the ground

state. Equation [V.5] is a collision in which a 21S helium atom

is converted to a 23S helium atom.and is only possible in the

forward direction. At the low pressures used in the scattering

region three-body collisions need not be considered.

Reaction [V.4] would not occur, since in a molecular

beam the number of collisions between the beam particles is

negligible. For reaction [V.3] to be possible the ionization

potential must be smaller than the excitation energy of the

metastable helium atoms and therefore will not occur in this work.

Using an optical absorption method for the determination

of metastable atom concentration with time in a gaseous discharge,








Phelps and Molnar (45) and Phelps (44) found the cross section

for the destruction of 21S helium in collisions with normal

helium to be 3 x 10-20 cm2 at 3000K and that of 23S to be less

than 1 x 10-22 cm2 at 3000K. These cross sections include the

processes in reactions [V.2], [V.2'] and [V.5] for 21S helium

and reactions [V.2] and [V.2'] for 23S helium and are therefore

negligible compared to the total cross section. In the scattering

experiments with helium in helium, reaction [V.1] would be the

only reaction expected to take place to an appreciable extent.

In this case, a collision in which excitation transfer occurs

is not distinguishable from a direct elastic collision.

The experimental results of the scattering measurements

at the different angles of resolution and their estimated

precision, obtained with a source temperature approximately

6600 and a scattering gas temperature of 2700, are given in

Table 5.



TABLE 5

CROSS SECTIONS
(cm2 x 1016)



Angle of Helium Helium Neon
Resolution 03 a1 Q3 Q1 03 01


1022' 985 54 4 754 41 3 815 324
30 68-4 41+4 52 3 31-3 64-4 21-3
5 554 344 423 263 534 204
6021' 524 334 403 253 504 183
8053' 42+4 30-4 32+3 23-3 44-4 16 3








The values obtained for the total cross sections are

dependent on the geometry of the apparatus. If the angular

definition or resolution is increased the cross section will

increase and the increase is shown in Figures 14 and 15. The

total cross sections, when quoted in literature, should be

accompanied by the angular resolution of the apparatus in order

that the data can be interpreted and used properly. Classically,

the cross section would increase without limit because at zero

degrees resolution everything would have to be counted as scattered

but it has been shown quantum mechanically that there is a limit

to the cross section beyond which the deflection of the beam

particles would be less than the uncertainty caused by the

uncertainty principle. Massey and Burhop (50) have calculated the

angular resolution necessary to obtain results within ten per cent

of the actual value and find this to be 3.60 in laboratory

coordinates for the case of normal helium in normal helium.

However, it has been shown (29) for metastable helium in helium

an angular resolution of 0.50 would give an error not greater

than 6 per cent.

The total cross sections for the scattering of metastable

helium in helium and in neon are larger in each case than the

respective cross sections for normal helium as given by the

kinetic theory values (51), 14.9 and 17.8 x 10-16 cm2, which

are based on the equivalent hard sphere model. It is also

evident that the cross section for the 23S helium is larger than

for the 21S in the same scattering gas. In the case of helium

as the scattering gas, this can only be caused by a difference








in the interaction potentials between the respective metastable

atoms and the scattering atoms. As mentioned in Chapter I, the

only cases for which any calculations of these potentials are

available are those for the interaction of normal and metastable

helium atoms. Buckingham and Dalgarno (10) have calculated these

potentials and found the interaction to be repulsive and essentially

the same for both metastable states at large distances. As the

interaction distance decreases positive maxima of 0.29 and 0.26 eV

(for the triplet and singlet states, respectively) occur at about

4ao and then pass through a minimum at 2ao and finally becomes

increasingly repulsive. Using a more refined type of calculation

Brigman, Brient, and Matsen (52) confirm the hump at 4ao for the

interaction of the triplet and normal helium atom but it is

lowered to 0.19 eV.

On the basis of these calculations one would expect to

observe a difference in triplet and singlet cross sections in

going from a high resolution, where small angle scattering is

observed, to a low resolution, where large angle scattering is

observed. The large angle scattering must be accompanied by

smaller interaction distances than that for small angle scattering.

As shown in Figure 14 the triplet cross section is larger than the

singlet at the low resolution but the difference, a3-rl increases

as the resolution is increased which is contrary to what was

thought might happen. The behavior would be altogether different

if the colliding particles could get over the "hump" into-the

region below 4ao but the average energy of the beam is approximately

0.03 eV and therefore not large enough to go over the "hump" based









on classical considerations. Furthermore, a simple calculation

of the fraction of the beam, having energy greater than five

times the average energy, is approximately one in one hundred

which is not large enough to be significant.

A transmission coefficient for tunneling can be calculated

by crudely approximating the "hump" by a rectangular potential

barrier. The transmission coefficient calculated was in the order

of 10-10, and therefore it is not likely that tunneling did occur.

One can only conclude from the data that there is some factor or

factors which have not been considered or that the "hump" is not

nearly as large as it has been calculated. It should be remarked

that the observed scattering at low energies is strongly influenced

by both repulsive and attractive forces which tend to make any

quantitative analysis of observed data quite complicated.

Buckingham and Dalgarno (53) have also calculated a

total cross section which they say is applicable to either of

*the metastable species of helium in normal helium and is shown

in Figure 14 by the shaded point at zero degrees resolution. Their

calculated value is 158 x 10-16 cm2 at 3000K. If this cross section

'is applicable to both species, the singlet cross section would have

,to rise quite rapidly at the higher resolution.

In 1938 Dorrestein and Smit (55) measured the collision

cross section of metastable helium atoms in normal helium. A

value of oT = 20 x 10-16 cm2 was found and because of the poor

resolution it was thought that this was caused by transfer of

excitation energy between the metastable and normal helium atoms.

No attempt was made to separate the two metastable states.









Hasted and Mahadevan (54) have determined the total

cross section for the triplet metastable helium atom in normal

helium at an angular resolution of 10 to be 145 x 10-16 cm2, or

corrected for initial momentum of the scatterer, to be 111 x 10-16 cm2.

The correction will be discussed later. However, to be consistent

in comparing the data, the cross section represented by the half

shaded circle is plotted in Figure 14 at a.resolution of 0.50 because

of the difference in the method of defining the angular resolution.

They used the same apparatus as that used by Stebbings (29) in

earlier measurements of total cross sections of 23S helium in

various gases. He found oT = 149 x 10-16 cm2 for 23S helium in

helium at 0.50.

Measurements of oT for both 23S and 21S helium in helium

have been made at a single angular resolution of 6021' by Smith

and Muschlitz (9). They obtained 49 and 37 x 10-16 cm2, respectively

(uncorrected). These are in reasonable agreement with the present

results.

The total cross sections determined for the two metastable

states of helium in neon at different angular resolutions are

depicted in Figure 15 and listed in Table 5. The behavior is quite

similar to the helium case but at all resolutions the difference

between a3 and 01 in neon is greater than that for helium. However,

these cross sections are the sum of the elastic and inelastic

cross sections. The only inelastic process that might occur with

appreciable probability is the exchange of excitation energy

depicted in reaction [V.1]. Benton et al. (56) have recently

reported cross sections of 0.28 x 10-16 cm2 and 4.1 x 10-16 cm2









for the de-excitation of 23S and 21S metastable helium atoms in

neon. They also point out that the singlet destruction cross

section may be too large by a factor of 2 or 3. These values

are small compared to the total cross sections and therefore the

difference in the total cross sections can only be caused by a

difference in the elastic cross sections. This can only be due

to a large difference in the interaction potentials at thermal

energies and should encourage further calculations such as those

of Buckingham and Dalgarno.

Hasted and Mahadevan (54) have reported a value of

aT = 122 x 10-16 cm2 for 23S helium in neon at 0.50 which is

shown in Figure 15 and is consistent with this work. There

is also reasonable agreement of the present results with those

of Smith and Muschlitz (9) at an angular resolution of 6021'.

The total cross sections a, defined in Chapter II are

actually absorption cross sections. There is a difference between

them and the mean collision cross section. If the average velocity

of the scattering gas atoms could be neglected compared to that of

the beam atoms, the two cross sections would be the same. To

obtain the total collision cross section, averaged over the

distribution of relative velocities fixed by the temperature of

the gases, one must multiply the observed cross sections by a

factor which is a function of the masses and temperatures of the

beam and scattering gases. The data necessary to make the

corrections are given in Massey and Burhop (50). The correction

factors are 0.766 for helium in helium and 0.916 for helium in

neon. The cross sections for metastable helium in helium, shown









in Figure 14, have been corrected while those for metastable

helium in neon, Figure 15, have not been corrected since there

would be only a small change in this case. Both the corrected

and uncorrected cross sections are given in Table 5. For the

metastable helium in helium case, the same correction factor

was used for the cross sections obtained at the different angular

resolutions. It is believed, however, that this correction

should not be the same at two given angular resolutions, but the

change would be small over the limited range of angular resolutions

used in these measurements.

Several possible sources of error in these experiments

should be considered. It is possible for the photons that

originate in the source to pass through the defining holes,

strike the target, and eject secondary electrons. All of the

photons will originate in the source since the lifetime of an

excited radiating atom is of the order of 10-7 to 10-9 sec and

could move about 10-3 cm in this time. If it is assumed that the

photons are emitted isotropically, the geometry of the defining

system is such that only one in 105 will reach the target. Attempts

by Smith and Muschlitz (9) to detect a current caused by photons

were made by increasing the pressure in the scattering region so

that all metastable atoms would be scattered and only photons could

reach the target. These experiments showed that with helium in

the source the current was negligible. However, in some preliminary

work by the author with argon in the source, a target current was

observed at very high krypton pressures in the scattering region

which is probably due to photons. To perform scattering experiments









using metastable argon as the incident beam, one would have to

use two shutters; one of collodion which would stop the metastable

atoms but not the photons and another which would stop both the

photons and atoms.

The ejection efficiency of the metastable atoms on metal

surfaces undoubtedly varies with type and amount of gas adsorbed

and with the nature of the surface. It is possible that the

ejection efficiency depends on the angle of incidence but throughout

the experiments this was small since small angle deflections are

the most probable.

There are numerous experiments to be performed with this

apparatus but only after some needed improvements. The first is

the construction of an electron gun with a narrow electron energy

spread. Also, the target electrode should be replaced by an

electron multiplier when beam composition measurements are to

be performed. Using an electron gun with a narrow range of

energies it would be possible to excite only the 23S state of

helium; then in conjunction with the inhomogeneous field magnet

if would be possible to determine the population of the magnetic

sublevels.

Also cross section measurements of metastable neon and

argon in helium, neon and the other rare gases would be of

extreme value in explaining these types of interactions especially

if a source could be constructed and operated over a wide range

of temperatures so that the interaction potentials could be

calculated by a method proposed by Mason (57).














CHAPTER VI

SUMMARY


A molecular beam method has been used to perform scattering

experiments with an atomic beam of metastable helium atoms in

helium and neon. The atomic beam, in which some of the atoms had

been excited to metastable levels by electron impact, was passed

through the scattering chamber at pressures of the order of

10-3 mm of Hg. The metastable atoms were detected by electron

ejection from gold surfaces.

The ratio of the product of the intensity of the singlet

metastable helium and its ejection efficiency to the triplet

intensity and its ejection efficiency, 71101/73103, has been

determined both as a function of electron energy and source

pressure. An increase in this ratio was observed with increasing

source pressure and was attributed primarily to imprisonment of

resonance radiation.

A total collision cross section which is the sum of the

elastic and inelastic cross sections has been measured for

metastable helium in helium and neon as a function of angular

resolution of the molecular beam apparatus. An increase in the

cross sections was observed as the angular resolution was increased.

In both cases the cross section for the 23S state of helium was

larger than that for 21S state; however, the difference between






56


triplet and singlet cross sections in neon was larger than in

helium. In both cases, this became larger with increasing

resolution. The differences in the cross sections can only be

caused by differences in the interaction forces between the

colliding particles.















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APPENDICES
















APPENDIX I


ORIGINAL BEAM COMPOSITION DATA


TABLE 6

BEAM COMPOSITION AS A FUNCTION OF SOURCE PRESSURE





Ps x 103 i i 101
0 0 73103


30 Volt Electrons

6.05
6.50
7.95
9.10
8.55
8.80
9.75


3.80
4.10
5.00
5.85
5.60
5.80
6.45


0.79
0.80
0.80
0.87
0.93
0.95
0.97


Slope = 4.84


Intercept = 0.43


35 Volt Electrons


7.40
7.40
8.30
9.65
8.65
9.25
10.25


5.00
5.00
5.65
6.75
6.00
6.50
7.25


1.05
1.05
1.08
1.22
1.17
1.24
1.28


Intercept = 0.63


71
79
83
93
100
105
115


71
79
83
92
100
105
115


Slope = 5.74









TABLE 6--Continued


71101
Ps x 103 io i 0 7110
73103


45 Volt Electrons

71 7.55 5.60 1.58
79 7.40 5.50 1.60
83 8.30 6.25 1.70
92 9.55 7.25 1.76
100 8.55 6.45 1.71
105 9.35 7.10 1.76
115 10.05 7.65 1.79

Slope = 4.65 Intercept = 1.27





TABLE 7

BEAM COMPOSITION AS A FUNCTION OF ELECTRON ENERGY AT
100 x 10-3 mm SOURCE PRESSURE




71y01
Electron Energy i i' 73103


30 8.55 5.60 0.93
35 8.65 6.00 1.17
40 8.50 6.30 1.58
45 8.55 6.45 1.71
50 8.30 6.40 1.91
55 8.15 6.40 2.10
60 8.15 6.45 2.20
65 7.90 6.35 2.40
70 8.30 6.70 2.46
75 8.45 6.80 2.41















APPENDIX II


ORIGINAL SCATTERING DATA


TABLE 8

METASTABLE HELIUM IN HELIUM, 30 VOLT ELECTRONS
ANGULAR RESOLUTION 8053' Ps = 34 x 10-3 mm


i
p x 104 iT+ SL+ iT_ iSL log
giT+

0.07 13.30 0.00 0.20 0.50 0.0224
2.75 11.80 0.20 0.30 1.05 0.0536
3.57 11.30 0.20 0.30 1.30 0.0642
7.07 9.70 0.35 0.35 1.85 0.1049
11.80 8.20 0.60 0.45 2.75 0.1654
14.90 7.10 0.85 0.45 3.05 0.2075
19.87 5.95 0.90 0.55 3.60 0.2669
23.70 5.05 0.95 0.55 3.95 0.3179
26.50 4.60 1.10 0.60 4.10 0.3543
28.83 4.15 1.15 0.60 4.20 0.3863
31.40 3.85 1.20 0.65 4.35 0.4167

Slope = 127.2 Intercept = 0.0170









TABLE 9

METASTABLE HELIUM IN HELIUM, 35 VOLT ELECTRONS
ANGULAR RESOLUTION 8053' Ps = 34 x 10-3 mm


p x 104 iiL+ iT iSL log-
sL iT+


0.07 12.60 0.00 0.20 0.50 0.0233
2.75 11.25 0.15 0.25 1.00 0.0509
3.57 11.00 0.15 0.25 1.25 0.0607
7.07 9.50 0.30 0.30 1.75 0.0960
11.80 8.05 0.55 0.45 2.60 0.1605
14.90 7.00 0.75 0.45 2.90 0.2002
19.87 5.90 0.80 0.50 3.45 0.2565
23.70 5.05 0.90 0.55' 3.80 0.3095
26.50 4.65 1.05 0.55 3.90 0.3390
28.83 4.25 1.15 0.55 4.00 0.3694
31.40 3.90 1.15 0.60 4.20 0.4024

Slope = 123.1 Intercept = 0.0148




TABLE 10

METASTABLE HELIUM IN HELIUM, 45 VOLT ELECTRONS
ANGULAR RESOLUTION 8053' Ps = 34 x 10-3 mm



04 i0
Sx 10 iT+ iSL+ iT_ iSL log --
iT+

0.07 12.45 0.00 0.15 0.45 0.0204
2.75 11.10 0.10 0.25 1.00 0.0498
3.57 10.60 0.10 0.25 1.20 0.0592
7.07 9.20 0.25 0.30 1.70 0.0950
11.80 7.75 0.45 0.40 2.45 0.1540
14.90 6.80 0.65 0.45 2.70 0.1927
19.87 5.80 0.75 0.50 3.30 0.2515
23.70 4.90 0.85 0.50 3.50 0.2988
26.50 4.60 0.95 0.55 3.60 0.3240
28.83 4.30 1.05 0.55 3.70 0.3488
31.40 3.85 1.05 0.60 3.95 0.3900

Slope = 117.6 Intercept = 0.0160









TABLE 11

METASTABLE HELIUM IN HELIUM, 30 VOLT ELECTRONS
ANGULAR RESOLUTION -6021' Ps = 40 x 10-3 mm


i0
p x 104 iT iSCLT+ iT_ SCLT log i



0.08 16.25 0.00 0.25 0.85 0.0284
3.25 14.10 0.25 0.30 2.05 0.0722
4.75 13.05 0.35 0.30 2.50 0.0939
7.28 11.90 0.50 0.40 3.15 0.1272
10.38 9.90 0.70 0.40 3.90 0.1776
11.73 9.20 0.75 0.40 4.15 0.1976
15.16 7.90 0.95 0.45 4.75 0.2501
19.43 6.75 1.10 0.45 5.40 0.3074
23.70 5.40 1.30 0.45 5.80 0.3799
25.93 4.80 1.35 0.45 5.90 0.4157
32.41 3.75 1.65 0.45 6.40 0.5141

Slope = 151.8 Intercept = 0.0197




TABLE 12

METASTABLE HELIUM IN HELIUM, 35 VOLT ELECTRONS
ANGULAR RESOLUTION -6021' Ps = 40 x 10-3 mm




piT+ SCLT+ iT_ iSCLT- logic
IT+


0.08 16.00 0.00 0.25 0.80 0.0276
3.25 14.40 0.25 0.30 2.00 0.0708
4.75 13.20 0.40 0.30 2.40 0.0916
7.28 12.00 0.50 0.40 3.10 0.1249
10.38 10.35 0.70 0.40 3.90 0.1712
11.73 9.40 0.75 0.40 4.05 0.1912
15.16 8.10 1.00 0.45 4.56 0.2438
19.43 6.95 1.15 0.45 5.30 0.2995
23.70 5.65 1.35 0.45 5.70 0.3669
25.93 5.05 1.40 0.45, 5.85 0.4022
32.41 4.00 1.65 0.45 6.35 0.4931

Slope = 145.7 Intercent = 0.0211









TABLE 13

METASTABLE HELIUM IN HELIUM, 45 VOLT ELECTRONS
ANGULAR RESOLUTION -6021' Ps = 40 x 10-3 mm


i0
p x 104 iT+ SCLT+ iT iSCLT- log -



0.08 15.20 0.00 0.25 0.75 0.0277
3.25 13.45 0.25 0.25 1.80 0.0682
4.75 12.50 0.40 0.30 2.15 0.0892
7.28 11.20 0.50 0.35 2.85 0.1240
10.38 9.70 0.70 0.35 3.55 0.1686
11.73 8.90 0.75 0.35 3.75 0.1889
15.16 7.80 1.00 0.40 4.25 0.2366
19.43 6.70 1.10 0.45 5.00 0.2961
23.70 5.50 1.30 0.45 5.20 0.3548
25.93 4.95 1.35 0.45 5.30 0.3864
32.41 3.90 1.60 0.40 5.85 0.4800
Slope = 137.8 Intercept = 0.0224




TABLE 14

METASTABLE HELIUM IN HELIUM, 30 VOLT ELECTRONS
ANGULAR RESOLUTION 50 Ps = 42 x 10-3 mm



io
p x 104 iT+ iSCLT+ iT iSCLT- log
l T+

0.09 16.50 0.00 0.20 0.70 0.0230
1.53 15.60 0.15 0.25 1.15 0.0412
5.94 12.00 0.50 0.25 2.70 0.1097
9.81 10.00 0.65 0.30 3.80 0.1688
13.88 7.80 0.85 0.30 4.65 0.2415
14.36 7.70 0.90 0.35 4.65 0.2470
18.36 6.35 1.00 0.30 5.05 0.3010
19.46 6.25 1.15 0.35 5.50 0.3263
21.55 5.40 1.15 0.35 5.45 0.3593
23.36 5.00 1.20 0.30 5.55 0.3820
27.24 4.30 1.35 0.35 5.95 0.4439
31.12 3.65 1.55 0.30 6.30 0.5096

Slope = 157.6 Intercept = 0.0172









TABLE 15


METASTABLE HELIil: IN HELIUM, 35 VOLT


ANGULAR RESOLUTION -50


Ps= 42 x


ELECTRONS
10-3 mm


i0
p x 104 T+ iSCLT+ iT_ iSCLT log


0.09 16.30 0.00 0.20 0.65 0.0221
1.53 15.40 0.10 0.20 1.15 0.0391
5.94 11.80 0.40 0.25 2.60 0.1056
9.81 9.95 0.60 0.30 3.65 0.1636
13.88 7.90 0.85 0.30 4.50 0.2343
14.36 7.75 0.75 0.35 4.45 0.2345
18.36 6.45 1.00 0.30 4.85 0.2908
19.46 6.40 1.05 0.35 5.30 0.3111
21.55 5.55 1.05 0.30 5.30 0.3421
23.36 5.15 1.10 0.30 5.35 0.3637
27.24 4.45 1.30 0.35 5.75 0.4254
31.12 3.85 1.50 0.30 6.10 0.4846

Slope = 149.8 Intercept = 0.0181




TABLE 16

METASTABLE HELIUM IN HELIUM, 45 VOLT ELECTRONS
ANGULAR RESOLUTION 50 Ps = 42 x 10-3 mm



i0
p x 104 iT iSCLT iT_ SCL log
TT- SCLT- iT+


0.09
1.53
5.94
9.81
13.88
14.36
18.36
19.46
21.55
23.36
27.24
31.12


15.50
14.60
11.40
9.55
7.70
7.45
6.25
6.25
5.40
5.05
4.40
3.95


0.00
0.05
0.35
0.55
0.75
0.65
0.90
0.95
0.95
1.00
1.20
1.35


0.20
0.20
0.25
0.30
0.30
0.30
0.30
0.30
0.30
0.30
0.30
0.30


0.60
1.05
2.45
3.40
4.05
4.20
4.45
4.95
4.90
4.90
5.30
5.70


0.0219
0.0370
0.1030
0.1599
0.2207
0.2282
0.2797
0.2993
0.3202
0.3498
0.4058
0.4638


Intercept = 0.0188


Slope = 142.6









TABLE 17


METASTABLE HELIUM IN HELIUM, 30
ANGULAR RESOLUTION 30 Ps =
0


VOLT ELECTRONS
36 x 10-3 mm


p x 104 iT iSCLT+ iT iSCLT- log
log iT+

0.06 14.15 0.00 0.20 0.00 0.0061
2.36 12.15 0.15 0.25 0.95 0.0457
3.78 10.80 0.10 0.20 1.50 0.0670
7.91 8.55 0.30 0.25 2.90 0.1472
8.24 7.80 0.25 0.20 2.95 0.1571
12.08 6.35 0.55 0.20 3.75 0.2327
13.56 5.80 0.50 0.20 4.10 0.2617
17.44 4.75 0.60 0.25 4.65 0.3340
21.99 3.60 0.75 0.20 5.00 0.4237
24.76 3.10 0.90 0.20 5.20 0.4818

Slope = 195.3 Intercept = -0.0043




TABLE 18

METASTABLE HELIUM IN HELIUM, 35 VOLT ELECTRONS
ANGULAR RESOLUTION -30 Ps = 36 x 10-3 mm



p x 104 iT iSCLT iT iSCLT- log -
-CT o iT+


0.06 13.90 0.00 0.20 0.00 0.0062
2.36 12.00 0.10 0.25 0.90 0.0430
3.78 10.70 0.10 0.20 1.45 0.0658
7.91 8.55 0.30 0.25 2.80 0.1436
8.24 7.90 0.25 0.20 2.80 0.1497
12.08 6.50 0.50 0.20 3.65 0.2225
17.44 4.90 0.65 0.25 4.60 0.3268
21.99 3.85 0.75 0.20 4.90 0.4013
24.76 3.30 0.90 0.20 5.05 0.4569

Slope = 185.5 Intercept = -0.0019








TABLE 19


METASTABLE HELIUM IN HELIUM, 45
ANGULAR RESOLUTION -30 Ps =


VOLT ELECTRONS
36 x 10-3 mm


i0
Sx 104 iTSCLT+ 'T i iSCLT- log
b'iT+


0.06 13.15 0.00 0.20 0.00 0.0066
2.36 11.40 0.05 0.25 0.80 0.0400
3.78 10.20 0.15 0.20 1.30 0.0651
7.91 8.20 0.30 0.25 2.60 0.1412
8.24 7.55 0.25 0.20 2.55 0.1453
12.08 6.30 0.50 0.20 3.20 0.2093
13.56 5.75 0.45 0.20 3.70 0.2446
17.44 4.85 0.65 0.25 4.15 0.3099
21.99 3.85 0.75 0.20 4.45 0.3807
24.76 3.35 0.90 0.20 4.65 0.4340

Slope = 175.1 Intercept = 0.0001




TABLE 20

METASTABLE HELIUM IN HELIUM, 30 VOLT ELECTRONS
ANGULAR RESOLUTION -122' Ps = 35 x 10-3 mm



p x 104 iT iSLT i_ SCLT- log
T SCLT+ T-iT+


0.10 9.00 0.35 0.20 3.75 0.1696
1.39 7.95 0.45 0.20 4.25 0.2085
2.13 7.75 0.40 0.20 4.40 0.2162
2.89 7.05 0.40 0.20 4.55 0.2382
5.62 5.70 0.60 0.20 5.35 0.3178
8.93 4.25 0.50 0.15 5.70 0.3969
9.99 3.95 0.70 0.15 6.00 0.4368
12.83 3.15 0.90 0.15 6.20 0.5187
15.32 2.65 0.90 0.15 6.50 0.5854
15.45 2.65 0.80 0.15 6.70 0.5896
19.79 1.95 1.05 0.15 6.80 0.7078

Slope = 276.2 Intercept = 0.1610









TABLE 21

METASTABLE HELIUM IN HELIUM, 35 VOLT ELECTRONS
ANGULAR RESOLUTION -1l22' P = 34 x 10-3 mm


i0
p x 104 i i i iCT- log .-
T+ SCLT+ T- SCLT_ IT+


0.10 8.95 0.35 0.20 3.65 0.1671
1.39 8.00 0.45 0.20 4.10 0.2024
2.13 7.75 0.50 0.20 4.25 0.2145
2.89 7.10 0.45 0.20 4.50 0.2368
5.62 5.75 0.60 0.20 5.25 0.3122
8.93 4.40 0.65 0.15 5.65 0.3920
9.99 4.05 0.75 0.15 5.95 0.4300
12.83 3.30 0.85 0.15 6.10 0.4985
15.32 2.80 0.85 0.15 6.40 0.5614
15.45 2.80 0.90 0.15 6.50 0.5678
19.79 2.10 1.10 0.15 6.65 0.6778

Slope = 260.9 Intercept = 0.1632




TABLE 22

METASTABLE HELIUM IN HELIUM, 45 VOLT ELECTRONS
ANGULAR RESOLUTION 1022' Ps = 34 x 10-3 mm



io
p x 104 iT+ iSCT+ iT_ SCLT log1 T-
DT+

0.10 8.35 0.35 0.20 3.35 0.1665
1.39 7.45 0.40 0.20 3.65 0.1960
2.13 7.30 0.40 0.20 3.90 0.2085
2.89 6.70 0.40 0.20 4.00 0.2270
5.62 5.45 0.50 0.20 4.80 0.3030
8.93 4.25 0.55 0.15 5.10 0.3733
9.99 3.95 0.75 0.15 5.30 0.4099
12.83 3.25 0.80 0.15 5.50 0.4749
15.32 2.80 0.85 0.15 5.75 0.5328
15.45 2.85 0.90 0.15 5.95 0.5386
19.79 2.15 1.00 0.15 6.00 0.6360

Slope = 242.7 Intercept = 0.1611









TABLE 23

METASTABLE HELIUM IN NEON, 30 VOLT ELECTRONS
ANGULAR RESOLUTION -8053' Ps = 31 x 10-3 mm


4ji0
Sx 104 iT_ SCLT+ iT_ iSCLT log --
Si-T+


0.07 12.05 0.00 0.15 0.50 0.0228
3.60 10.75 0.15 0.30 1.10 0.0585
5.00 10.25 0.35 0.30 1.30 0.0756
7.50 9.20 0.45 0.35 1.70 0.1044
11.00 7.35 0.60 0.40 2.40 0.1438
12.75 7.35 0.60 0.40 2.40 0.1651
15.65 6.40 0.60 0.40 2.65 0.1960
21.45 5.30 0.90 0.50 3.20 0.2714
22.30 5.40 0.95 0.50 3.25 0.2719
25.35 4.70 1.00 0.55 3.35 0.3102
29.03 4.25 1.05 0.50 3.65 0.3470
30.40 4.10 1.10 0.55 3.80 0.3672

Slope = 114.6 Intercept = 0.0183




TABLE 24

METASTABLE HELIUM IN NEON, 35 VOLT ELECTRONS
ANGULAR RESOLUTION 8053' Ps = 31 x 10-3 mm



p x 104 iT+ iSCLT iT iSCLT log -0
oT+

0.07 11.70 0.00 0.15 0.45 0.0217
3.60 10.50 0.15 0.30 1.05 0.0580
5.00 10.05 0.25 0.30 1.20 0.0697
7.50 9.10 0.35 0.30 1.60 0.0960
11.00 8.10 0.45 0.40 2.10 0.1349
12.75 7.40 0.50 0.40 2.25 0.1540
15.65 6.50 0.55 0.40 2.45 0.1827
21.45 5.45 0.75 0.45 2.95 0.2459
22.30 5.50 0.75 0.50 3.10 0.2531
25.35 4.85 0.85 0.50 3.20 0.2874
29.03 4.50 0.95 0.50 3.40 0.3176
30.40 4.25 1.00 0.50 3.55 0.3401
Slope = 104.9 Intercept = 0.0191









TABLE 25

METASTABLE HELIUM IN NEON, 45 VOLT ELECTRONS
ANGULAR RESOLUTION -8053' Ps = 31 x 10-3 mm


i0
p x 104 i iSCLT+ iT SCLT- logT


0.07 11.20 0.00 0.10 0.40 0.0190
3.60 9.95 0.10 0.25 1.00 0.0553
5.00 9.60 0.20 0.25 1.05 0.0631
7.50 8.70 0.30 0.30 1.45 0.0919
11.00 7.75 0.35 0.35 1.90 0.1256
12.75 7.10 0.45 0.35 2.00 0.1444
15.65 6.25 0.45 0.35 2.20 0.1703
21.45 5.35 0.60 0.40 2.60 0.2235
22.30 5.40 0.60 0.45 2.80 0.2338
25.35 4.80 0.80 0.45 2.75 0.2632
29.03 4.45 0.85 0.45 2.95 0.2920
30.40 4.25 0.85 0.45 3.10 0.3086

Slope = 94.7 Intercept = 0.0206




TABLE 26

METASTABLE HELIUM IN NEON, 30 VOLT ELECTRONS
ANGULAR RESOLUTION -6021' Ps.= 38 x 10-3 mm



i0
p x 104 iT+ iSCLT iT iSCLT log
iT+

0.06 15.25 0.00 0.15 0.65 0.0222
4.25 13.00 0.30 0.25 1.95 0.0764
5.31 12.00 0.40 0.30 2.15 0.0925
8.62 10.80 0.60 0.30 2.90 0.1309
9.16 10.30 0.65 0.35 2.90 0.1394
13.56 8.70 0.90 0.40 3.70 0.1972
15.06 8.10 0.95 0.35 4.00 0.2186
19.48 7.00 1.10 0.40 4.60 0.2722
21.96 6.10 1.15 0.40 4.75 0.3081
26.21 5.35 1.40 0.40 5.10 0.3598
29.83 4.75 1.50 0.40 5.40 0.4043

Slope = 127.7 Intercept = 0.0210









TABLE 27

METASTABLE HELIUM IN NEON, 35 VOLT ELECTRONS
ANGULAR RESOLUTION -6021' Ps = 38 x 10-3 mm


i0
p x 104 iT+ iSCLT+ iT_ iSCLT- log
iT+


0.06 15.30 0.00 0.15 0.65 0.0221
4.25 13.10 0.25 0.25 1.90 0.0730
5.31 12.10 0.30 0.30 2.10 0.0875
8.62 10.95 0.50 0.30 2.85 0.1249
9.16 10.55 0.55 0.35 2.85 0.1321
13.56 9.00 0.75 0.40 3.60 0.1841
15.06 8.50 0.80 0.35 3.80 0.1993
19.48 7.40 0.95 0.40 4.40 0.2497
21.96 6.60 1.05 0.40 4.55 0.2808
26.21 5.80 1.30 0.40 4.90 0.3300
29.83 5.25 1.40 0.40 5.30 0.3715

Slope = 116.2 Intercept = 0.0249




TABLE 28

METASTABLE HELIUM IN NEON, 45 VOLT ELECTRONS
ANGULAR RESOLUTION -6021' P = 38 x 10-3 mm



jo
p x 104 iT+ iSCLT+ iT iSCLT- log i
iT+


0.06 14.45 0.00 0.15 0.60 0.0220
4.25 12.40 0.20 0.20 1.70 0.0680
5.31 11.55 0.25 0.25 1.75 0.0773
8.62 10.75 0.40 0.30 2.50 0.1131
9.16 10.10 0.50 0.30 2.40 0.1195
13.56 8.80 0.65 0.35 3.10 0.1661
15.06 8.35 0.70 0.30 3.30 0.1804
19.48 7.35 0.85 0.35 3.85 0.2271
21.96 6.70 0.95 0.35 4.05 0.2549
26.21 6.00 1.10 0.35 4.35 0.2937
29.83 5.40 1.15 0.40 4.75 0.3358
Slope = 104.5 Intercept = 0.0233









TABLE 29

METASTABLE HELIUM IN NEON, 30 VOLT ELECTRONS
,:AULT.' RESOLUTION -50 P, = 37 x 10-3 nm


io
p x 104 iT iSCLT+ iT_ iSCLT log
iT+

0.07 14.70 0.00 0.10 0.60 0.0202
5.76 11.40 0.50 0.25 2.25 0.1015
7.77 9.50 0.45 0.25 2.45 0.1244
11.11 8.80 0.70 0.25 3.20 0.1678
11.97 8.35 0.70 0.25 3.25 0.1770
15.77 7.20 0.85 0.25 3.85 0.2272
17.45 6.90 0.95 0.30 4.10 0.2493
20.03 5.85 1.00 0.30 4.30 0.2917
24.51 4.85 1.15 0.25 4.70 0.3537
27.37 4.45 1.25 0.30 4.90 0.3891
27.80 4.45 1.35 0.25 5.10 0.3989

Slope = 136.1 Intercept = 0.0173




TABLE 30

METASTABLE HELIUM IN NEON, 35 VOLT ELECTRONS
ANGULAR RESOLUTION -50 Ps = 37 x 10-3 mm



io
p 04 'T. 'SCL logr i
Sx 104 iSCLT+ iT_ iSCLT- log
'T+


0.07 14.55 0.00 0.10 0.50 0.0175
5.76 11.50 0.40 0.25 2.15 0.0946
7.77 10.05 0.40 0.25 2.40 0.1151
11.11 8.90 0.60 0.25 3.10 0.1595
11.97 8.50 0.60 0.25 3.10 0.1658
15.77 7.40 0.75 0.25 3.75 0.2153
17.45 7.10 0.85 0.30 3.95 0.2351
20.03 6.10 0.95 0.30 4.15 0.2754
24.51 5.15 1.10 0.25 4.45 0.3276
27.37 .4.75 1.15 0.30 4.60 0.3567
27.80 4.75 1.25 0.25 4.85 0.3686

Slope = 124.7 Intercept = 0.0199









TABLE 31

METASTABLE HELIUM IN NEON, 45 VOLT ELECTRONS


ANGULAR RESOLUTION -50


Ps = 37 x 10-3 mm


p x 104 iT iSCLT iT iSCLT log
I -iT+


0.07 13.75 0.00 0.10 0.45 0.0170
5.76 11.00 0.30 0.20 1.85 0.0841
7.77 9.95 0.35 0.20 2.15 0.1043
11.11 8.65 0.55 0.25 2.75 0.1493
11.97 8.15 0.50 0.20 2.75 0.1570
15.77 7.20 0.65 0.20 3.30 0.1977
17.45 6.95 0.75 0.25 3.55 0.2187
20.03 6.05 0.75 0.25 3.65 0.2476
24.51 5.20 0.95 0.25 3.85 0.2947
27.37 4.85 1.00 0.25 4.20 0.3271
27.80 4.85 1.10 0.25 4.30 0.3354

Slope = 112.8 Intercept = 0.0203




TABLE 32

METASTABLE HELIUM IN NEON, 30 VOLT ELECTRONS
ANGULAR RESOLUTION 30 Ps = 44 x 10-3 mm



p x 10 i+ iSCLT+ iT iSCLT- log



0.08 17.30 0.00 0.20 0.00 0.0050
2.67 14.80 0.15 0.25 1.35 0.0485
5.82 9.35 0.25 0.20 1.95 0.0992
6.44 12.05 0.35 0.25 2.80 0.1080
9.12 7.80 0.35 0.20 2.65 0.1493
12.93 8.65 0.70 0.25 4.45 0.2107
13.35 6.30 0.50 0.25 3.45 0.2219
16.38 7.25 0.80 0.30 5.00 0.2651
21.53 5.60 0.95 0.30 5.75 0.3522

Slope = 160.5 Intercept = 0.0048









TABLE 33


NET.-.:STABLE liiLLl IN NEON, 35 VOLT


ANGULAR RESOLUTION 30


Ps = 44 x


p x 104 iT+ iSCLT+ iT_ iSCLT_ log
'T+


0.08 17.40 0.00 0.20 0.00 0.0050
2.67 15.00 0.20 0.25 1.25 0.0466
5.82 9.55 0.25 0.20 1.90 0.0956
6.44 12.45 0.35 0.25 2.65 0.1007
9.12 8.15 0.30 0.20 2.50 0.1361
12.93 9.00 0.60 0.25 4.30 0.1965
13.35 6.60 0.40 0.25 3.30 0.2037
16.38 7.65 0.80 0.30 4.80 0.2483
21.53 6.05 0.90 0.30 5.45 0.3221

Slope = 146.4 Intercept = 0.0072




TABLE 34

METASTABLE HELi.u IN NEON, 45 VOLT ELECTRONS
ANGULAR RESOLUTION -30 Ps = 44 x 10-3 mm



'0
p x 104 iT+ iSCLT+ iT_ iSCLT- log
T7+

0.08 16.35 0.00 0.20 0.00 0.0053
2.67 14.25 0.15 0.25 1.10 0.0435
5.82 9.10 0.15 0.20 1.65 0.0863
6.44 11.85 0.25 0.25 2.35 0.0936
9.12 7.90 0.25 0.20 2.20 0.1256
12.93 8.85 0.50 0.25 3.75 0.1785
13.35 6.60 0.35 0.25 2.90 0.1848
16.38 .7.65 0.60 0.30 4.10 0.2184
21.53 6.25 0.70 0.30 4.80 0.2851

Slope = 128.9 Intercept = 0.0110


ELECTRONS
10-3 mm








TABLE 35

METASTABLE HELIUM IN NEON, 30 VOLT ELECTRONS
ANGULAR RESOLUTION 1022' Ps = 32 x 10-3 mm


p x 104 iT+ iSCLT+ iT iSCLT- log io
iT+


0.06 9.70 0.30 0.20 3.75 0.1578
1.67 8.70 0.40 0.20 4.30 0.1940
3.05 7.90 0.45 0.20 4.60 0.2213
4.31 7.15 0.45 0.20 4.75 0.2443
6.10 6.50 0.55 0.20 5.45 0.2909
8.60 5.55 0.65 0.20 5.70 0.3385
9.36 5.05 0.65 0.20 5.80 0.3649
12.18 4.25 0.75 0.20 6.10 0.4247
15.11 3.70 0.80 0.20 6.45 0.4791
16.81 3.30 0.85 0.20 6.50 0.5169
19.16 2.95 1.00 0.20 6.80 0.5696

Slope = 215.5 Intercept = 0.1569




TABLE 36

METASTABLE iiLLlF.! IN NEON, 35 VOLT ELECTRONS
ANGULAR RESOLUTION 1022' Ps = 32 x 10-3 mm




p x 104 iT iSCLT+ iT iSCLT- log0
iT+


0.06 9.65 0.30 0.20 3.65 0.1553
1.67 8.75 0.45 0.20 4.20 0.1915
3.05 8.00 0.45 0.20 4.55 0.2175
4.31 7.30 0.45 0.20 4.65 0.2370
6.10 6.60 0.60 0.20 5.35 0.2859
8.60 5.75 0.60 0.20 5.55 0.3231
9.36 5.35 0.65 0.20 5.70 0.3472
12.18 4.55 0.75 0.20 5.90 0.3989
15.11 4.00 0.85 0.20 6.35 0.4548
16.81 3.65 0.85 0.20 6.45 0.4861
19.16 3.15 0.85 0.20 6.55 0.5375

Slope = 197.1 Intercept = 0.1581









TABLE 37


METASTABLE HELIUM IN NEON, 45 VOLT


ANGULAR RESOLUTION 1022'


Ps = 32


ELECTRONS
x 10-3 mm


0i
Sx 104 iC iLT iT_ iSCLT_ log
SCLT+ iT+


0.06 9.00 0.30 0.20 3.35 0.1547
1.67 8.20 0.40 0.20 3.90 0.1900
3.05 7.55 0.45 0.20 4.00 0.2084
4.31 6.90 0.40 0.20 4.15 0.2275
6.10 6.35 0.50 0.20 4.80 0.2709
8.60 5.60 0.60 0.20 4.95 0.3068
9.36 5.25 0.60 0.25 5.05 0.3271
12.18 4.50 0.70 0.20 5.20 0.3721
15.11 4.00 0.80 0.20 5.75 0.4294
16.81 3.75 0.80 0.20 5.95 0.4553
19.16 3.30 0.90 0.20 6.05 0.5006

Slope = 179.3 Intercept = 0.1561















VITA


Hubert Lyle Richards was born in Russell, Kentucky,

on August 22, 1935. After attending elementary and secondary

schools in Russell, he attended Eastern Kentucky State College

in Richmond, Kentucky, from which he received the B. S. degree

in May, 1957. In September, 1957, he entered the Graduate School

of the University of Kentucky in Lexington, Kentucky, where he

received the M. S. in 1960. Since September, 1960, he has been

enrolled in the Graduate School of the University of Florida

working toward the Ph. D. degree.














This dissertation was prepared under the direction of

the chairman of the candidate's supervisory committee and has

been approved by all members of that committee. It was submitted

to the Dean of the College of Arts and Sciences and to the

Graduate Council, and was approved as partial fulfillment of the

requirements for the degree of Doctor of Philosophy.



June 20, 1963




Dean, College of Arts an- Siences



Dean, Graduate School


Supervisory Committee:



Chairman '







Pr^~ ja i
I\ L^ ^ w










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AUTHOR: Richards, Hubert
TITLE: Angular dependence of the scattering of metastable helium atoms in
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PUBLICATION DATE: 1963


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