ATOMIC BEAM MEASUREMENTS OF LIFETIMES OF
METASTABLE EXCITED STATES.
with particular reference to
TEE INFLUENCE OF ELECTRIC FIELDS ON TEE
LIFETIMES OF ATOMS IN METASTABLE STATES.
A Thesis for the Degree of Doctor of Philosophy in the School of Physics, University of New South Wales.
Submitted by:
A.S. PEARL. October, 1967 ABSTRACT
An atomic beam method was used to examine the influence of an electric field on the lifetime of the 2^S metastable state of o the helium atom.
The (21S - 1^S) transition probability in the presence of an electric field was observed to depend on the electric field strength, F, according to
2 w (F) = w + aF o where wq is the natural decay rate of the
2^S state and
a = 0.40 (KVcm ^sec ^
Evidence Is presented to show that the natural decay rate is given by
w ^ 770 sec ^ o corresponding to a maximum lifetime of 1.3m sec. TABLE OF CONTENTS
Page No.
Chapter 1 INTRODUCTION 1
Chapter 2 HISTORICAL BACKGROUND 8
Introduction 8
2.1 Discovery and Classification of Forbidden Transitions 8
2.2 Forbidden Transitions Induced by Electric and Magnetic Fields 12
2.3 The i'etastability of the 2S < State in Hydrogen ~ 24
2.4 Electrostatic Quenching Measurements 30
2.5 Recent Work on Double Quantum Emission 31 1 2. G The Metastability of the 2 S and 3 2 S Helium Levels 34
Chapter 3 THEORY 36
Introduction 36
3.1 Spontaneous Forbidden Transitions in Radiation Theory 37
3.2 The Selection Rules 42
3.3 Higher Multipole Radiation 45
3.4 Multiple Quantum Transitions 47 1 3.5 The Natural Lifetime of the 2 S State of Helium 49 I d re No.
5.6 Forbidden Transitions in External Fields 51
3.7 Lifetime of He 2^S in an Electric Field 53
Chapter 4 METHODS AND BJJIBLSNT 61
Introduction 61
4.1 Method - General Description 61
4.2 Formation of Beam 62
4.3 Production of •¥etastable Sta tes 67
4.4 Detection of Atoms in Meta stable States 71
4.5 lhoton Detection 76
4.6 Calibration of lhoton Detection 78
4.7 The Electric Field 84
4.8 Experiment 1 and 2 - Analysis and Description 85
Chapter 5 E PERTH ENTAL RESULTS 94
5.1 Experiment 1 94
5.2 Sources of Spurious Photon Detector Signal 99
5.3 Estimate of the Lifetime of the 1 2 S Level by ihoton Counting 105
5.4 Deduction of the He 2^S Natural Lifetime from Data on Helium Afterglows 110
5.5 Experiment 2 - Electric Field Attenuation of ;:efcastable Flux 115
5.5 Summary and Comparison of Results 116 Chapter 6 ADDITIONAL EX] FJRIiv: ENTS 122
Introduction 122
6.1 Ratio of the He 2XS and 2 S Electron Impact Excitation Functions 122
6.2 Pressure Dependence of Photon Signal 127
6.3 Attenuation of Feta stable Beam by Helium Gas 133
6.4 Test for Double Quantum Decay 140
Chapter 7 CONCLUSION 142
7.1 Resume 142
7.2 Discussion 145
APPENDICES 150
A1 Solid Angle Determination 150
A2 Electron Impact Deflections 155
A3 He (n^F - l^S) Resonance Radiation 159
A4 Distribution of Velocity in the Atomic Beam 163
A5 Voltage Calibration 167
A CKNOVt LEDG'3’ ~EPiT 168
BIBLIOGPAPHY 169 1
CHAPTER 1. INTRODUCTION.
The purpose of this research was to investigate the influence of an electric field on the radiative decay of the metastable 2^S
Ievel of helium.
Forbidden Transitions.
When an atom emits or absorbs radiation It does so in discrete amounts determined by the restrictions on changes In Its Internal energy and angular momentum. The most general of the selection rules which apply to all atoms are:=
(i) In an electric dipole (allowed) transition the total
angular momentum of the atom either remains unchanged
or changes by unity I.e. the permissable changes In the
angular momentum fJT in units offiare described by relation
AJ = 0, ± 1
with the additional restriction that transitions between
zero angular momentum states
J = 0 —J = 0
are strictly forbidden, I.e. forbidden for all first
order (single photon) processes.
(ii) In an electric dipole transition, there must be a change
of parity between the initial and final states.
For light atoms, In which there is negligible Interaction between the magnetic moments associated with the spin and orbital angular momentum, the above selection rule for J may be resolved info two independent rules, viz., AL 0 ± 1
L *■ 0 —L = 0 strictly forbidden where L Is the total orbital angular momentum of the atom, and AS = 0 where S is the total spin of the atom.
For example, the He (2^S - 1^S) transition Is doubly forbidden, because the Initial and final states are spherically symmetric (J = 0) and because both states have the same parity. Since there are no alternative downward transitions available, (Fig. 1.1), the 2^S state Is metastable. There is a small probability of the occurrence of transitions which contravene these selection rules. Such transitions have been called forbidden transitions. Forbidden transitions can be spontaneous or enforced.
Spontaneous forbidden transitions fall into two classes:
(i) first order (higher multipole) transitions.
(ii) second order transitions which Involve the simultaneous
emission of two photons.
In the absence of a field, the He 2^S state is expected to decay via the emission of two photons, because all single photon transitions are strictly forbidden.
Perturbations external to or within the atom can lead to the occurrence of forbidden transitions. An external electric field modifies the charge distribution of an atom In a particular state and hence the applicability or "goodness" of Its orbital quantum number. In wave mechanical terms, an electric field "mixes" the wave function of the E n erg yin eV 2
I I
2 3 I
's s S
20.61 2
1.1. P __ Ionization 2
1.22 2-1° Vi
'
nw
24.59 2 3
jiff 3 3
S S ]
ji
eV r;
vcfy 19.82 22.72 3 2
3 3p P P
20.96 3D 3 initial state with components of the wave function of energetically adjacent levels to which it is optically coupled. Thus it was anticipated that application of an electric field to helium atoms in the metastable 2^S state, would enhance the probability of the doubly forbidden (2^S - 1^S) transition. Interatomic and ionic electric fields in the cathode fall of discharges can cause the appearance of forbidden lines: lines arising from the electric field weakening of the azimuthal selection rule are known to spectroscopists as "enforced dipole lines". Some experiments on enforced dipole radiation were conducted in the 1930’s. The essential qualitative features were elucidated by a series of experiments in which the enforced lines were observed by the application of external electric fields to absorption cells. The Zeeman spectra of enforced radiation were studied by the simultaneous application of external electric and magnetic fields. The Hydrogen Metastable State, H2Si ______2_* The choice of topic of this thesis was influenced by a series of post war experiments with atomic beams containing hydrogen atoms in the metastable 2S,state, (Lamb & Retherford (1951), Fite et a I 2 7 (1959)). The H2S± level is metastable because transitions to the ground 2 state are forbidden, both by the rule which strictly prohibits transitions between L = 0 states, and by the requirement of a change of parity. However, because of the near degeneracy of the 2S, and 2P± levels, the 2 2 wave function of the 2Si level is particularly susceptible to electric 4
field mixing with the 2P± wave function, weakening the metastability 2 of the 2S± level by causing it to undergo enforced dipole transitions 2 to the ground state.
In these experiments which are described In the next
Chapter of this thesis, the density of 2SL atoms was determined by 2 completely guenching them in electric fields/v 50Vcm \ Although
Bethe (1933) and Lamb & Retherford (1951), had calculated the life
time of the H2S± level in an electric field, no attempt was made to 2 measure it.
Fite et al (1959) measured the natural lifetime of the
H2S± level, and found that it decays by single quantum emission at 2 a rate about fifty times greater than the theoretically predicted
(double photon) decay rate.
Subsequent to the commencement of the present project,
I.A. Sell in (1964) verified experimentally, the calculations of
Lamb and Bethe (loc cit) pertaining to the lifetime of the H12S, 2 state In the presence of an electric field.
Description of Present Project.
Thus the present project, was concerned with two kinds of forbidden transition -
(i) Two photon transitions, the expected mode of decay
of the He 2^S level In the absence of a field.
(il) Enforced dipole single photon transitions, with
particular referenced the influence of an electric
field on the decay rate of the He 2^S state. 5
In the case of the latter, since the relevant dipole matrix
elements were known (Schiff & Peskeris, 1964) and calculation of the
theoretical ’’quenching'’ is a relatively simple matter, it was possible
to effect a direct comparison between experiment and theory. In the
former case, the quest for an experimental estimate of the natural
lifetime of the He 2^S level, was given added impetus by the
publication (Dalgarno, 1966) of an accurate theoretical calculation
in which the lifetime of the 2^S state was limited by double quantum -2 emission to a value of 2.2 x 10 sec.
The basic plan of the experiment is illustrated schematically
in Fig. 4.1. An atomic beam method was chosen as useful densities of
helium atoms in the metastable 2^S and 2^S states could be achieved,
in a small volume. By use of a flat, rectangular section beam large
fields could be achieved with closely spaced electric field plates.
A beam of helium atoms in metastable states was produced by electron bombardment of a thermal atomic beam of helium. Because of the longevity (^10 ^sec) of these levels on a gas kinetic time scale, the majority of the atoms In metastable excited states (hereafter called metastables) can traverse the length of the system without undergoing radiative decay, to strike the platinum beam target. The metastables were detected by their electron ejection from the beam target which was electrically connected to ground through an electrom eter; the detector did not respond to the (thermal energy) ground state atoms. 6
En route to the detector, the metastable beam passed through an electric field applied between two plane parallel condenser plates.
A (windowless) electron multiplier, capable of responding to photons emitted during the radiative decay of the metastables, viewed the beam between the electric field plates, transverse to the field. Changes
In the lifetime of the 2^S level by the electric field, could be detected in two ways:
(i) by the reduction In the beam target signal due to
the increased decay rate In the electric field.
(ii) by the corresponding field induced photon emission
fromi the beam, registered by the electron multiplier.
By measuring the field dependent attenuation of the beam, and the enhanced photon emission from the beam, it is possible In principle to estimate both the ’’^quenching coefficient" and the field free lifetime.
Dlscussion.
The theoretical importance of the hydrogen and hydrogen like atoms lies In the fact that quantum mechanical calculations of their properties have exact analytical solutions.
The helium and helium like atoms (H , Ll+, etc) are the simplest atomic systems in which the interaction between electrons may be examined. It is this interaction which has frustrated attempts to find exact analytical solutions to calculations relating to the helium atom and its isoelectronic sequence. The relative simplicity of two electron systems, however, make them amenable to highly accurate 7
calculations using approximation methods. Some of the energy values of
the helium atom have been calculated to a degree of accuracy which
exceeds the limits of spectroscopic precision.
Thus an experimental study of the helium atom provides a
test for the various approximation methods of calculation which can be
extended to more complex systems. In addition, the quantum electro
dynamic theories of the interaction between electrons, can be tested
by an experimental study of the helium atom.
A study of the metastable states of one and two electron
atoms and ions is also interesting because they are zero angular momentum states with a high electron probability density close to
the nucleus, where quantum electrodynamic effects, involving
relativity and the radiation field, are largest. 8 CHAPTER 2. HISTORICAL BACKGROUND.
INTRODUCTION.
In this chapter we do not aspire to historical completeness: reviews of forbidden transitions may be found in
Mrozowski (1944), Borisoglebsku (1958) and Garstang (1962).
The aim here is rather to describe those developements which influenced the choice of the topic of this thesis.
As the present investigation is primarily concerned with the influence of an electric field on the lifetime of the 2^S state in helium, attention is directed to the two types of forbidden transition relevant to this question. I.e. enforced dipole transitions and two quantum processes.
2:1. DISCOVERY AND CLASSIFICATION OF FORBIDDEN TRANSITIONS
The establishment in 1908, of the Ritz Combination rule was the culmination of twenty years of work on the empirical organization of spectra. The fact that few of the transitions energetically consistent with the Ritz Combination Rule actually occurred, led to the empirical formulation of the optical selection rules for atomic spectra. Bohr was subsequently able to justify these rules smd on the basis of the correspondence principle and Schrodinger derived them quantum mechanically. 9
As early as 1915 lines which violated these rules were observed. Koch (1915) noted the appearance of Mnew" helium lines when the spectrum was produced in an electric field. Following this
Stark (1915) and his associates were able to produce long series of
''forbidden” lines in helium whose intensities increased with the electric field strength. The lines produced were 3C 23S —* n S, 23p n3P (4| = 0)
23P —- n3F etc. ( A 1 = 2) contravening the restriction (Al = :£1) on the azimuthal quantum number. The term "forbidden" is used in this context to describe transitions which contravene the selection rules.
(a) Forced Dipole Radiation
J.S.Foster (1924,1927) used matrix mechanics in the developement of the theory of the Stark Effect for non hydrogenic atoms and applied it to his own observations on helium. The agreement between the calculated and observed shifts was good. The appparance of forbidden lines whose intensities were field dependent was explained and there was qualitative agreement between the calculated intensities and the observed intensities.
Forbidden transitions arising from the weakening of the azimuthal selection rule in an electric field were called "enforced i. dipole transitions". The forbidden lines were In the majority of cases, observed to increase in intensity with increasing pressure and current.
In fact, the intensities often increased quadraticaI Iy with the current. 10
The occurrence of such forbidden transitions was correctly attributed
to enforced dipole radiation.
(b) Mu Itipole Radiation.
Initially, all forbidden lines were thought to be due to
enforced dipole transitions, but more careful work at low pressures and currents revealed the existence of a second class of forbidden
transitions whose intensities were a maximum at low currents and low
pressures. The observations by Datta (1922) and Lord Rayleigh (1927) of forbidden transitions in absorption provided further evidence for the existence of spontaneous forbidden transitions.
In the eatrly 1920's most of the spectral lines which could be produced in the laboratory, had been identified. Some lines observed
in the spectra of planetary nebulae, the solar corona and aurorae were not able to be produced in laboratory sources and hence defied classi fication. Perhaps the greatest impetus to the study of forbidden transitions per se, came from the identification by McLennan (1925) of the auroral A5577 line with a forbidden transition in 0 I, and the' later identification of the nebular lines by Bowen (1928) with forbidden lines in ionized oxygen and nitrogen. The fact that forbidden transitions occurred in nebulae was the most striking evidence for their spontaneous nature, as atom densities in nebulae are~10cm
The explanation of the occurrence of these spontaneous forbidden lines was given by Rubinowicz (1928-30) and Brinkman (1932).
A re-examination of the classical theory of a radiating dipole revealed 11
that, when the dimensions of the dipole were non-negligible in
comparison with the radiated wave length, in a higher approximation
electric quadrupole and magnetic dipole terms are included and some
forbidden lines in spectra can be associated with this classical
multi pole radiation.
(c) Intercombination Transitions.
The occurrence of intercombination lines (contravening the AS = 0 rule) was successfully interpreted in terms of the inter action between electrons in the heavier atoms and the breakdown of
Russel Saunders coupling.
(d) Nuclear Perturbations.
The(>2270 and 2656 forbidden lines in mercury and corresponding lines in atoms isoelectronic with mercury, could not be accounted for in terms of external perturbations, multipole radiation or electronic interactions.
It was not until 1938 that Opechowski and Mrozowski showed that such transitions were caused by the existence of non zero nuclear magnetic moments in the Hg isotopes 199 and 201. The magnetic moment
interacts with the orbital angular momentum to cause electric dipole transitions in apparent violation of the^J = 0, ± 1 selection rule.
(e) Two Photon Transitions.
Whilst transitions between spherically symmetric (J = 0) states are strictly forbidden for all single photon processes, they are weakly permitted for two photon processes. The two photons are emitted 12
r simultaneously and the energy of the transition is arbii/arily divided 2 between them. The probability of double quantum decay Is^(Zof-) smaller than that for allowed single photon transitions, i.e.^/IOsec \
Maria Goppert-Mayer (1929,1931) first discussed the possibility of double quantum decay In the optical region and showed that its prob ability can be expressed as a summation over a continuum of virtual intermediate states.
Subsequent theoretical calculations on the double quantum decay of the metastable states of helium and hydrogen are discussed in Section (2.4). The decay of these states contributes to the con tinuous spectra of planetary nebulae, with the major contribution coming from the decay of the H2Si state. (Seaton 1960).
2:2 FORBIDDEN TRANSITIONS INDUCED BY ELECTRIC AND MAGNETIC FIELDS.
As was mentioned earlier the origin of the forbidden lines whose intensity increased with current and pressure was ascribed to enforced dipole radiation from interionic and intermolecular fields.
Most of the work to be described below was on atomic spectra excited in gas discharges in which electric fields are usually the randomly oriented ionic fields in the cathode fall region. Some more precise work was done in which enforced lines were observed by the application of external electric fields to absorption cells. The helium and alkali forbidden series received the most attention. The work on lines enforced by external fields and observed in absorption 13
enabled a qualitative assessment of the general features of enforced dipole radiation to be made and compared with theory. Studies of the
Zeeman spectra of enforced lines enabled the unambiguous distinction between electric quadrupole and enforced dipole lines, to be made in cases where there was confusion.
Generally speaking there has been relatively little study of enforced dipole radiation and even less of a strictly quantitative nature.
(a) Early Work on Enforced Dipole Radiation.
One of the greatest achievements of the early quantum theory, was the successful interpretation of the Stark effect. Epstein (1916) and SchwartzchiId (1916) showed that the observed Stark splitting of the H Balmer lines, could be explained on the basis of the Bohr theory of the atom. Kramers (1919), by reference to the correspondence principle, was able to estimate the intensities of the hydrogen Stark components.
The Stark effect for elements other than hydrogen was markedly different from that of hydrogen. The spectra showed no splitting proportional to the field, but new lines appeared whose frequencies were sums and difference of the frequencies of lines in the old spectrum. Bohr showed that these facts could be explained by quantum theory and that the intensities of the "new” or enforced lines should depend on the square of the electric intensity. 14
Pauli (1925) calculated the intensities of enforced dipole
lines from the Kramer - Heisenberg dispersion theory (Kramers -
Heisenberg, 1925). He extended the expression for the dipole moment
induced by an oscillating electric field to the special case in which the atom is exposed to radiation of zero frequency, showing that in a static field forbidden transitions become possible. Pauli compared his calculations with the observations of Takermaine and Werner (1926) on the Stark spectrum of mercury and found "substantial" agreement.
Early work of particular relevance to this thesis was under taken by Miss J.M. Dewey (1926,1927) at Copenhagen. The relative
intensities of some enforced lines in the Stark spectrum of helium were calculated by the application of the theory of dispersion. The
intensities of enforced lines, relative to the intensities of the nearest permitted lines, were determined experimentally. The spectra were produced in a Lo Surdo discharge source in which the entire range of fields arises from variations of the space charge in the cathode fall region. The lines examined were:
He 1 2P « nM, 2P - nM, 2S - 4M
where n = 4, 5, 6, 7
M = P, D, F, G etc.
Miss Dewey found approximate agreement between the calculated and observed intensities. She did not discuss the measurement of the electri field, but estimated the overall errors in the observations to be 40$.
The relative intensities were determined photographically. Further calculations of the intensities of some enforced helium lines were done by Fuji oka (1929) 15
Foster (1924,1927) developed the theory of the Stark effect for non hydrogenic atoms, using matrix mechanics and applied it to his observations with remarkable success. The agreement between calculated and observed Stark shifts was good.
In most of Foster’s photographs forbidden lines appear with field dependent intensities which at the highest fields are comparable with the intensities of allowed lines. The lines violated the azimuthal selection rule and had a group symmetry like that encountered in the
Paschen Back effect.
(b) Distinguishing Features of Enforced Dipole Radiation.
The sensitivity of a forbidden transition to being enhanced in an ! electric field is dependent on the proximity to the initial level of neighbouring levels to which it is optically coupled, and which neighbouring levels are optically coupled to the final level.
This sensitivity also depends on the magnitudes of the dipole matrix elements connecting the rrrtHVCTTt levels.
As the principal guantum number increases the energy spacing between levels decreases, but so also do the dipole matrix elements between levels. These two counteracting variations cause the intensittes of the enforced lines in a given field, to increase with ascending principal quantum number, pass through a maximum and decrease at a slower rate than for a permitted series.
On such considerations Sambursky (1932) showed that the abnormally slow diminution in intensity in the forbidden series 2 2 2 P - m P of Na, can be explained on the assumption that forced dipole radiation is present. 16
Sambursky (1931) calculated the relative intensities In forbidden mu I tip lets and found "tolerable" agreement with measurements of Ag I and Cu I forbidden doublets. Mi Iianczuk (1934,1935) discussed the limits of applicability of the sum rules of Ornstein and Burger to enforced multiplets and made accurate calculations for the intensities . of the enforced multiplets of Cd I, Ag I and Cu I.
From the requirement of an optically connected perturbing level in energetic proximity to the initial level it was easy to deduce the selection rules for enforced electric dipole radiation. They were shown to be
A J = 0, ± 1, ±2, ^ M = 0 ± 1, ±2.
no change of parity.
With the exception of the rule 2, enforced dipole radiation has the same selection rules as electric quadrupole radiation and it was sometimes difficult to distinguish between the two, since they may 2 2 occur simultaneously. An example of such an overlap was in the D - S forbidden series in Kl observed by Kuhn (1930).
In most cases however, provided there was adequate spectro scopic resolution available, it was not difficult to distinguish between enforced electric dipole radiation and electric quadrupole radiation, as enforced lines were usually considerably broadened by the fluctuating ionic fields inducing them. Also for a series, the characteristic dependence of the intensity on the principled quantum number served to distinguish it from an electric quadrupole series. 17
(c) Ihhomoqenous Fields.
In most discharge work, it is a reasonable approximation to assume the constancy of the randomly directed ionic fields over the dimensions of the atom, because of the long range of Coulomb fields.
The uniform field approximation breaks down in a discharge when the current density is large and the atoms are in high excited states.
The electric dipole radiation induced by weak inhomogeneous fields was studied theoretically in great detail by Miliyanchuk (1949).
The selection rules for such radiation are essentially similar to those for electric octupole radiation. The intensity varies more rapidly with principal quantum number, than in the uniform field case, but otherwise the dependence has the same form.
(d) External Electric Field Enforcement.
It was clearly desirable, if the phenomenon of forced dipole radiation were to be investigated systematically, for an external electric field to be applied. Ionic fields are randomly oriented, fluctuating, only approximately constant over the dimensions of an atom, and difficult to evaluate. The most systematic observations of forced dipole lines were made in absorption in the presence of an external electric field.
Kuhn (1930), Bakker (1933), Segre (1934) and Amaldi (1934) 2 2 showed that the high members of the forbidden S - D series, as well 2 3 as those of the S - S series (in the alkali spectra) can be obtained in absorption by application of an electric field to sodium or potassium vapour. 18
The results of these experiments were discussed and success fully interpreted by Segre & Wick (1933). In zero field about 31 terms of the 4S - nP permitted series could be detected, but in the presence of a field, the higher members decreased in intensity and the limit of the series receded towards lower principal quantum numbers.
Complementing this fading of the higher members of the permitted series was a corresponding increase in the intensities of the higher members of the 4S - nD, 4S - nS forbidden series. The forbidden lines became visible at a certain value of n, and increased in intensity with
increasing principal quantum number passing through a maximum and fading away.
Segre & Wick showed that forced ionization, which had been previously postulated, could not explain this behaviour. Instead, by an examination of the perturbation theory of enforced dipole radiation they were able to demonstrate the existence of a sum rule connecting the disappearance of the permitted series with the appearance of the forbidden series. According to this rule, the sum of the intensities of all lines, (permitted and forbidden), having a common initial term, is Independent of the field, i.e. in the presence of a field the intensity of the permitted lines is transferred to the forbidden lines.
There was qualitative agreement between experiment and theory.
(e) Zeeman Spectra of Forced Dipole Radiation.
As was mentioned previously in some cases, for example in 2 2 the D - S series of it was not possible to decide whether electric 19
quadrupole or forced dipole transitions were responsible for the observed lines. However, enforced lines may be unambiguously
identified by their characteristic Zeeman spectrum which differs from that of electric quadrupole lines both in transverse and longit udinal observation: in the longitudinal direction electric quadrupole
compenents with 4m - ±2 are absent, but appear in the case of enforced dipole lines. The same applies to the 4m = 0 component in transverse observation.
Jenkins & Segre (1939) reviewed earlier work on the Zeeman effect for forced dipole lines. In the introduction to their paper these authors remark that relatively few cases of forced dipole lines are known and for only two of them had the Zeeman effect been studied.*
Bakker & Segre (1932) showed, by an examination of the 2 2 Zeeman spectrum, that the first member of the alkali S - D forbidden series, which is absorbed by sufficiently dense alkali vapour, was due to electric quadrupole radiation. Bakker & Segre studied the Mg ^3680 3 3 P2“ P2 line induced by unordered ionic fields and found a ’'satisfactory” agreement with a theoretical calculation by Majorana.
Jenkins & Segre (1939) studied the Zeeman spectrum of the
S - S and S - D forbidden lines in potassium. Lines from the continuous spectrum of a hydrogen lamp were absorbed by potassium vapour in an electric field of about 2000 V cm ^. The Berkley cyclotron magnet was used to produce a magnetic field of 27,000 gauss, perpendicular to the electric field. No effect on the series 4S - mS (m = 14 to 19) was observed except for a slight broadening of the last few lines. The
They overlooked the work of Steubing^&^Rej|ep|mng 20
Zeeman spectra of the 4S - nD (n = 12 to 15) series, were resolved, with the magnetic field perpendicular to the electric field and to the
direction of observation. The observed pattern agreed with the
theoretically predicted pattern and showed qualitatively the expected
intensities. It was also noted that the sum of the s components differs
from that of the ir components, whereas these sums are equal when the
lines are enforced by ionic fields.
One of the main difficulties with the experiment was the
nthe actual electric field in the vapour was less than the indicated
value by an indefinite amount, since a current of a few milliamperes
flowed continuously between the electrodes". 2 2 Although the S - D lines in the alkali vapours have
received the most attention, some work was done on enforced lines in
helium. J.S. Foster (1929 and 1931) studied certain singlet and
triplet lines produced in the Stark effect (ionic fields), but was
unable to resolve completely all the Zeeman patterns.
(f) Zeeman Effect of Enforced Lines in Helium.
Foster (1929,1931) investigated the helium spectrum in
parallel and perpendicular combinations of electric and magnetic fields.
He showed that the shifts due to parallel fields are additive and that
the Zeeman effect for the "sharp", "principal" and "diffuse" series
is independent of the magnitude of the electric field. The Zeeman
splitting of the enforced lines in helium was obtained by Foster only
for the Stark components 7} S,P,D - 5^ P,F, series. These 21
components are least shifted by the electric field. The higher components of the enforced lines, for which the shifts of the electric
fields are much larger, were too diffuse to allow observation of the
Zeeman spIittings.
Steubing & Redepenning (1935) examined enforced lines in the
heliijm spectrum in crossed electric and magnetic fields. They employed essentially the same system as Stark in which the electric field was applied between an external electrode and the perforated cathode; i.e.
the influence of the electric field on the "canal rays", was examined.
The magnetic field was applied perpendicular to the electric field we rg and observations or-ee made at right angles to both field directions.
The results were essentially qualitative and although the Stark and
Zeeman shifts of some lines were observed, the intensities were too
low to be measured.
L. Janssons (1935) performed a similar experiment in which a magnetic field was applied parallel to the electric field. In this experiment a Lo Surdo source was used in which the field arises from the space charge distribution in the cathode fall. The whole tube was placed between the poles of an electromagnet. The aim of the experiment was to study the Zeeman effect of enforced lines in helium, as knowledge of this phenomenon was "fragmentary" and such a study was
important for theories of their origin. 22
The Zeeman spectrum of the following helium transitions was studied;
21P - 51Q where Q = S,P,D,F,G whose wave lengths lie in a convenient part of the spectrum. The enforced lines were from the transitions
21P - 51P, 21P - 51F, 21S - 51G.
The total shift of a line due to the simultaneous influence of the electric and magnetic fields was the sum of the shifts due to these fields acting independently. On the other hand the total shifts in the case of Steubing & Redepenning's work (fields mutually perpen dicular) were greater than the shifts due to each field.
Janssons observed that the usual intensity rules for the
Zeeman components did not apply in the electric field, for example the sums of the intensities of the cr and tt components were not equal,
(implying a nett direction of the ionic fields). Theoretical and experimental wave lengths and relative intensities of the Zeeman components were tabulated and the agreement was good except for lines too close to be separated.
(g) Post War Work.
Jacquinot and Brochard (1945) were able to show by use of the Zeeman effect, that the lines,
21p - 41F ( * 4921)
23P - 43F ( *> 4471 ) and 51P ( A 4383) 23
in the helium spectrum were enforced (by ionic fields). The
2^P - 4^F line was of particular interest as it occurs in certain
B class stars, indicating the presence of electric fields.
The P - G transitions in the helium spectrum were also shown by their Zeeman effect to be forced dipole, rather than electric octupole transitions as had been previously supposed.
Another line studied by these authors was the 2V - 6^G transition and since the principal quantum number for the initial level is quite high, the ionic fields are "strong” fields and there are no restrictions on the original azimuthal quantum numbers. (A "strong" field is defined as one in which the Stark splitting of the Initial
level is comparable in magnitude with the field free multiplet splitting).
A further example of enforced electric dipole radiation was cited by Garstang (1962) in the spectrum of Pd I. Forbidden 9 3 9 transitions between the 4d 5d P, and the odd terms in 4d 5p were shown to be enforced lines. (Shenstone,1953).
(h) Magnetic Field Enforcement.
Forbidden lines induced by a magnetic fields have been observed by Vavilov (1950) in the P - D triplets of Ca I, Zn 1,
Cd I and in the (P - C>) doublets of A1 I and Ca II. Goudsmit &
Bakker (1930) observed the appearance of "extra" h.f.s. zeeman components whose intensity was proportional to the square of the external magnetic field strength. 24
Condon & Short ley (1963) describe on p.390 the appearance of forbidden lines in the Paschen Back effect. The 4s4d^D - 4s4p^P multiplet in Zn I was studied by Paschen & Back (1921) and by Van
Geel (1928). Van Geel measured the intensities of the forbidden
lines as a function of the magnetic field strength, and the agreement with the theoretical calculation of Zwaan (1928) was "very satisfactory".
For transitions in which J = 3 the intensity varied as the cube of the field, but for J = 2 transitions the intensity was proportional to the square of the field strength. Condon & Shortley (p.394) describe the Paschen Back breakdown of Russel Saunders coupling in
Hg I which leads to a magnetic field dependent intercombination line.
2:3 THE METASTAB11ITY OF THE 2S^ STATE IN HYDROGEN.
The metastability of the 2S± state in the hydrogen atom has 2 been the subject of considerable discussion and disagreement. (For a summary see Lamb and Retherford 1951). The elucidation of this question has played an important role in quantum electrodynamics. A discussion of it is pertinent to the present investigation for two reasons; as in the case of the 2^S and 2^S states of helium, the most probable mode of decay is, theoretically, by two photon emission, secondly, the quasi degeneracy of the 2S± and 2P± states (separated only by the Lamb Shift 2 2 (4x10 cV)) makes the 2S± state highly susceptible to electric field 2 quenching. 25
(a) Electrostatic Quenching:
According to the Dirac theory, the 2P± and 2S± states in hydrogen should be degenerate, and for this reason Rojansky and Van
Vleck (1928) argued that the 2S± state could never be metastable as 2 it would be mixed with the 2P± state in arbitarlly small electric 2 fields. Bethe (1933) published a systematic theory of the effect of an electric field on the fine structure of hydrogen and showed that an external field must be strong enough to cause a Stark splitting larger than the difference between the radiation widths of the two states before the metastability of the 2S± state was destroyed 2 According to Bethe the lifetime of the 2S± state varies inversely as the square of the field strength; in a field of 10V cm ^
Bethe estimated the lifetime to be about five times that of the 2P, 2 state. In zero field, the lifetime of the pure 28^ state supposedly 2 limited only by relativistic effects was of the order of months.
(b) Double Quantum Decay:
Breit & Teller (1940) discussed the role of metastability of the hydrogen and helium levels in astrophysics. They showed that inclusion of hyperfine structure splitting increased the stability of the H2S^ state against electric field quenching by a factor of four
The most significant feature of their paper was that they showed that by far the most probable mode of decay of the hydrogen and helium metastable levels was by double quantum emission. In the 26
usual approximation, the spontaneous single quantum decay of the
2S state in hydrogen is strictly forbidden and they showed that
such transitions are also strictly forbidden in the Pauli approxim
ation. If exact relativistic wave functions are used, magnetic
dipole radiation becomes weakly permitted with a transition probability -5 -1 of 10 sec . (i.e. a lifetime of about 2 days), the doubIquantum -1 1 decay, however, was estimated to be—7sec . The 2 S state in helium
was presumed to have a comparable lifetime but due to the prohibition
of intercombination transitions the lifetime of the 2^S state was 5 estimated to be of the order of 10 sec., although the dominant mode
of decay was still two photon emission.
(c) Nondegeneracy of H2S1 and 2P± States; the Lamb Shift. 2______2______
The first experimental demonstration of the metastability of H2S± state came when Lamb and Retherford (1947) produced an atomic 2 beam containing atoms in the 2S± state, by electron bombardment of a 2 beam of atomic hydrogen. The aim of the experiment was to use a magnetic resonance technique to investigate the fine structure of the
n = 2 levels In hydrogen.
Atoms in the metastable 2S± state were detected by their 2 electron ejection from a metal target. By observing variations in
this signal as a function of applied magnetic and microwave fields, they were able to show that, contrary to the prediction of the Dirac Theory, the 2S± and 2P± levels were not degenerate but the 2S± level was dis- 2 2 2 27 placed towards the continuum by 1051 Mc/s. Bethe (1947) success fully explained the shift of the 2S± level in terms of the interaction 2 of the electron with the zero point fluctuations of the radiation field in the vicinity of the nucleus.
The fact that there is an energy separation between the
2Sl and 2PL levels, enhances the stability of the 2S± state against 2 2 2 electric field quenching. Lamb and Retherford modified Bethe's expression for the lifetime\of the 2S± state in electric field, to 2 include the Lamb shift separation of the 2S± and 2PL states. The 2 2 lifetime in an electric field "^(F)" is 442 times as great as if there were no removal of the degeneracy.
1 = ys(F) Yp |<2S,|eFz| 2P,'>|2' where ys(F> V(PJ-+ 5 Vp2-)
= 2780 F2 sec-1 where }L(F) is the decay rate of the 2S, state in a "moderate'’ ^ 2 electric field of strength F applied in the negative 'z' direction.
Xj, is the reciprocal lifetime of the 2P, state and 1i^Lis the Lamb
Shift. The zero field (double quantum) decay rate has been neglected.
(A 'moderate' electric field is one which causes a stark Shift greater than the hyper-fine structure separation, but less than the Lamb shift.)
Lamb & Retherford found that a potential difference of
fa I cm opart~ 25 volts applied between two parallel wires/was sufficient to quench all the metastable states. The electrostatic quenching of the 2S± 2 state was used to determine the fraction of the electron ejection signal due to atoms in the 2S± state. 28
(d) Lifetime of the H2Si State: 2
Sal peter (1958) suggested that a sensitive test for the existence of a permanent electric dipole moment of the electron, would be to measure the sinqle photon decay rate of the 2S, state 2 in hydrogen. If there were an electronic electric dipole moment it would mix the 2S± and 2P± wave functions and the 2S± state would undergo 2 2 2 single quantum electric dipole transition to the ground state with a lifetime somewhere between the 1/7 sec. of the unperturbed 2S± state 2 -9 and the 1.6 x 10 sec. of the 2P± state, depending on the strength 2 of the perturbation.
Fite Brackmann Hummer & Stebbings (1959) measured the zero field, sinqle quantum decay rate of the H2Si state and found it to be 2 420 sec \ considerably greater than the 7sec ^ theoretically predicted for the double quantum decay of this state. A beam of 2S± atoms was 2 generated by electron bombardment of a hydrogen atomic beam. The
H2S± beam was viewed by an iodine vapour filled ultra violet photon 2 counter, which responded to the Lyman radiation of the single quantum decay of the 2Sj state, (range of response 1050 - 1270A). 2 From the count rate observed when an external electric field was applied across the beam, they were able to determine the product of the counter efficiency and the 2S± atom current; in 2 an attempt to assess the role of stray electric fields in the observed mixing of the 2S± and 2P± states, they plotted counter output as a 2 2 function of electric field and obtained a parabolic dependence of the 29 count rate on the field. By this means they were able to conclude that the minimum of the parabola lay between ±0.2Vcm \ which would acoount for less than 10$ of the total observed count rate of 930sec \
Of this, 510sec ^ was ascribable to collision quenching by the four most abundant residual gases in the vacuum system. The final result was that a lower limit of 2.4x10 ^sec. could be placed on the natural lifetime of the H2S± level. The figure could only be regarded as a 2 lower limit because the observed count rate could be accounted for by stray electric fields (^0.4Vcm not normal to the quench plates.
For the lifetime to have its theoretical zero field value, stray fields would have to be less than 0.05Vcm \ Collisions with ground state H atoms could also have contributed substantially to the decay rate.
If the lifetime cannot be less than 2.4m sec., on the basis of Salpeter’s (loc cit) calculation, the strength of the electric dipole moment of the electron cannot exceed 0.0045 eh/mc or 10~^e.cm, where e is the electronic charge. *
Although the experiments of Lamb & Retherford and of Fite et a I, employed the electrostatic quenching of the metastable state in hydrogen neither attempted an explicit investigation of quenching itself.
* Subsequently, Goldenburg & Torizuka (1963) were able to reduce -15 this limit to 1.25 x 10 e.cm on the basis of high energy electron scattering experiments. Sandars & Lipworth (1964) reduced it -21 further to 2 x 10 e.cm, by showing experimentally that the cesium atom has a permanent electric dipole moment whose magnitude -19 is less than 2.2 x 10 e.cm. 30
2:4 ELECTROSTATIC QUENCHING MEASUREMENTS.
(a) H2S± ______2_
The decision by the author to investigate the influence of
electric fields on the lifetime of the 2^S state in helium was taken
in 1963. In 1964 I.A. Sell in published a paper entitled ^Experiments on the Production and Extinction of the 2S state of the Hydrogen Atom".
A fast beam of hydrogen atoms in the 2S± state was produced by the 2 passage of a 15 ke V proton beam through a gas cell containing molec
ular hydrogen. The stated aim of the experiment was to determine the efficiency of production of H2S± and to compare observations on the 2 electrostatic quenching of this state with the theoretical descrip tions of Bethe (1947) and Lamb & Retherford (1951). Sell in concluded that the perturbation theory treatment of the quenching is verified.
(b) Electrostatic Quenching of He+ 2S± ______%_•
Harrison et a I (1965) constructed a sensitive detector for
He+(2S,) ions, in which the metastable states were quenched in an electric field and the resulting 40.8eV photons were counted. The hfgh sensitivity (detection efficiency 8.3x10 ~>) was achieved by using a photo multiplier whose cathode almost completely surrounded the quenching field.
The field dependent lifetime 't. (F) sec. of the He+ 2S± 2 state was found to be
T(f) = U. 4 ±f0.2) x 1Q.~2
in the field of F volt cm \ 31
This was compared with the theoretical dependence of the lifetime on the field given b f (f) = l-6 11-Q— F (Lamb & Skinner^1950). In Harrison’s experiment about 90$ of the metastable ions were quenched by accelerating them through a distance of 0.5cm in a static field of ca 2 KVcm \ (the metastable ions spending about 2.5 lifetimes in the field). 2:5 RECENT WORK ON DOUBLE QUANTUM EMISSION. Theoretical: Further theoretical work on double quantum processes was undertaken in the 1950's. Spitzer & Greenstein (1951) and Kipper (1952) calculated the frequency spectrum of the double quantum decay of the 2S state in hydrogen and obtained a more accurate value for the field free decay rate of 8.2 sec. Shapiro & Breit (1959) made a more accurate calculation of the two quantum transition probability and 6 ““1 obtained a probability of 8.266x Z sec for the 2S states of hydro- genic atoms. FxperimentaI : Until 1965 the existence of two photon spontaneous emission had never been demonstrated experimentally. In the microwave region 39 Kusbh (1956) observed in K atoms transitions with 32 ^ F = 0,A m = ±1, ±2, ±3. and the theory of these was examined by Sal wen (1955). As was mentioned earlier, although the theoretical expec tation is that the 2S± state in hydrogen should have a Iifetime ^ 1/8sec., 2 limited by double quantum decay to the ground state, Fite et al (1959) measured the single quantum decay of this state and found a lifetime of 2.4 m sec. within ca 50$. Attempts which have been made to detect two photon decays in excited nuclei, are summarised in a paper by Alburger & Parker (1964). A considerable number of observations of multiple photon processes have been made with intense laser fields; e.g. Abel la (1962) Kaiser & Garrett (1961), Hall Robinson & Branscomb (1965), McMahon Soret & Franklin (1965). Induced multiple photon emission and absorption process, in the radio frequency spectrum have been studied by molecular beam and optical pumping techniques. This work is summarized in Salwen (Ioc c i t). The 2S, state in He+ was known to be metastable and its 2 displacement from the 2P± state was measured by a magnetic resonance 2 method to be ca 14,00Cmc/s. (Lamb & Skinner, 1950). This value for the Lamb Shift agrees with the value calculated by Bethe (1947), and 4 is^Z (16) times greater than the value for hydrogen. Comm ins et a I (1962) showed, by counting the photons emitted from a He beam containing a known flux of ions in the 2S± state, 2 that the lifetime of the 2S± state was in excess of one millisecond. 33 Lipeles Novick & To Ik (1965) set out to observe directly the double quantum decay of the 2S± state of the He+ ion, by coincidence 2 counting the simultaneously emitted photons. In this paper they reviewed past attempts to detect spontaneous two photon emission and conclude that there is no definite experimental evidence for the existence of such transitions. Since the theoretical two quantum decay rate of a hydro- genic 2S± state is proportional to Z 2 = 8#226 Z6 (Shapiro & Breit (1959)). it is(experimentaI Iy)better to use He+ 2S± metastables, as the 2 theoretical decay rate is 64 times greater than for the hydrogen 2S± state. Further the larger Lamb shift makes the He+ 2SA state 2 2 64 times more stable against electric field quenching. An electron bombardment ion source was used to produce helium ions of which ca 0.5$ were in the metastable excited state. The ions were formed into a beam which passed into the field of view of two E.M.I. 9603B electron multiplier tubes whose angular separation ( 0) could be varied from 67° to 292° . The ions in the metastable state could be quenched by the application of a microwave field at 14 GHz . (The Lamb separation of the He+ 2S± and 2P± states). 2 2 The coincidence count rate was expected to depend on the angular separation ( 9) of the 2 photon detectors according to 1 t cos"' 9 34 The observed coincidence count rate (^5 min S exhibited the expected angular dependence, vanished when the He+ 2S± state was 2 quenched by the 14 GHz r.f. field and exhibited the expected dependence on the electron bombarding energy. It was contended that these results constituted strong evidence that two photon decay of the metastable state of the helium ion had been directly observed. 2:6 THE METASTABILITY OF THE 21S and 25S HELIUM LEVELS. TheoreticaI : Until quite recently, the only estimates of the lifetimes of the He 2^S and 2^S metastable levels were those of Breit & Teller (1940) which were mentioned in 2:3; these were, at best, order of magnitude estimates. The lifetime of the singlet state in helium was expected to be of the same order of magnitude as that of the H2S± state, 2 3 1 i.e. 1/7 sec. Because the 2 S - 1 S transition must contravene the AS = 0 selection rule prohibiting intercombinations they obtained 5 an order of magnitude estimate of~'10 sec. for the lifetime, for the 2^S state. In 1966 Dalgarno calculated the He 2^S double quantum decay rate and obtained a reciprocal lifetime of 46 sec \ (see §3.5). ExperimentaI: No experimental determination of the natural lifetimes of the metastable states in helium or any of the rare gases appears to have been published. The decay of metastable populations in the afterglows of terminated discharges has been investigated by several workers. A 35 description of these experiments may be found in books by Mitchell & Zemansky & Dushman. The conditions in a discharge afterglow are not suitable for a determination of the natural decay rate of a metastable state, although later in this thesis, we extrapolate the results of an afterglow experiment to estimate the lifetime of the He 2*S state, (5:4). 36 CHAPTER 3. THEORY INTRODUCTION, In this chapter we outline briefly the basic theory relevant to the occurrence of forbidden transitions. As in the previous chapter the principal concern is with the decay of the 2^S level in helium and the influence of an electric field on it. The calculation of the natural and perturbed lifetimes is discussed and evaluated, enabling a comparison with the experimental results of chapter 5. In the previous chapter it was seen that forbidden transitions can be enforced or spontaneous. The spontaneous transitions fall into two categories. (i) the higher multipole, single photon, pcocesses (ii) the multiphoton processes. If the dipole matrix element between two states vanishes the higher multipole transitions become significant. If the two states are spherically symmetric, all single photon transitions are strictly forbidden and under these conditions the most probable transition is by the simultaneous emission of two photons. The 2^S and 1^S states in helium are spherically symmetric and the most probable mode of decay of the 2^S level is by double quantum emission. The dominance of the two photon process in the decay of the He 2^S level, pre-supposes that there is no mixing of the 2^S wave function with the wave functions of neighbouring (principally 2V) levels which are optically coupled to the ground state. Such a mixing can be caused by an external (or internal) electric field. 37 3:1 SPONTANEOUS FORBIDDEN TRANSITIONS IN RADIATION THEORY. In this section we outline the Dirac radiation theory to illustrate the occurrence of forbidden transitions. Reference was made to the books by Dirac (1928), Heitler (1954) and McConnell (1960). The essential problem is to determine the probability of an electron emitting or absorbing light. The total Hamiltonian (electrons plus radiation field) includes a term which represents the Hamilto nian of the interaction between the electrons and the radiation field: it is treated as a perturbation and is responsible for the system undergoing transitions from one state to another, thus we can write, H (total) = H (electrons) + H (field) + H^. The transition probability per unit time between the states A & B is related to the matrix element of H^ by A^AB = 2fr p(E) (B | H1 | A) I 2 11 ] ...3.1 where p(E)dE is the number of final states (B) in the frequency range Eg, Eg+dE, i.e. p (E) is the density of states function in the vicinity of the final states of the system. To determine Tw' it is necessary to evaluate the matrix element (B | H^ \ A) If we confine our consideration to emission and absorption by a single electron, H^ may be obtained from the relativistic Hamil tonian for a single particle in an electromagnetic field 38 H =c‘Jiff!) -4 H = M + 2. /vl rw d. 2.WC1 if the motion is non relativistic, the interaction term is h' f.A + ff- ric. - 2^c ...3.2 where p is the momentum of the electron and A is the vector potential V " of the field at the site of the electron. The nonrelativistic approximation is quite good for atomic electrons which emit and absorb radiation in the visible and near U.V. regions of the spectrum, First Order Approximation: The second term in equation 3.2 can usually be neglected 2 as it is of order ( e/c) . Only when the first order term vanishes does the second order term become significant, hence e (p. A) me ...3.3 (first order approximation.) In quantum electrodynamics the radiation field is represented by a quasi continuous set { ** ^ of quantized harmonic osciIlators, whose states are characterized by the quantum number 1n1, and the vector potential A then represents a superposition of plane wave fields 39 i—-z V r ^a'-c t A =^rC / exj + V ( > ...3.4 where e^and k^are the polarization and propagation vectors of the X th photon and q and q+ are the emission and absorption operators for the field. If an electron emits a photon we may represent the change of its state by (al -----^ (b | , then the photon must be absorbed into the radiation field by a field oscillator, changing its quantum number by unity and its state function from (n I —► (n+1 I i.e. the total state function for the system changes from (a, n| —(b,n+l) or (A l -----— (Bl Combining equations 3.3 and 3.4 the first order interaction Hamiltonian pertinent to the emission of a photon by a one electron atomic transition, and its absorption by the field is: H = H J 4TTcz- Q e mC v, ...3.5 40 The probability of emission of a photon In a first order transition is given by 27T o f£" | C bj n ■+■ \j H' J cl, n ) | W , -1 kr C b, nti) h' | a, n) _ Jlire1 (bj^e |a) J 2 because the absorption matrix element (n + 1 1 q+ | n) of the >th oscillator is given by ^7+7 p (k) = (2ir)3 whence z (% + l) Cb| nn Cl k> c ...3.6 where the term n^has been replaced bywhich denotes the number of light quanta per oscillator of frequency v# and propagation vector k. This expression for Is the sum of two terms: the first is proportional to the intensity of radiation of frequency w, before emission, and is the stimulated emission transition probability. 41 The second term, independent of the photon density, is the transition probability for spontaneous emission, and arises from the zero point vibrations of the radiation field. The Dipole Approximation. For optical transitions the wave length of the radiation is large compared with the dimensions of the atom ( k a ~10 and the exponential term in equation 3.6 may be replaced by unity, in the evaluation of the matrix element. This is the "dipole approximation" which gives ...3.7 dipole approximation Integrating over all directions of polarization and emission we finally obtain for the total spontaneous emission probability per unit tfme between the states a and b since or I dL if , = r . __ b a t> — ic° 4b c 2.TT 3 T^)C3 ...3.8 where p*b = ( b I £ ) is the electric dipole moment matrix element between the states a and b. Forbidden Transitions. For some initial and final states the dipole matrix element may vanish and the dipole approximation is no longer appropriate. If the matrix elements of the higher terms in the expansion of the exponential 42 in equation 3.6, are non zero then transitions may still occur, albeit _2 with a considerably reduced intensity rj (ka) , with respect to dipole transitions. Such "higher multipole'' processes are called "forbidden’ transitions, since they occur when dipole transitions do not occur and _8 their intensity is 10 that of a typical "allowed" transition. A second class of forbidden transitions becomes significant when the first order approximation (equations 3.2 & 3.3) breaks down. For example if the initial and final states are spherically symmetric, the matrix element of the first order Hamiltonian (equation 3.6) is identically zero. The first order approximation is no longer valid and 2 one must consider the second order term «c A in the expression for the interaction Hamiltonian (equation 3.2), leading to "2nd. order", double quantum transitions. 3.2 The Selection Ru lessor Sing I e Particle. The restrictions on the wave functions for which the dipole matrix element does not vanish are the "selection rules" for electric dipole radiation. These rules are easily derived for a single electron in a centra I field. Consider two states specified by the quantum numbers n,l,m &n^m the problem is to determine under what conditions (n V| ^ rrJ \ r 1 nlm) #=■ 0 *sJ 1 The energy eigen functions for a spherically symmetric potential can be written as products of functions of the radial distance f " and spherical harmonics Y ( ) defined by 1 I ro ; rr, .A B im (j> (21+ 1) . (I - Iml (cos G) e y, [ 4IT (I + lm] ) 3 ...3.9 43 where the P™ (cos© ) are the associated Legendre functions. It may be shown (Schifff 37) from the properties of these functions that the dipole matrix element (n^l^ml 1 r \ nlm) a/ vanishes unless . I = I ± 1 m 1 = m, m +± 1 (there is a parity change) i .e. Al = ± 1 Am = 0, ± 1 (parity change) which are the single electron selection rules for allowed transitions. Selection Rules for many Electron Systems. In the simplest case of a system of weakly interacting particles the considerations for a single particle may be easily generalized. The wave functions of the system is then simply a product of single particle wave functions (symmetrized) and the Hamiltonian, the sum of the individual Hamiltonians. Under these conditions the same rules apply as in the single electron case, with the additional restriction that only one electron can undergo a transition at a time. If the interactions of the electrons cannot be ignored, rigorous selection rules still hold. They can be derived from quantum electro dynamics and are consequences of the conservation laws for angular momentum and parity. 44 The Three Rigorous Selection Rules. The rigorous selection rule which applies to all atoms, whether there are interactions between the electrons or not, is that in a dipole transition the total angular momentum of the electrons, either remains unchanged, or changes by unity. (1) AJ = 0, ± 1, with the added restriction that transitions between spherically symmetric ( J =0): states J = 0 J = 0 are STRICTLY FORBIDDEN, for all first order processes. (2) and A Mj = 0, ± 1. (3) electric dipole transitions can only occur between states of opposite parity, (since the electric dipole moment is an odd function of the coordinates). Approximate Selection Rules. In the case of weak interactions between the electrons and RusseI-Saunders coupling, the rule AJ = 0 ± 1 may be resolved into (1) AL = 0 ± 1 and (L = 0 L = 0 strictly forbidden) (2) AS = 0 (3) AM = 0 ± 1 (4) one electron jumps, obeying A' = ± 1. The foregoing are the selection rules for dipole radiation in the absence of external fields. 45 3.3. Higher Multipole Radiation. If the dipole matrix element between two states vanishes, the replacement by unity of the exponential in the interaction Hamiltonian matrix element of equation 3.6 is no longer justified and higher, terms in the expansion ,-i k r 1 ~ = 1 - i k«r + ( i k-r ) ...3.10 must be taken into account. The term(i k*j)can be associated with electric quadrupole, and magnetic dipole radiation. These transitions are analogous to the electric quadrupole and magnetic dipole radiation of a classical oscillating dipole whose dimensions areIssnejligibIe with respect to the wave length of the associated radiation: i.e. effects arising from the neglect of retard ation of radiation over the dimensions of the dipole. (a) Magnetic Dipole Transitions: The spontaneous transitions probability for a magnetic dipole transition between the levels a(n^ I rrJ ) & b(nlm) is given by ab i (Wat^ j (b | M | a) I 2 3 -Kc3 “ 1 where M is the magnetic dipole moment between the two levels, defined by e M = - 7Tr2mC ( L + 2 S) Magnetic dipole radiation obeys the following selection rules, (1) A J = 0, ± 1 transitions between spherically symmetric states strictly forbidden (J = 0 to J = 0) (2) AM 0 ± 1 46 (3) No parity change in the transitions. (b) Electric Quadrupole Transitions: Aab “ F IV * 4 "5 1 (b ' gla,\ r where Q, the electric quadrupole moment is a dyadic which depends on the si- con f iguration of the electrons within the atom and is defined by Q = e Y Cl Co t, where rt- is the position vector of the ith electron. The rigorous selection rules for electric quadrupole radiation are (1) AJ = 0, ± 1, ± 2. Jr with transitions between J = 0 and = 0 J = i and J1 2 3 - { J = 0 and J = 1 strictly forbidden (2) AM = 0, ± 1, ± 2. (3) There is no parity change. 47 3.4 MULTIPLE QUANTUM TRANSITIONS. If the two electronic states (a) and (b\ of the atom are spherically symmetric, all single quantum transitions between them are strictly forbidden because the matrix element of equation 3.6 is then identically zero O’| % | a) 53 O _ 3 n Under these conditions, the first order approximation to the interaction Hamiltonian (equation 3.3) is no longer adequate and the second order term in (equation 3.2) must be considered. The matrix element for second order processes may be written, C2-) ( 6 l H 'jn) HqIi hi!!* ...3.12 (0 w where we have rewritten equation 3.2 to define H and H through » U) (2) H = H + H The states ’m' are "virtual” intermediate states, which may have any energy in the range E ^ E E The states (m) differ from (A) by one photon and differ from B by * This may be seen by choosing cartesian co-ordinates so that the x axis is in the direction of polarization "e ". Then pg (=^^.) is an odd function of x, whereas the state functions (bl and (a| are even functions of x; exp (i k.r) = exp[i ( + kzz: )j since k is perpendicular to the direction of polarization and hence lies in the y-z plane and is therefore an even function of x. Thus the integral is an odd function in x and must vanish. (Schlff p.254) 48 one photon so that B differs from A by two photons. From equation 3. 2 it may be seen that since H<2) oc a2 (2) the matrix element must contain products of the emission and absorption operators and thus contributes to the two quantum emission. Features of Double Quantum Emission: (3) Double Photon emission proceeds via a virtual intermediate state, which may have any energy between the initial and final levels and hence the lifetime of the virtual state is^'KAE - EL) and the emission of the two photons is described as simultaneous. (b) The radiation is electric dipole radiation, and because of the arbitrary division of energy between the two photons a continuum of wave lengths is emitted. The sum of the photon energies is equal to the energy of the transition. The continuous distribution of wave lengths has a broad maximum, symmetric about the centre of the energy gap between initial and final levels (See Fig. 3.1). (Detailed calculations of the shape of the two photon spectrum were done by Spitzer and Greenstein (1951), for the H2S£ - ISi transition and by Dalgarno (1966) for He 2^S - 1^S.). (c) The photons are emitted isotropically. The probability that there will be an angled, between the directions of emission of the two 2 photons varies as (1 -f-cos &). SPECTRUM OF DOUBLE QUANTUM He /5-1‘S TRANSITION 130 120 110 100 90 80 70 60 50 40 30 20 10 0 01 02 03 04 05 0-607 08 09 10 Energy 2XS FiS* 3>1 Plotted from Table 1 in DA.LGAEN0 (1966). A(^r) is the probability of a photon being emitted in the energy interval, y and y -r dy, 49 Whilst single photon processes (electric dipole and higher multipole) are quite analogous to the radiation from classical charge configurations, there is no classical analogue of the multiple quantum processes predicted by the quantum theory of radiation. The theoretical importance of second order transitions is summed up by Heitler (loc cit). "Multiple processes are a very valuable test for quantum electrodynamics. They are a characteristic result of the combination of quantum theory and relativity applied to the electro magnetic field, in realms where the correspondence principle can no longer be applied. The test is all the more valuable because quantum electrodynamics is, as yet, far from satisfactory and it is not a priori obvious that all its predictions agree with the facts. However, so far no contradiction has been found". Heitler (p.229). 3.5 THE NATURAL LIFETIME OF THE 2*S STATE IN HELIUM. Both the singlet metastable (2^S) and the ground state (1^S) of the helium atom are spherically symmetrical (J = 0) and hence radiative transitions between them are strictly forbidden (in first order). One therefore expects that the most probable mode of decay to be via a two quantum process, provided that these states are purely spherically symmetric. Dalgarno (1966) made a precise calculation of the probability of the two photon decay of the 2^S state in helium, described by He (21 S) He (11S) + h V + h V 2 If the energy of the 2^S to 1^S transition Is h and (1 - y) y y y v V 12 50 the probability A (y) dy that a photon is emitted with a frequency lying between YV^ & (y + dy)V^ 's given by A(y) __ 3.07,I03 f (,- 7/ wheree ^ <2lSlz,-l-Zzl'VPXr''P|z,-Zz|l'S> , <2'£l2,->Za.lm'P> Em is the energy of themth, excited ^p’ state, and y (E^ - E^) is the energy of the virtual intermediate state. and Z2 are the cartesian coordinates of the two electrons and the summation over the m states includes integration over the continuum. The Einstein coefficient for two photon emission is given by Jo The function A (y) is plotted in Fig. 3.1 from a table of values in Dalgarno’s paper. The primary mode of decay of the helium triplet metastable (2^S) state is also by two quantum emission. In the case of the 2^S state, the virtual intermediate states are optically coupled to both the initial and final states. An intermediate level which is coupled to the triplet metastable state cannot, by the prohibition of intercombin ation transitions rule (AS = 0), be optically connected to the ground state. Conversely the virtual intermediate state may be optically 51 connected to the ground state then, for the same reason, it cannot be coupled to the upper state. In other words the two photon decay of the 2^S state in helium is prohibited by the AS = 0 rule. The extent to which these transitions can occur is expected to be of the same order of magnitude 3 1 -6 as the admixture of P and P which leads to a factor of 10 for the ratio of the intensities of the singlet and triplet transitions,ie. 5 the lifetime of the state should be sv 10 sec. (Breit & Teller, loc cit {§ 2.3 & 2.6). 3.6 Forbidden Transitions in External Fields. The selection rules for optical transitions may be contravened in the presence of an external electric field, because the field modifies the charge distribution i.e the wave functions of the atomic levels. Consider a particular state whose field free wave function is j nlm ^ .In the presence of a weak electric field it has components of the wave functions of adjacent levels, to which it is optically coupled, ’’mixed” into it and may be represented by | n I m ^ + a j | n, I + 1, mS + a £ | n, I - 1,m^> If the electric field mixes theJnlm^wave function with components of the wave functions of neighbouring levels which are optically coupled to it and to lower levels, then forbidden transitions obeying the selection rules 52 AJ = 0, ± 1, ± 2. no parity change AM = 0, ± 1, ± 2. can occur in the presence of an electric field. In the case of Russel Saunders coupling, theA'-l =0, ± 1, ±2 rule becomes AL = 0, ± 1, ± 2 AS = 0 The degree of admixture of the wave functions, represented by the coefficients a^ and adepends on the proximity of adjacent energy levels and can be calculated from 1st order perturbation theory, and hence the probability of forbidden transitions caused by an electric field, is proportional to the square of the electric field strength. As was mentioned in the last chapter such field dependent forbidden transitions are known to spectroscopists as "enforced dipole radiation"| and often occur in the cathode fall of discharges. While an electric field thus weakens the AL = 0, ± 1 selection rule, a magnetic field may induce transitions which violate the AS = 0 rule, prohibiting intercombination transitions. This rule holds only for Russel Saunders coupling in which there is negligible spin orbit interaction. In a strong magnetic field Russel Saunders coupling breaks down (the Paschen Back effect) and S and L are no longer "good" quantum numbers, and transitions contravening the AS = 0 rule can take place with a probability which depends on the field strength. (A "strong" magnetic field is defined in this context as one in which the Zeeman splitting exceeds the spin mu I tip let splitting) 53 3.7 LIFETIME OF He 2*S IN AN ELECTRIC FIELD. (a) Consider an excited state whose field free wave function is specified by the quantum numbers n|m and which can be represented by ]nlm)>. If an electric field F is applied in the negative 'zf direction, we may write down, from first order perturbation theory, an expression for the modified wave function, |nlm, F^> nlm, F>= C |n'/W> where = _ ef ■ ( c,- ~0 = e F (3, ■+33.) _ e F z r^ and r^ are the position vectors of the two extranuclear electrons and and are their z components, and ^E^ 1 j 1 ^ 1 - E^^is the energy separation between the states \n^l^m^)and |nlm^ in zero field. The expression e<^n^l^nJ ) z| nlnry> is the z component of the electric dipole moment connecting these states, and is only non zero under the following conditions . r 1 1 ± 1 y 1.1 1 l ^ (Bethe & Sal peter, 1957 p.328) 54 Applying these considerations to the 2^S state in helium, we may write oo \ 21 S, f) = ^21s\ t Q °'=l ...3.14 The summation in reality starts from n = 2 (since the n = 1 term is zero) and includes integration over the continuum. The field dependent (2^S - 1^S) transition probability, w (F), is obtained from the dipole matrix element between the perturbed 2^S state and the ground state. Thus 21 S 2- w k (co) Z axis the matrix elements of x and y are zero. Thus w (F) w + o(F" o ...3.15 where o( = k(IoiK ...3.16 55 and we have included a term which represents the field free decay rate of the 2^S state. The summation of equation 3.16 is rapidly convergent. As a first approximation w« assume that the 2V wave function Is the only one mixed with the 2^S wave function. In this approximation, 2 o( = e^ 1 O*1P 1z 1 ^3V ^ 2'P|z| i's)> E 2’ P £ 2.1 S 2 P eZ <1'P |z.|-2-'S> 0.91 W E 2’ p E 2.' s because 3 f l'S) _ i------7------= 0.91 C Co(VP- i'S) From the relation fl'P / \ | . , v 1 2. ■ (E^ -En.P)|<"'pl7z’5>| e2- 2'P ?,p 0.91 WV.5 T a'S using the figures quoted tn table 3.1 ^ | .02- sec 56 TABLE 3.1 (1) (2) (3) (4) E ( E)J 1 ,n p nV rydbergs rydbergs ♦f 1 2 S "l1S (sec"1)* 21 - 21P 0.044 2.a.u. 9.11x10 0.3773 1.78x109 n = 2 - 31P 0.182 6.03x10"3 4 *0.1513 * 5.71x108 - 4]P 0.230 1.22x10-2 0.0493 2.460 - 51P 0.252 1.60x10”2 0.0224 1 .270 - 61P 0.264 1.84x10~2 0.0121 0.740 - 71P 0.272 2.01x10"2 0.0074 0.466 - 81P 0.276 2.10x10_2 0.0047 -.310 (1) from the computations of Green, Johnson & Koichin (1965). (2) The atomic unit of energy is two Rydbergs, to convert these into atomic units, they must be divided by 8. (3) Green, Johnson & Koichin (1966). (4) Gabriel and Meddle (1960). 16 * the atomic unit of frequency is 4.1341 x 10 sec 57 In summing the series of equation 3.16 forO(, the magnitudes of the appropriate dipole matrix elements for the first few terms, can be calculated from published f values (oscillator strength), but the sign of the matrix element remains undetermined. Holt & Krotkov (1966) considered this problem and assumed that the signs could be inferred from a calculation using hydrogenic wave functions. On this basis they concluded that all terms in the series, had the same sign except the first (n = 2). Thus the inclusion of terms with n>2 in equation 3.16actually reduces the value of<< . Holt and Krotkov (loc cit) obtained = 0.89 (KVcm ^) ^sec ^ after summing the series, and concluded that the contribution of terms with n>2 was ca 20$. If we add 20$ to this value we obtain << = 1.07 in good agreement with the approximate value calculated above. Thus we conclude that = (0.9 ± 0.04) KVcm ^sec ^ ...3.18 where the error is estimated from the uncertainties in the published oscillator strengths. (b) Anisotropy of Enforced Radiation. The radiation arising from the field enforced transitions will be emitted an IsotropicaI Iy. One would expect that the electric field Inducing a dipole in an atom in the 2^S state, would cause it to be 58 aligned with the field and the resulting radiation to be completely polarized parallel to the field. Only the m = 0 component of the 2^P wave function is mixed with the 2^S wave f unction, so we wish to determine the polarization 1 1 1 of radiation emitted in a transition from a level n J M-*n J M where n = 2 n^ = 1 J = 1 and J1 = 0 M = 0 M1 = 0 Condon & Shortley (1963), p. 411, give the relative strengths of lines emitted in an electric field with polarization perpendicular ( TT cr 2(eJ2 - M2) eJ(J-1) + M2 where 6 = { for M = 0 and £ = 1 for M^O. using M = 0, J = 1 we get: TT 1 0 i.e. radiation from a transition in which there is no change in magnetic quantum number is totally polarized in the direction of the field. 59 In experiment 1, which Is described in sections 4.8 and 5.1, the emission is viewed in a direction perpendicular to the field, and the anisotropy factor is described by the relation I ( Q ) = / I - P cos 9 \ l \1 - P/3 / where I is the mean intensity averaged over all directions, P is the polarization fraction and 9 Is the angle between the directions of observation and polarization. Here P = 1,0 = TT^ So that: ICt) ce= = 2 1 2 ...3.19 (c) Cone I us ion: Anticipated Fractional Change in Lifetime. We have seen that the (2^S - 1^S) transition, whilst strictly forbidden in first order, may take place in an electric field, F, at a rate W (F) = W +c*F? o Whereof, the”quenching coefficient” is calculated from theory to be -1 -2 -1 0.9 (KVcm ) sec and w^ the zero field decay rate Is in sec Thus, in an electric field of 10KVcm \ the Increase in transition probability should be 90 sec \ In other words, if 21S W 1 -1 1 S (01W has the theoretical value of 46 sec calculated by Dalqarno (1966), and the calculated value ofoCis correct then a field of IQKVcm ^ 60 will double the (2^S - 1^S) transition probability. The decay rate of this metastable state is therefore very sensitive to a perturbation which would be obscured in a spectroscopic study, the fractional 1 1 Stark shift of the 2 S - 1 S line in this field being extremely small: ■Ai ~ uf6 E (Bethe & Sal peter § 56). As we have seen in section 3.5, the most probable mode of decay of the 2^S state in the absence of external fields, is by double quantum emission. The transitions induced by a field however are due to single photons whose wave length is effectively 600.5$ , corresponding to the energy difference between the unperturbed 2^S state and the ground state. A study of the zero field decay rates of metastable states is particularly interesting because a perturbation too small to measureably influence the energy levels and transitions probabilities in an atom, can cause a large change in the decay rate of its metastable states. 61 Chapter 4= METHODS AND EQUIPMENT. INTRODUCTION: In this chapter we describe the method adopted and the equipment used. In Section 4.8 a description and analysis of the two main experiments is given. 4.1 METHOD - GENERAL DESCRiPTION An atomic beam method was chosen for the investigation of the natural and perturbed lifetimes of the He 2^S metastable state. A beam containing atoms In the metastable 2^S and 2^S states, was produced by electron bombardment of a helium (thermal energy) atomic beam. Atoms excited to metastable states, ("metastables”), con tinued for the most part, in the general direction of the ground state atom beam. Ions and electrons produced as a result of the electron bombardment, were swept out of the beam by two small electro static deflection plates. The beam, containing metastables, then passed into the main observation chamber (See Figs. 4.1 and 4.2) through the electric field and on to the target. The metastable atoms were detected by their electron emission from the beam target. The main electric field was applied to the beam between two plane parallel electric field plates. An electron multiplier, capable of responding to photons emitted during the radiative decay of the metastable states, viewed the space between the plates, in a direction perpendicular to the electric field. Fig. 4.0 Two General Views of the Apparatus SCHEMATIC DIAGRAM OF SYSTEM U OJ •H a: LAYOUT OF VACUUM SYSTEM Scale- 1 in-4 ins 62 Field dependent changes in the lifetime of the 2^S metastable state could be observed in two ways. (i) by the increased rate of photon emission from the metastable atom beam, in the electric field. (ii) by the field dependent reduction in the metastable atom signal at the beam target. These two independent experiments provided information on the influence of an electric field on the decay rate of the 2^S level and an estimate of its natural lifetime. Choice of Method. Most of the early observations on the influence of electric fields on atomic transition probabilities, (described in Chapter 2) were with the atoms In the environment of a discharge. An atomic beam method was chosen for this project, because ionic and interatomic fields are negligible in a beam and a perturbation free environment is essential to a study of the natural decay of a metastable level. In addition, application of an electric field to atoms in metastable states is facilitated by the fact that within the beam relatively high densities of metastable atoms are possible, while outside the volume of the beam, a good vacuum can be maintained. 4.2 FORMATION OF THE BEAM. The atomic beam was formed in a vacuum system consisting of three cylindrical chambers, the source, the collimator and detector chamber. Helium was bled into the source chamber through a needle 63 valve after passing through a 4ft. long copper "U" tube, packed with No. 5A molecular sieve and cooled in liquid nitrogen. The flow rate was adjusted to maintain the pressure in the source at about 1 Torr. Helium atoms from the source effused through a slit (1/8ln. long and 0.003ins. wide) into the collimator which was maintained at less than -4 19 Torr. by a diffusion pump. Because the mean free path at this pressure (>100cm) was greater than the largest dimension of the collimator (2.5In), the motion of the atoms was rectilinear and after reflections from the walls the majority of them passed into the diffusion pump. Those atoms whose trajectories lay in the solid angle subtended by a second slit (1/6in. long and 0.006ins. wide) on the opposite sides of the collimator, passed through it into the detection or beam chamber which was maintained at a pressure between 10 ^ and _5 10 Torr. by another diffusion pump. Thus the two slits which connect the source, collimator and detection chambers, served to define an atomic beam in the detection chamber. Rough criteria for the formation of the beam are: > width of first slit. "Xc > distance between first and second slits. ^t> >beam path length in detection chamber, where^ = mean free path and S, C, D represent the source, collimator and detector chambers respectively. A limit on the beam density is impesed by the first condition and the pumping speeds limit the number of atoms in the beam due to the second and third conditions. 64 Construction of the Vacuum System. The system Is largely constructed from standard 2” diameter pyrex glass plumbing components, supplied by the Crown Crystal Company. Vacuum sealing of demountable joints was achieved by 2iin. neoprene O-rings, retained by stainless steel l/8In. thick cyIindrtcaI square section rings fitted inside and outside the 0-rings. The source chamber was a 2in. i.d. pyrex ”TM 8in. long with a 1in. diameter side arm, on which was mounted a Pirani gauge head. One end of this chamber was sealed with a stainless steel plate onto which was fitted an Edwards needle valve and the helium gas line.. The beam defining slits were constructed from stainless steel razor blades and tin soldered onto stainless steel supports; these units can be removed and the slits replaced by circular apertures of similar areas. The second beam defining slit is wedged shaped in order to reduce attenuation of the beam by back scattering from the second slit. The shape of the beam chamber may be seen in Fig. 4.C&. It consists essentially of a 5" diameter 8" long cylindrical tank of brass, silver soldered together and chromium plated. There are eleven ports in the chamber to accomodate electrical connections, an electron multiplier, a glass observation window and a pumping line. In the front section of the tank are additional ports for electrical connections to the ion sweeper plates of the electron gun. 65 Production and Measurement of Vacuum. The collimator and detection chambers were connected via glass sheathed in copper, reentrant, liquid air traps to 4" and 2" oil diffusion pumps, respectively. They were backed by a common 250 1/min 2 stage rotary pump. The source chamber was not separately pumped. The 47’ pump was a Dynavac model with an Edwards water cooled baffle valve. The 2" pump sas an Edwards Model 203. The pressure in the source was measured by an Edwards Pirani gauge, the pressures in the collimator and detection chambers were monitored by Edwards IG3H ionization gauges, the ion currents being measured with an electrometer; the emission current was supplied by an emission stabilized power supply. Typical operating pressures were of the order of: 1 Torr , in the source 4x10 J M j in the collimator -5 2x10 " y in the beam chamber, with the beam running. With no beam, the base pressure was (1 to 2) x10 Torr; without liquid Nitrogen trapping this rose to 5 to 10 xIO ^Torr. x The beam density Nb(x), at a point on the beam axis distant/from the first slit is given by NL (x) - NoA 0 b . -l. • 2 4 TT x where Nq = the atom density in the source and A~ - +he area of the first slit. 66 For the slit dimensions and the pressures cited above, this corresponds to 7 x 10 -3 cm (at 20UC) N, (x) b Helium Purity. The helium was supplied by C.I.G. Australia Pty. Ltd. Its purity was quoted to be U.S. Bureau of Mines, Grade A, corresponding to an impurity concentration of less than 50 parts per million. Upper limits to the concentrations of the main contaminants were claimed by the suppliers to be: £ C02 6 ppm CH4 1 ?! 10 ?! H2 Ne 15 ?! A r 1 ?! N2 18 ?! O CM 5 ?! 25 ?! H2° *ppm : volume parts per million. 67 4.3 PRODUCTION OF METASTABLE STATES. It Is difficult, in exciting helium atoms to the 2^S and 2^S levels, to avoid excitation of the 2^P level resulting in the production of A 5848 (2V - I^S) resorAnce radiation, since one must use electron impact energies considerably in excess of the metastable state thresholds to obtain useful fluxes of metastables. Atomic beams containing atoms in metastable states have been produced In three ways (a) extraction of a beam from a discharge tube, i.e. electron impact excitation under swarm conditions. (b) excitation by electron impact using an electron beam in the source chamber of an atomic beam system. (c) electron impact excitation after col I innation of the atomic beam, e.g. crossed electron and atom beams. Production of Helium Metastable Beams in Past Work. (a) Production of metastable beams from discharges: Hughes et a I (1953) measured the magnetic moment of the He 2^S atom, by magnetic deflection of a beam containing 2^S metastables. Weinrigh & Hughes (1954) investigated the hyperfine structure of helium 3 in the 2^S state. The metastable atom beams were obtained from a d.c. discharge tube. Stebbings (1957) and Hasted & Mahadevan (1958) used hot cathode discharge tubes to produce beams of He and Ne containing atoms in metastable states, to investigate the efficiency of electron 68 ejection by metastables from metal surfaces, (see Section 4.4) The disadvantages of the discharge method of producing metastable beams are: i) lack of knowledge of excitation conditions, ii) high ultraviolet background contribution -'50 to 10% to the metastable signal (Hasted & Mahadevan). iii) in the case of helium^only metastables are produced, due to the rapid conversion of to by superelastic collisions with thermal electrons (Phelps,1955). An advantage is that large fluxes of metastables are possible. (b) Immersion of an electron gun in the source chamber of an atomic beam. This method has been used most frequently. Muschlitz et al at the University of Florida have used helium metastable beams obtained in this manner to investigate a variety of problems, including Penning ionization, elastic scattering and excitation functions. Holt & Krotkov (1966) and Dugan, Richards & Muschlitz (1967) used this method for obtaining excitation cross sections for the He 2^S and 2^S states. McLennan (1966) used a similar arrangement to measure the electron ] 3 ejection efficiency ( /'VJ ) of He 2 S and 2 S metastables from a tungsten surface. The advantage of this method of metastable beam production over the discharge method, is that by maintaining a sufficiently low pressure in the source, single collision conditions are obtained. The beam then contains 2^S and 2^S atoms in concentrations proportional to their electron impact excitation cross sections. 69 The disadvantages are: i) there is a significant ultraviolet background, although there is some disagreement about its importance. Holt & Krotkov & McLennan (loc cit) found that resonance radiation was negligible, whereas Dugan, Richards and Muschlitz (loc cit) found that resonance radiation could contribute up to 35$ to the total signal. Below 30V bombarding energy, however, the photon contribution was found to be less than 10$. 2 ii) Because of the high scattering cross section ('v'lOOTT a^) for helium metastables, the metastable fluxes are lower than can be achieved by electron bombardment of a collimated beam, by a factor of ten or twenty. (c) Crossed electron and atom beams: the advantages of this arrangement are: (i) As was mentioned previously, higher metastable fluxes are possible than in the case where excitation preceded collimation of the atomic beam. (ii) Single electron collision conditions obtain and the beam i contains metastable state populations in proportion to their electron impact excitation cross sections. 70 (iii) Perhaps the most important advantage of this method, is that it discriminates strongly against the photon background from resonance radiation.* The most serious disadvantage is that the electron impact excitation of the metastable atoms causes them to suffer momentum recoils and the resulting metastable beam to become spatially indefinite. (discussed in appendix II.) Electron bombardment of the atomic beam after its formation, was adopted in the present work, principally for the advantages (i) and (i i) Iisted above. The Electron Gun: The electron gun consisted of a directly heated tantalum filament, an accelerating grid, a field free space and a Faraday cup. The atomic beam passed through the field free space, perpendicular to the cylindrical axis of the electron gun i.e. the general direction of the electron. The disposition of the components is illustrated in Fig. 4.3 and the electrical connections in Fig. 4.9 * In this work, the slit 'S’ (Fig. 4.1) which is 0.125" wide limits the solid angle subtended by the metastable detector, at the inter section of the electron and atom beams to ca 0.06 steradians - i.e. about 0.7$ of the photons produced,reach the detector. This question is discussed further in Appendix III. CROSS SECTION OF ELECTRON GUN Scale.- full scale 3/16 dia Copper rod Teflon Bushes Electron collector x * 3 Glass tome lead throug Stainless steel Housing Fig. 4.3. ELECTRON GUN CIRCUIT Heathkit 0-1S0V Supply Collector Filament Accelerator grid Stabilised Emission filament supply Fig. 4.4, 71 The tantalum filament was about 1cm. long (0.005" diameter) and positioned parallel to the atomic beam. The grids were of 95$ transparency molybdenum gauze. In front of the Faraday cup was a slotted disc so that only those electrons which passed through or close to the atomic beam, would be registered as a current in the cup. The components of the gun were of nonmagnetic stainless steel mounted on teflon (PTFE) bushes. 4.4 DETECTION OF ATOMS IN METASTABLE STATES. The metastables*were detected by their electron emission ar\ from a metal target. When/atom in a metastable state impinges on a metal surface it may liberate an electron from it, provided the internal energy of the atom exceeds the work function of the surface. Since the energies of the metastable states in helium are 19.82 and 20.61 eV, any metal surface could be used. Electrode system: Atoms which had been excited to metastable states continued in the general direction of the beam until striking a metal beam target, which was connected to earth through an electrometer. The ejected electrons were collected by an adjacent electrode which was maintained at a positive potential of 22 volts with respect to the target electrode. The positive current "I" registered by the electrometer and the flux *ff metastables per second which strikes the target, are related by I = en f ...4.1 m * We use the term "metastable" to denote an atom in a metastable state. The current I wiI I hereafter be referred to as the "metastable current". 7 2 where "nm" is the electron ejection efficiency, "eM is the electronic charge f = f + f , ...4.2 s t ^ and f and f^ are the separate fluxes of the 2^S and 2^S states respectively, related by s- (c.f % 6.1) ...4.3 t where qs and are the electron impact excitation cross sections for the singlet and triplet states respectively. *> ' The detection electrodes were rigidly mounted to a stainless steel end plate sealing the observation chamber. For quenching experiments it was necessary to keep these electrodes away from the high field region and the detector was mounted in the position indicated in Figs. 4.2 and 4.1. For the lifetime experiment a more elaborate electrode system was installed (15.4). It was mounted through the auxiliary port adjacent to the PMT viewing port (Fig.4.2) to ensure that all metastables ’’seen” by the photon detector, were collected by the target. Also the electrode system was divided into sections to determine the spatial extent of the beam. Measurements of Metastable Electron Ejection Efficiency M7m!' Few measurements of the efficiency (*7 ) of this process have been made. The first accurate measurements were those of Stebbings (1957) for the electron ejection efficiency from gold by He 2^S metastables. 73 Hasted and Mahadevan (1958) extended this work to Include Pt, W, Mo. A beam of metastable helium atoms from a discharge tube, was used. The absolute metastable flux was determined by measuring the Penning ion current associated with the attenuation of the beam in argon. Because of the rapid conversion of He 2^S to 2^S by superelastic collisions with thermal electrons in the discharge, the beam was thought to have contained metastables in the triplet state only. (Phelps, 1955) Determinations of n are listed in Table 4:1. m Target Reference ns nt Pt 0.48* 0.24 Dorrestein (1942) Pt 0.26±0.03 Hasted (1958) Pt (d) 0.25 II Mo 0.19 ft II Mo (d) 0.11 W 0.17 II W (d) 0.14 II W (d) 0.29±0.03 0.32±0.03 McLennan (1966) Au 0.29±0.03 Stebbings (1957) (d) Denotes degassed. * Reevaluated by Phelps (1958) to be 0.24. n and n. refer to electron ejection efficiencies of the He 2^S and 5 T 3 2 S atoms respectively. Table. 4.1. 74 The only precise measurements of the efficiency of electron ejection by metastables from atomically clean surfaces are those of McLennan (1966) Employing low energy electron impact excitation in the source of a helium atomic beam system! McLennan was able to produce a beam containing both singlet and triplet metastables. Apart from the fact that ultra high vacuum cleanliness of surfaces was possible, he used the same technique as Hasted (loc cit) for determining the absolute flux of metastables. Unfortunately the only surface studieo was tungsten. Contrary to the results of Hasted et al, degassing was found to ?ncrease the electron yield by as much as 80$. McLennan attributed the discrepancy to incorrect assumptions of cleanliness in earlier work. EquaIity of n and n. ______S______T • The only direct evidence for the equality of nc and is the result for tungsten obtained by McLennan (loc cit). This equality is required by the theory of metastable ejection put forward by Hagstrom (1954b). According to Hagstrum’s theory, the excited electron tunnels to the conduction band of the surface leaving the incident atom ionized, the ion then undergoes Auger neutralization and an electron is ejected from the surface. On the basis of this mechanism, ions and metastables have equal ejection efficiencies and this is borne out by the measure ments of Hagstrum (1953) and McLennan (loc cit). A further consequence of Hagstrum's theory is that the efficiencies for singlet and triplet metastables should be the same. 75 In a paper on Penning ionization by helium metastables Scholette & Muschlitz (1962) argue that n s and are equal on these grounds. Dorrestein & Smit reported a ratio of 2:1 for ns : on platinum, but a reappraisal of this work by Phelps (1958) on the basis of more accurate metastable excitation functions, Indicates a ratio of unity. Furthermore, the results of Sholette & Muschlitz (loc cit) led to an indirect confirmation of the equality of the 2^S and 2^S ejection efficiencies. Varnerin (1953) and Hagstrum (1954) have also argued that these efficiencies are equal. Cone I us ion: On the basis of the foregoing, the electron ejection efficiency for helium 2^S and 2^S metastables, incident on the undegassed platinum beam target used In the present work was assumed to be n = 0.26 ± 0.03 m This value has been used In the estimation of the lifetime of the He 2 1S state. ( §5.4) 76 4:5 PHOTON DETECTION. Photons emitted during the decay of the metastables were, for the most of the work, detected by an EMI 9603B particle multiplier in conjunction with a pulse amplifier, scaler and ratemeter. The particle multiplier was mounted in a side arm of the vacuum tank and viewed the space between the field plates (Figs. 4.1 & 4.2). The multiplier envelope was cemented into an aluminium or stainless steel collar, which had an O-rlng groove in it. It was vacuum sealed on to a 2M long spacer which in turn was sealed on to the main tank. The field of view was limited by a slit, ca 2" long and 1/8" wide parallel to the beam and distant 2.5" from it, and by the dimensions of the photo cathode. The dimensions are given in Appendix 2 PMT gain: One of the most troublesome experimental problems encountered in this work was the rapid deterioration of the electron multiplier gain 5 3 Within a period of eight to ten weeks the gain fell from ca 10 to 10 , when the tube became unusable for photon counting. Various unsuccessful attempts were made to curb this deterioration. The dynodes were exposed to the air for as little time as possible (^minutes) during installation. As soon as the envelope was opened, the tube was put into the system and immediately evacuated. Whenever the system was opened, it was brought up to atmospheric pressure by the admission of dry Argon. None of these precautions 77 lengthened the useful life of the multipliers. Continuous pumping of the system, when not in use, was also unsuccessful. The gain of the tubes could be measured by using them to detect the metastables in place of the usual metastable detector. By observing the ratio of the currents from the 1st, dynode and the anode when the tube was multiplying one had a direct measure of the gain. PuIse Countinq System. The output of the PMT was fed into a 31.5 dB pre-amp Iifier and thence into a Dynatron AERE type 1430 D pulse amplifier. The total available gain was 118dB, but with a new PMT this could be attenuated by 30dB. The pulse amplifier output was fed into an Ecko automatic scaler type N530g and an I.D.L. ratemeter model 1810. The output of the ratemeter was attenuated to 10mV f.s.d. and connected to one of the 4 channels of a Leeds and Northrop potentiometric recorder. A second channel of the recorder was connected to the metastable beam target via a Kiethly 610A electrometer. The third channel was connected to a IK resistor at the bottom of the 10^JL potential dividing chain across the Bavaria 0-100 KV high voltage supply. The recorder display was useful for monitoring the stability of the system during the accumulation of counts by the scaler. 78 4.6 CALIBRATION OF PHOTON DETECTOR: In the lifetime experiment (Section 5.4) it was required to determine the number of photons per second issuing from the length of the atomic beam lying in the field of view of the particle multiplier. The probability that a photon Incident on the first dynode will be registered as a pulse is the product of the photo electric efficiency^ (%) for the first dynode and a factor 'gf, which is the probability that a photo electron liberated at the first dynode be registered as a pulse In the scaler. Photoelectric Eff iciency'H () The curve in Fig. 4.5, reproduced from one supplied by EMI Ltd., indicates the way in which the photoelectric efficiency of a BeCu surface, varies with wave length In the range 5008 - 13008,^ (>>); no other determination has been published. Photoelectric Efficiency for Single Quantum Decay ^ ^: The wave length of a single quantum He 2^S - 1^S transition is 600.58, correspond Ing to a photoelectric efficiency of ^ 1 =0.19 (read from Fig. 4.5) Corroborative evidence In support of this figure Is scarce. Measurements of photoelectric yields in the vacuum ultraviolet have been published by Walker, Wainfan & Weissler (1955) and Hinteregger & Watanabe (1955). Some of the results are shown in Table 4.1, along with other measurements to illustrate the variability of photoelectric yield determinations. APPROXIMATE QUANTUM EFFICIENCY (%) QUANTUM Fig. 4.5. EFFICIENCY OF Be Cu 79 PHOTOELECTRIC YIELDS FOR UNTREATED SURFACES j Surface n(600A°) n(1300A°) n(1400A°) Reference Cu/Be 0.19 0.02 - EMI Ltd. Be 0.2(est’d) - - Hinteregger (1954) Cu 0.07* 0.02 - Wa1ker et a 1 (1955) Au 0.14 - - *1 tt ft t! Pt 0.13 0.005 ~0 ft tf ft 11 Pt - ~0 ~0 Weissler (1956) Be - ~0 ~0 tt tt Au 0.20(584$) - - Stebbings (1957) Pt 0.19(584$) - - Hasted &Mahadevan (1958) * thought to be more characteristic of CuO than Cu. TABLE 4.2 The uncertainties in the above photoelectric yield measurements are # usually quoted to be about 20$. The results of Walker et a I indicates that photoelectric yields from metals, rarely exceed 0.2 and are usually less than 15$. However, the other results quoted in Table 4.2, suggest that photoelectric yields are closer to 0.2. One can conclude from the published yields, that n(X) (Fig. 4.5.) is more likely to have been overestimated than underestimated. The main obstacle to comparisons between different determinations of photoelectric quantum efficiencies, is that differences 80 between the histories of the various surfaces are difficult to assess. However for wave lengths below 1200$ , where the ’’volume” effect predominates, surface contamination is less important than at higher wave lengths. Effective Photoelectric Efficiency for Double Quantum Decay ( , The effective photoelectric efficiency for a double quantum (2^S - 1^S) transition is more difficult to evaluate as there Is a distribution of wave lengths described by the (theoretically calculated) function A(y), see Fig. 3.1, §3.5. Using the notation of § 3.5, we wish to determine rp*from the expression 82 = I o A(y) ^(y) . dy to A(y). dy n (y) can be deduced fromn (A) (Fig. 4.5). The average was estimated graphically from the following considerations; (i) 600 < 12008, A(y) and n (y) were obtained from Figs. 3.1 and 4.5 (ii) 1300 Cu, Pt, Ni in Walker et a I (loc cit) } (i i i) for A > 14008 , (y< 0.4) s 0, In comparison with the yields at lower wave lengths. Whence we obtained rf? - 6$.. 81 Since there are two photons involved in every transition, the effective photoelectric efficiency, for a double quantum (2^S - 1^S) transition is given by •h (2) xr P = 2^2 = '2%. These determinations could be overestimated as much as 30$, but it is not likely that they were underestimated. Determination of the Counter Efficiency "q" Secondary emission multiplication leads to a distribution of pulse heights at the anode arising from the liberation of electrons at the cathode. Consequently some of the pulses are of insufficient height to be registered above the discrimination level of the scaler. The fraction of pulses lost must be estimated in the determination of the efficiency of the counting system 'gr. The amplified photoelectron pulses were fed into a Nuclear Data (model ND 110), 128 channel pulse height analyzer. The pulse height spectrum was printed out on a Teletype page printer and points were plotted on a semi logarithmic scale. The form of the spectrum shown in Fig. 4.6 was exponential. Since no maximum could be detected, the linear graph of Fig. 4.6 was extrapolated to zero pulse height. The total number of pulses accumulated during the recording of the spectrum was determined by using the pulse height analyzer In Counts 10 20 30 PULSE PULSES 40 50 HEIGHT 60 GENERATED 70 Fig. 80 Channel ANALYSIS 90 4.6. 100110 BY na OF Ha 120130140150 2*S 9603 DECAY B EMI C0 170 82 and its multiscale mode, and the fraction of the pulses lost was determined by dividing the pulse n° zero intercept of Fig. 4.6 by the total number of pulses. For two different tubes the resulting vaIue of ’g! was g = 92 ± 2% (for the "zero” discrimination level of the pulse height analyzer.) The Shape of the Pulse Height Distribution. On the assumption that the statistics of the individual secondary emission events are Poissonian, one would expect a Poisson distribution of the anode pulse heights arising primarily from fluctuations in the secondary emission at the first multiplication stage. (Lombard & Martin (1961) - Tusting (1962) and Dieltz (1965)). The pulses height distribution would have a maximum whose position would move toward higher channel numbers as the gain of the pulse amplifier and/or the gain of the particle multiplier tube were increased. Lombard & Martin (1961) calculated the distribution to be expected from Poisson statistics, but were unable to observe the theoretical distribution, obtaining instead a decreasing exponential. They concluded that the assumption of Poisson statistics was not valid. They did not identify the tubes used. Baldwin & Friedman (1965) investigated the pulse height distribution and detection efficiency of an E.M.I. U.S. 9603 electron multiplier. The Ag/Mg dynodes had been frequently exposed to laboratory 83 air. Photoelectrons were accelerated to 250 volts and focussed onto the first dynode. A TMC 404 multichannel pulse height analyzer was used to obtain the pulse height spectrum which was accurately exponential. These authors showed that their results could be explained in terms of inhomogeneities in the secondary emission surfaces. By into- ducing a general function, ^ to describe the local variations of secondary emission coefficients over the dynode surfaces, they showed that unless it was close to a delta function (little variation in ^ ) the pulse height distribution should be exponential. Tusting & Kerns & Knudsen (1965) obtained maxima in the pulse height distributions arising from photoelectrons in several types of photomultiplier tubes. Baldwin & Friedman explain this by asserting that SbCsO dynodes in photomultiplier tubes probably have uniform emission properties, in contrast to the randomly oriented crystallites in the surfaces of the Ag Mg or CuBe alloys used in windowless multiplier tubes. Overall Detection Efficiency £(X). The absolute detection efficiency, e , of the photon detection system is given by: e ( X ) = n (X ) q P y for 600.58 photons the detection efficiency is given by: (1) e (600,58) = 17.5% and for double photon (2^S - 1^S) transitions (2) £ = 10.8% The greatest uncertainty In these figures arises from the uncertainties in the determination of the photoelectric efficiency curve supplied by E.M.I 84 4.7 THE ELECTRIC FIELD. The electric field was produced by the application of voltages up to 35 KV across a pair of plane parallel stainless steel plates, 4.4 cm long, 2*5 cm wide and 0.36 cm apart. All the edges of the plates were rounded and polished in order to prevent field emission. The plates were mounted on a stainless steel base with teflon (PTFE) spacers and teflon bolts. The spacers were0.5in. long corrugated cylinders and were able to withstand potential differences up to 35 KV between their ends. The high voltage source was a 0-60 KV (nominally 0-100KV), luA supply. It comprised six voltage doubling stages operating at 15kHz and the 15KV supply to the doublers was stabilized giving an output essentially free of ripple. This equipment was designed and constructed locally by "Bavaria Television". The high voltage vacuum lead through consisted of a 1/8in. diameter 2in. long kovar rod sealed into a B39 standard pyrex cone. The other end of the cone was cemented with epoxy resin Into the centre of- a 3in diameter aluminium disc which could make an 0-ring seal with one of the ports on the main vacuum tank. The path length between the central "hot" conductor, was increased by thermally bonding a 2in. length of heavy duty 1in. diameter polythene tubing onto the glass tube. The voltage was measured from a meter on the supply which was g graduated 0-100KV, and whose current was supplied from a 10 jfL 85 potential dividing resistor chain. The meter was calibrated against a commercial (Hansen Vohmet) vacuum tube voltmeter with 0-30KV high voltage probe. The V.T.V.M. was then calibrated by Mr. L. Medina of the National Standards Commission, (High Voltage Section). The resulting calibration graph of the Bavaria Supply Meter is reproduced in Appendix 5. The accuracy was expected to be better than 2%. The field plate spacing was measured, in situ, with a travelling microscope, to an accuracy of ca 3%. 4.8 EXPERIMENTS 1 and 2, ANALYSIS AND DESCRIPTION. In this Section we describe the two principal quenching experiments. The first, in which the rate of photon emission from the beam is measured as a function of the electric field, gives a measure of the relative change in lifetime induced by the field. It was necessary to make an independent measure of the zero field lifetime of the He 2^S level before the results of experiment 1 could be compared with theory. In experiment 2, the absolute change in lifetime could be obtained directly from a measurement of the field dependent attenuation of the metastable beam. The results of these experiments are presented in Chapter 5. EXPERIMENT 1. In this experiment, the electric field dependence of the photon emission from a helium beam containing atoms in the metastable 2^S state, is observed directly. The flat atomic beam passes through the electric field betwedn two plane electrodes, the emission of photons being detected by an electron multiplier tube which views the space between the fi^ld plates, perpendicular to the field. (i) Relation between Photon Signal and Transition Probability: Consider a parallel beam of flux f (x) metastables per second moving in the positive ,x' direction, with a velocity V. If the life time of the metastable state is 1/wo then the beam will be attenuated by the natural decay when it traverses a length dx according to df = -f(x).dx_ .wo V ...4.4. where df represents the loss of metastables per second. To simplify the exposition, attenuation of the beam by scattering is neglected: the question is considered in§ 6.2. Assuming that the only mode of decay of a 2^S metastable Is by the emission of two photons (Section 3.5, Dalgarno (1966)) the number of photons emmitted per second from an element of the beam of length dx is given by Z f(x) . wo . dx V The factor of two arising from the fact that each decay is (supposedly) accompanied by the emission of two photons. 87 If isotropic emission be assumed, (Lipeles, Novick & Tolk 1965) then the number of photons per second arriving at the detector from the beam element dx is equal to 4TT ^ where-fi-(x) is the solid angle subtended by the detector at the beam element dx; it is a function of x. If the photoelectric efficiency of the detector cathode isn q^ and G represents the probability of a photo electron at the cathode being registered as a pulse in the scaler, then the number of counts per second registered by the pulse counter is given by cLc(x) = G (z'vAJlcy) .f oo.wn cL* 4TTV (The factor G represents the probability that a photon incident on the detector will be registered as a pulse in the scaler and is evaluated above in Section 4.6.). Then the number of counts per second arising from the element of beam dx is given by cU(x) = ZTl G Si 00 f (x) Wo d* 4TTV and the total number of counts per second from the beam is X2 C. {z-'y12)^° \ f (Ii) Influence of Electric Field on Counting Rate In Chapter 3 it was anticipated that the (2^S - 1^S) transition probability would have a quadratic dependence on the electric field F i.e. 2 w (F) = WD -+- r (equation 3.15) Aw = ^ ...4.6 Thus the field dependent contribution to the count rate is given by r*2- aw ou G ^ f decay rate, has been neglected. The factor ’a’ determined in $3.7, arises from the anisotropy of the emission in the field: it is shown in $ 3.7 that a = 3 2 r]1 is the detector cathode photo electric efficiency for 600.5$ : photons from the field induced (2^S - I^S) transition. (The Stark shift of the 2^S level is 10 4% at 100 KVcm ^ (§ 3.8.). Substituting for 'a' in equation 4.7 and dividing equation 4.7 by equation 4.5 gives the relation between the experimental observable, A c , and the change in transition C probabiIity kW/, AC 3 A w Z. (Z^) i .e. Ac 3 n, ck F Z (Z^) VA/0 ...4.8 89 We finally obtain the statement that the anticipated fractional change in count rate is proportional to the relative change in transition probability and is expected to vary directly as the square of the applied electric field. Experimental Procedure: For various field settings the count rate was observed over 100 sec. intervals for each point. Reproducibility and freedom from drift were checked by repeating the measurement of each point during a run. The errors arising from the electric field setting and from the random fluctuations in photon signal level resulted in variations in the observed photon counting rate, at a chosen field setting, of typica1 Iy 10 counts sec ^. Before switching the atomic beam on, the high field setting was varied from zero to the point where counts appeared due to limited breakdown and/or field emission photons, to establish the useful range of the high field. The exact origin of these spurious counts was difficult to trace. They usually limited the maximum field strength to about 100 KV cm ^. Next the electron beam was switched on to check that no spurious signals arose from the interaction of the electron beam with residual gases in the system. The atomic beam was switched on by opening the needle valve until useful count rate (ca200c/$) was established. Depending on the state of the particle multiplier, such signal levels could be achieved 90 _5 for X helium background pressures of ca 1 x 10 Torr. As a preliminary check on the operation of the counting system and the particle multiplier tube^ions from the ion gauge or from the electron bombardment region were permitted to reach the PMT. The ion sweeper plates were then switched on to check their operation and then switched off allowing the ion current to return. The operation of the high field plates was then checked in a similar manner: switching the high voltage supply on resulted in the disappearance of the ion signal. The results of this experiment are presented in § 5.1. 91 EXPERIMENT 2. Field dependent Attenuation of Metastable Flux. While the attenuation of the metastable flux by the field enforced decay is small enough to be neglected in the previous section, it can be measured if the field extends over an appreciable length of the beam. In this experiment, the 4.4 cm plates used previously, were replaced with plates 8 cms long. 2.5 cm wide and (0.35 ± 0.01) cm apart. The plates were of stainless steel gauze in stainless steel frames. An independent determination of the quenching coefficient, (X, may be determined from this measurement. Consider, as before, a metastable beam moving in the positive ’ xT direction with a mean velocity v. If the beam contains both singlet and triplet metastables, and y represents the fraction of the metastables which are In the 2^S state then $ is given by y = -----— ] ...4.9 from equations 4.2 and 4.3 ( $4.4 )t where qs and q+ are the electron impact excitation cross sections for the 2^S and 2^S levels respectively. The metastable beam will be attenuated by scattering collisions with the background gas and by natural decay of the 2^S state. The metastable current which would be registered In a detector at X is given by 1 (0,x) _ y 1(0,0) exjsj- 4- \x) + (1-y) I (o,o) (-**) ...4.10 92 1(0,X) is the total metastable current at X: the first term in the bracket refers to the electric field, F, and the second to the length of the atomic beam path, X. We have assumed that the 2^S state does not decay significantly, (see section 3.5). We have also made the approximation that the attenuation (coefficient» of the metastable beam by gas scattering, is the same for both 1 3 2 S and 2 S atoms, (c.f. discussion of Section 6.3 - Q and Q. s t for $*,^3°, table 6.2). In the presence of the electric field the decay rate of the 2^S level increases by 2 Aw = if the field extends for a length X^ of the beam path (X^ l(F,x) = yI(o,o)ex|p y + (1- Y) 1 (°;°) e*h •••4*11 subtracting equation 4.11 from 4.10 and dividing by equation 4.10 K°;y)-I(r,x) = ! ~ [~(W°V )}----- ico,x) exji (— wo y/ -t 41 I - ~V ^ I I + % /o\s (w° yf! ...4.12 93 where A I is the decrease in the metastabie current at X due to the action of the field, F. For small fields, AW <<. V /x ' Al = V______ 1 | e^jo (wD A) “s ...4.13 whence may be determined from the expression o( -A [ | + — ^ (^fj • x' ( ”i* ...4.14 94 CHAPTER 5 EXPERIMENTAL RESULTS. 5.1 EXPERIMENT 1. In this experiment, the influence of an electric field on the rate of photon emission by atoms in metastab Ie states is observed directly. The beam containing helium atoms in metastable states passed between two plane parallel electric field plates, and the photon detector Can electron multiplier) viewed the space between the plates. (The experimental procedure and theory is described in Section 4.8). (a) Dependence of He (2^S - 1^S) transition probability on Electric Field Strength. Typical results are displayed in Fig. 5.1 which shows the photon detector count rate as a function of the applied electric field. Fig. 5.3 shows the same signal as a function of the electric field squared. Its linearity is in agreement with the expectation that the (2 ^ S - 1^S) transition probability should depend quadraticaI Iy on the electric field strength i.e. AC = 3 l*h \ <±_ . ' Co 2UJ'Wo ...4.6 (b) Insensitivity of Argon Metastable Decay Rate to Electric Field. This experiment was essentially a repitition of the one above, in which the helium beam was replaced by an argon beam. Fig. 5.2. illustrates the observed invariance of the decay rate of metastable argon -1 3 3 atoms In fields up to 64 KVcm . Because the pQ and p^ metastable states in argon are triplet states and the ground state C^S ) is a singlet state, Counts sec”1 (C) Counts sec 4oo Zoo O ©— 10 £ = O $ 20 ---- o Electric Electric eV Fig. O Electric decay (4 F^ — 30 3 ARGON g. i EL 5.2. 2 Field =- 2' 4 AO HELIUM S Field. 3 ----- an P decay in ? KVcm EVom ) Electric an O SO ” — 1 rate ^ o (F) ’ ) tO u n ts sec He 2 ’ S Decay of Electric Fig. the rate applied 5.3 Field as a field Squared function strength (?2) of the square 95 an electric field was not expected to change the lifetimes of the metastable levels. (Section 3.6). The main significance of the result of Fig. 5.2 was that it provided a useful control experiment. (c) Variation of Electron Bombarding Energy. Variation of the electron bombarding energy changes the relative proportions of 2^S and 2^S metastables in the beam and the proportion of (nV - 1^S) resonance radiation reaching the photon detector. If, as was assumed in 5.1(a) above, the photon detector signal is primarily due to photons from the decay of the 2^S level, the fractional change in count rate in a given electric field, should be independent of the electron bombarding energy, i.e. the experimental quantity "Se’! defined by: S = AC / F2 9 C ...5.1 o should be Independent of the electron bombarding energy E. In Table 5.1 the values of for various electron bombarding energies are shown; calcyla.te.d -jjrom Se = ^ ^ ^ £ /°c pi ^5ee p. J c x' E (Volts) S (KVcm 1) 2 e 50 6.5x10~4 70 6.9 70 6.4 80 6.4 100 6.2 108 7.0 108 6.0 115 6.7 TABLE 5.1. 96 The absence of any significant change in Sq is consistent with the following conclusions: 1) The 2 ;S level was not radiating at an observable rate in the absence of the field. An estimate of Breit & Teller (loc cit) shows that the probability of a transition from the 2^S level is /v 10 ^ of that for a transition from the 2^S level, because of the extra prohibition on intercombination transitions (AS = 0). (Section 3.5). 11) The 2^S level was not radiating in the presence of the field, because an electric field does not weaken the AS = 0 rule, (Section 3.7). ...j There was no significant contribution to the photon detector ] ^ signal from (n P - 1 S) resonance radiation. In the above range of electron bombarding energies, the ratio of the flux of resonance photons to the flux of metastables is expected to increase rapidly. Exact figures are not available, but an assessment of the relative proportions of resonance photons and metastables is discussed in Appendix 3. Iv) The major contribution to the photon detector signal was from the radiative decay of the 2^S level. (d) Analysis of Results: The values of TS’ quoted in Table 5.1 were obtained from the direct observations illustrated in Figs. 5.1 and 5.3 after two corrections 97 i) The photon detecter viewed a greater length of the beam, than lies between the field plates. The appropriate correction factor to the field free decay rate is calculated in Appendix 1 to be 0.59. ii) The field free count rate has a pressure dependence which is described in Section 5.2, and corrections of 20 to 30$ had to be made to it in each determination of S . e The final value for S was: e S = 6.5 x 10'4 (KVcm-1) "2 ...5.2 e with an estimated overall error of ca 15$. The uncertainties in each point in Fig. 5.1 are of the order of 5$, and arise from the uncertainty of the field setting and the random fluctuations 4 in ca 2x10 counts. Since nS ” depends on the quotient of the gradient of the line and the zero field intercept, a figure of \S% was estimated for the overall uncertainty in Its value. (e) Comparison Between Experiment and Theory. From equation 4.6 viz: we may substitute In equation 5.1 AC C and obtain an expression for S, which depends on the theoretical values ofoCand w^ I.e. calling this S^, then (± ) . * ' -Id I wo ...5.3 98 (i) The calculated zero field decay rate of the He 21S level is (2) -1 Wo = 46 sec ' ( ...§ 3.5) (ii) Since this theoretical decay involves the emission of two photons the factor '*') in equation 5.3 is given by 2*)2 where was estimated in $ 4.6 to be V: 0.06 (iii) The factorin equations 4.6 and 5.3 arises from the fact that the electric field enforces single photon transitions c sec nop ( $3.7): f rom oqiint I on 4.6 0.19 Thus the photoelectric yield ratiofor field enforced (single photon) and zero field (double photon) transitions is ^7, 1 .57 ...5.4 7p (iv) In Section 3.7 we obtained for the electric field quenching coefficient the theoretical value 0.9 (KVcm 1) 2 sec. Substitution of these values into equation 5.3 yields: S^ 4.7 x 10 2 (KVcm"1) 2 in contrast to 6.5 x 10 4 (KVcm-1) "2 (equation 5.2) 99 Thus, although the photon signal had the anticipated quadratic dependence on the electric field strength, the theoretical value of 'S’ is almost two orders of magnitude greater than the experimental value. This discrepancy Is far too large to be accounted for in terms of the uncertainties in the photoelectric yield ratio ^ /rj . On the basis of the discussion in§4.4, such an error is not likely to exceed 40$. It was anticipated, for reasons which are essentially outlined in the conclusion of this thesis, that a gross disagreement between experiment and theory was more likely to reside with wq than with O^. In following sections, experiments are described in which c 5•2 SOURCES OF SPURIOUS PHOTON DETECTOR SIGNAL. In order to measure lifetime of the 2^S level (1/w ), it o was necessary to assess the contributions to the photon detector signal, of processes other than the radiative decay of 2^S atoms. From the observations described In Section 5.1(c) it was concluded that the major proportion of the photon detector signal was due to the radiative decay of the 2^S level. In this section by an examination of the pressure dependence of the photon detector signal, the proportion is estimated to be about 80$. The production of a helium metastable beam by electron bombardment, is usually accompanied by the generation of resonance radiation arising from the (nV - 1^S) transitions (*£ 584.8). 100 Scattering of this radiation and of metastables could have contributed to the electron multiplier signal, giving an apparent zero field (2^S - 11S) transition probability in excess of the true value. Resonance radiation and metastables can be scattered by residual gas atoms or by surfaces. The role of background gas in the production of spurious counts can be assessed by varying its pressure. The role of surfaces is more difficult to determine, but multiple reflections of photons and metastables from surfaces was considered to be an unlikely source of spurious signal. The results of Section 5.1 lend support to this contention. Pressure Dependence of Photon Detector Signal. (a) Increaslnq Beam Density: If the atom beam source pressure is raised, the beam density and hence the metastable flux will be increased. In the absence of appreciable attenuation by gas scattering, the background pressure Increases in direct proportion to the atom beam density, provided the pumping speed remains constant. Under these circumstances the (2^$ - 11S) photon signal should increase linearly with the background pressure, while the signal due to the scattering of resonance radiation and metastables should be proportional to the square of the background pressure. The X-Y recorder trace in Fig. 5.4, is the result of such an experiment and shows the photon detector signal as a function of the helium background pressure due to the beam. The linearity of this dependence supports the contention that the scattering of resonance t £ O •H 4-’ O £ £ 09s sq.imoQ - xbu2tS tio^oiy; 101 radiation and helium metastables, by helium atoms, contribute little to the "photon” signal. (b) Constant Beam Density: A more sensitive measure of the role of scattering was obtained by maintaining the beam density constant and varying the background pressure independently. For a constant helium metastable atom flux and an increasing background pressure, one would expect any signal arising from gas scattering to increase linearly with the background pressure. On the other hand the signal due to the radia tive decay of the 2^S atoms ("photon" signal) would be independent of the background pressure. From the point of view of the empirical investigation of spurious counts arising from metastable collisions, one need not be explicit about the mechanisms involved. The immediate problem was simply to assess the total contribution made ^^by photon scattering and metastable collisions which can produce signals in a variety of ways. In the case of metastable collisions, for example, one might expect such processes as: elastic scattering excitation transfer penning Ionization collisional deactivation or collision induced radiation to play a role, all of which would have a linear dependence on back ground pressure for a constant beam density. This guestlon is discussed in Section 6.2 In the light of the experimental results reported in this 102 Section. Calling the total background helium pressure "p” and the base pressure due to residual gases other than helium, ^ was anticipated that the photon detector signal should have a pressure dependence described by the eguation: C = C ( 1 + A + Bp o (where p^ is the component of the base pressure due to the ith chemical species). Co is the count rate arising from the radiative decay of the 2 S level and A and B are empirical constants which are determined below. (c) Techniques: To measure the coefficients A and B, for a given set of excitation conditions, the background pressure was varied and the corresponding count rate measured. To determine "A" the count rate from a given metastable atom flux was measured. To reduce the base pressure, liguid nitrogen was gradually added to the trap and for each background pressure, the count rate was recorded by accumulating counts in the scaler over 100 second intervals for each point. The ■~6 background pressure could be varied, in this way from 8 x 10 Torr to 1.5 x 10 ^Torr. Typical results obtained in this manner are shown in Fig. 5.6. The value of MA” was determined by extrapolating the linear graph to zero residual pressure, measuring the gradient of the straight line and dividing by the zero pressure intercept, i.e. The validity of this procedure might be questioned on the grounds that not all of the residual background gas is condensible at liquid Counts sec x 100 - p j Counts sec non 1 on Impendence dua Helium r i esidual ga Impendence ? ,108 Fig. or pres Fig. press of eV gas helium 108 so 5.6 Count 5.5 re ;re pressure of eV \ ■. r torr Count ■ late torr r ensure x x ]« 1 O' 10 to ' ) 103 nitrogen temperature, that there may be non condensible components such as oxygen present whose influence is significant. Analyses of the residual gas in systems similar to that used in the present work have been made. For example a note from J.R. Young (1958) reports that the pressure limitation of a vacuum system sealed with neoprene 0-rings was due to the outgasslng of the 0-rings. (A mass spectrometer analysis showed that the principal component was butane.) Replacement of the neoprene 0-rings by teflon (PolytetrafIuorethyIene) 0-rings resulted in —6 -8 a reduction of the ultimate pressure from 10 to 10 cTorr. On this evidence it is not unreasonable to assume that the base pressure is limited by condensible components and hence extrapolation of the counts versus residual pressure graph to zero pressure is a valid procedure. The low count rate in Fig. 5.6 arises from the use of a low beam density to amplify the effect of the condensible gases. The determination of ,!B” was by a similar technique. With the liquid nitrogen traps full and a constant atom beam density, helium was admitted independently to the beam chamber through a needle valve. The pressure was noted and the count rate recorded for each pressure. The count rate for each point was determined by the accumulation of counts in a 100 second interval. Typical results are displayed In Fig. 5.5. The linear graph of count rate versus total helium pressure was extrapolated to zero helium pressure. The gradient divided by the zero pressure inter cept gave "B", according to: B = 1 b c ...5.7 104 (d) Results: F rom Fig. 5.6 a «-L T ^ = 0.07 x lO^Torr ^ Co 4-i and from Fig. 5.5. B = 4- Cc 2>P = 0.005 x 106Torr"1 These two empirical factors are peculiar to the system in question being functions of the solid angle subtended by the detector at the beam and of the residual gas, characteristic of a system sealed with neoprene 0-rings and pumped by silicon oil diffusion pumps. Under typical conditions of: p = 2 x 10 ^Torr andJT^ = 2 x 10 ^Torr. Co C = 80$ i.e. 80$ of the signal is unaffected by the background pressure, which is a necessary condition for 80$ of the signal to be due to 2^ S - 1^ S photons. Such a result permits the evaluation of the lifetime by calibrating the photon detection system as an absolute detector. In section 6.2 we show that the helium pressure dependent signal is mainly due to excitation transfer collisions between helium metastables and helium atoms. 105 1 5.3 ESTIMATE OF THE LIFETIME OF THE 2 S LEVEL BY PHOTON COUNTING From the previous two sections we were able to conclude that ca 80$ of the photon detector signal was due to (2^S - 1^S) photons from the metastables in the beam. By counting the photons em emitted from a known length of the metastable atom beam, one can, in principle, determine the lifetime of the decaying level (1/w^). Such a determination requires a knowledge of the absolute detection efficiency of the photon detection and counting systems. An estimate of the detection efficiency "€ (h)" for single and double photon transitions from the 2^S level, *ts&. descr i bed in Section 4.5., was used here in the experimental determination of W . The lifetime Was determined by evaluation of the quant ities in equation 4.3 which describes the relationship between the photon count rate C and the 2^S metastable flux (f (x). r o s C - - *2_ o 9 It* Wo -f Jl(x) cU 4-IT \1 J ¥ ...4.5 (a) the factor A r f5 OOjG-OO cix may be rewritten ___ /- X 2. f5 (x) Si (*)d/ since fs(x) Is slowly varying function of fx’, the distance along the beam path. In this experiment, fairly low helium background pressures were used (<5x10 Torr), to minimize attenuation of the metastable flux by scattering, so that the average beam flux could simply be equated ...p.t.o. 106 to the flux at x , the position of the metastable detector. I .e. f (x ) f (x) s o s We shall drop the reference to x, merely calling the 2^S atom flux at the detector, "f s By combining equations 4.1, 4.2 and 4.3 (of Section 4.4) we obtain the following relation between f and the experimental observable, I, the metastable detector current, 1 + q. e^ ...5.8 where e is the electronic charge, oj the metastable electron ejection efficiency and qg and q^. are the electron impact excitation cross sections for the 2^S and 2^S levels respectively. Evidence Is reviewed, in Section 4.4, to support the value °7 = 0.26 ± 0.03 for helium metastables incident on an undegassed platinum beam target. The value of q^/q^ as a function of excitation energy Is discussed in Section 6.1. It was assumed that I arises only from electron ejection by He 2^S and 2^S atoms i.e. contributions to I from the irradiation of the Ft detector by resonance photons, are negligible. The validity of this assumption is justified in Sections 5.6, 6.1 and Appendix 3. Combining equations 4.6 and 5.8, wq was determined from the 107 expression (To _) 4irM 1 sec + ...5.9 %3 s J I (b) "g" the counter efficiency was estimated in Section 4.5 to be (92 ± 2)%. (c) The velocity of the beam V, was taken to be the average velocity of a He beam whose distribution of velocities is Maxwel Man V (1.26 ± 0.07) x 10^cm sec ^ This question is discussed further In Appendix 4. (d) The geometric factor _fi(x). dx evaluated in Appendix 1, represents the solid angle subtended by the detector averaged over the beam length ” Xj) Iytng in the field of view of the detector. From the calculation of Appendix 1 (0.091 ± 0.004) (corresponding to an average solid angle ^0.01 sterad). Substitution of the above values for V, ^ , e, ancj g |n equation 5.9 gives -J 0.790 Co sec I ...5.10 % % where I is measured in units of micro microamperes. 108 ResuIts: The quantity C /I was measured at 108eV excitation energy. Only this bombarding energy was used as the ratio of q^./q was not known at other energies, at the time this experiment was performed. From the results of Dugan et a I (1967) (Section6.1) ^ ^108eV so that w = 1.15 Co sec -rjr I ...5.11 C /1 was measured on different occasions but under similar experimental conditions and the following values were obtained. VL 125 127 135 123 123 120 131 corresponding to an average value of Co = (127 ± 8) sec ^ amp ^ x 10^z I Substitution of the average value for C /I into the expression (5.10) for w gives w = / 4-5 Sec o ------7P. ...5.12 109 The magnitude of ^ depends on the mode of decay of the 2^S level, i) If the 2^S level decays by double quantum emission (2) 1 2T 0.12 the factor of two arises from the fact that two photons are associated with a single (2^S - 1^S) transition. ( 0 is estimated in section 4.6). ii) If the 2^S level decays by a single quantum emission ^ = 0.19 Thus the result expressed by equation 5.11 is ambiguous, corresponding to a single quantum decay rate given by w^ = 770 sec ^ (Single photon) ...5.13. or a double quantum decay rate given by w^ = 1210 sec (Double photon) ...5.14 Of the two possibilities, the two photon decay Is by far the most probable because it is Impossible for a single photon transition to occur between two J = 0 levels. However, it is conceivable that, in the absence of an external field, a single photon transition may arise through an intraatomic perturbation of the 2^S level; c.f. the discussion of the lifetime of the H2S, level in Section 2.3. 2 The cumulative physical uncertainties in the values of the quantities used in determining w lead to an overall possible error of 40# in the vaIue of W . 110 5.4 DEDUCTION OF Til' HI 21.' -v iJRAL LIFETjMt PROM DATA ON HEL~l UM"AFTERGLOWS In this sec'ior we reassess •>n experiment by Phelps (1955), cr the decay of rreiastable p.opu I at i ons In helium d i sc he roc afterglows. By including a term w , in the expression for the r~\ pressure dependent destruction frequency of 2* S metastab Ies, we obtain evidence in support of the lower decay rate reported In 1 he p rev ious sect- i on. (a ) Ear I y_ A f ter c |_qw_ F xper Irnents. P.xperimeets on the decay of the populations of atoms in metastab Is states in the afterglow of a terminated discharge have been performed by a number of workers, an:-' are described by Mitchell <5 Zemanskv (1954). The first Investigations of this kind were under taken by '-'eissher A Graf funder (1'EE7). A c Ischarqe wes terminated a no the decay of ihe m-etastable population in the afterglow was measured from observations of the time dependence of the absorption of light by the a •horns in metastable states. Py study i r the depends nor- ,-f the decay rates on pressure arc temperature Me {ssner & Graf funcer ( Toe c It) -were able to conclude that metastables were primarily destroyed by diffusion to the wails at iow pressures, and by two body collisions at high pressures' ( >10Torr). T r.o I ifeti me ^ m o i 11 a mot a :: t ; I e popu I at i on f i tt ed a n equation of the for: : ^ m = A + Bp p ...5.15 where A one B are empirics I constants which depend on the dimensions of the system and the discharge conditions. 111 (b) The Experiments of Phelps and Molnar. The work of Phelps (1955) and Phelps & Molnar (1952) added further Insight Into the mechanisms responsible for the destruction of metastables in discharge afterglows. Their experiments were based on the same principles, but by using photomultipliers and electronic timing circuits, they were able to Improve the earlier observations. Phelps & Molnar (loc cit) studied the lifetimes of the metastable states In helium neon and argon as functions of pressure, temperature and the size of the container. At low pressures destruction by diffusion to the walls predominated. At high pressures ( >20Torr), two body collisions, between metastables and atoms of the parent gas, were mainly responsible for the destruction of metastables, although there was a small contribution from three body collisions. At high metastable concentrations, collisions between two metastables contributed significantly to their destruction. The work of Phelps (loc cit) led to the identification of another important process contributing to the decay of the 2^S population; singlet metastables are converted by superelastic exchange collisions with thermal electrons to triplet metastables: He (21S) t e} —^ He <23S) + e2 t 0.79 e V -14 2 The cross section is large (3 x 10 cm ) and was obtained by measuring the linear dependence of the 2^S destruction frequency on the free electron density. (The density of the free electrons was measured by their absorption of microwaves). 112 (c) Re-evaIuat ion of_ Afterglow Experiments: Phelps (loc cit) showed that the decay of the concentration, ’S’ cm of atoms in the 2^S state in the afterglow of helium discharge, can be represented by the differential equation: ^s = D 72S - V(N)S n S „ ^7 s f e ...5.16 D is the diffusion coefficient for 2^S metastables in s helium, V(N) is the frequency of destruction of the 2 S metastables as a result of collisions with single ground state atoms whose concentration is N cm p> is the frequency, per electron, of con version of atoms in the 2^S state to the 2^S state by collision with thermal electrons whose density is n^ cm Assuming that the time and space variation of ng can be neglected, a solution of this equation is: S = SQexp (-yst) (Phelps loc cit) ,1 where S is the concentration of atoms in the 2 S state, at time o / T = 0, and Vs is the total decay rate. From the earlier paper of Phelps & Molnar (loc cit) we substitute for V(N) V(N) = Bp + Cp2 where B, the coefficient for two body destruction, is the destruction frequency per metastable at 1 Torr., and C is the corresponding coefficient for three body collisions. The total destruction rate of singlet metastables, per metastable is given by: vs = Ds + Bp + Cp + |3n^ A2 ...5.17 113 where A is the characteristic diffusion length of the container. Si nee D ^ 1 we can write s °c — P Vs = A + Bp + Cp + pn( ...5.18 where A is the diffusion coefficient in helium at 1 Torr., contained in a vessel whose characteristic diffusion length is 1cm. In the expression above, it has been assumed that the natural decay rate is negligible. At the time of these experiments, the only available estimate of the 2^S decay rate, w , of the 2^S level was o ^ (Breit & Teller 1940. see §3.5). which is negligible In comparison with the rates of the other destruction processes. However, in the Iight of the evidence presented in the previous section for a natural decay rate, almost two orders of magnitude greater than this early theoretical estimate, the data of Phelps & Molnar (loc cit) is reconsidered. Accordingly we modify equation 5.18 to Include a term w , representing the natural decay rate of the 2^S level. Vs " p + Bp + Cp2 + P "e + wo ...5.19 If we determine the coefficient B, over a range of pressures in which the first and third terms are small enough to be neglected, we can then estimate wq by extrapolation to zero pressure in a container of infinite extent. Fig. 5.7., which is reproduced from Fig. 5. of Phelps (1955) paper, shows the way in which the destruction frequency, y , depends MOO Htttwm PrMMn (mm of Hg) f .7 ^after .....T >» 1 §■ 2 U• g O v£ •» Hollwn i r**Bur* (torr) 114 on the helium pressure. These observations were made at negligible 8 “"3 electron densities (n < 10 cm ), the density of the free electrons being monitored by microwave absorption. In Fig. 5.8., we have replotted these results on a linear scale in the pressure range 25 Vs is accurately linear with p, i.e. the non linear terms A/p and 2 Cp may be neglected in this pressure range and equation 5.19 reduces to Vs = Bp t (?>ne t WQ The Zero pressure intercept In Fig. 5.8 is w +(3n = (720 ± 100) sec ^ o r e from three graphical determinations. The fact that the electron density Is unknown between the limits 0 < n < 108 cm"3 e + °i contributes a further uncertainty of - 30J sec Conclusion: The extrapolation procedure described above, Indicates that 550 < w K 850 sec ^ o The result of the determination of w by photon counting, described in Section 5.3, was ambiguous: either 0) w = 770 sec ^ (single photon) o or w = 1210 sec ^ (double photon) o The greatest single source of uncertainty in these determinations of wQ was in the estimation of the photoelectric efficiency f 1, which was discussed in Section 4.6. 115 1+ was Inferred from this discussion that the photoelectric efficiencies quoted for >7 ^ and ^ 2 were more likely to have been over estimated than underestimated and hence from equation 5.12 it is probable that w > 1210 sec"1. o We conclude that the result of this section seems to support ^ the value for the single quantum decay rate of 770 sec 1 obtained In§5.3, u) u) but the difference between wq and wq is not large enough to discount the possibility of the two quantum decay mode. 5•5 EXPERIMENT 2 - ELECTRIC FIELD ATTENUATION OF METASTABLE FLUX. In this experiment, the quenching coeff iclent (X>, was measured directly, from the attenuation of the metastable flux by the electric field. The attenuation of the metastable flux by the electric field, is illustrated in Fig. 5.9. The ordinate represents the current 1 regist ered in the metastable detector which, in this case, was an electron multiplier (EMI 9603B) operating at a gain of ca 2000 (gain measurement is described in Section 4.4). The abscissa represents the square of the electric field applied between the electric field plates. (Further experimental details are supplied In Section 4.8). The parameter in Fig. 5.7 is the electron bombarding energy, E. The quantity is expected to change with E but the quantityoLshouId be Independent of E. Resu I t_s: With a knowledge of the ratio q_j_/qs ( §6.1), can be evaluated from equation 4.14, V e ta s ta b leC u rren t( I) x ICT^'A ■M 1 Attenuation by ( Experiment the E 1 o?t :' Electric : r. ri of c feta 5. Fi 2) ■ 1 e 1 Field stable d 3qua red Beam 116 Inserting the experimental values = (8.0 ± 0.2)cm, X = 25 cm V = (1.26 ± 0.07) x 10^ cm sec ^ w = 770 sec ^ o X; * we obtain from Fig. 5.7, the values of oL shown in Table 5.2, below q+/qs (56.1) E eV oC __ | 0.48 90 0.39 0.57 70 0.39 0.83 50 0.42 . Table 5.2 ^ ly a k. I ck tecay r A~t fi t C © w '£/' i b u-t e d 5~/o to Y A £ v a I u. 6 o$ <*. Thus we obtain oC = 0.40 (KVcm ^sec ^ The overall uncertainty was ca 40$, the major contribution coming from the possible error in the determination of A| /f^ which was estimated I / to be ~ 30$. 5.6 SUMMARY AND COMPARISON OF RESULTS: We can calculate another value of from the values of Se obtained in Section 5.1 and of w determined in Section 5.3. o From Equation 4.6, AC = 3 / '1± 1 ^ . F2 Co 2 \ I Wo 117 and equation 5.1 which defines we obtain an expression for , c< = From Section 5.1 S = 6.5 x 10'4 (KVcm"1)"2sec_1. e The value of c< is independent of whether the 2^S level decays by a single quantum or double quantum emission; recalling equation 5.12 of Section 5.3 w °7 = 145 sec o 1 p whence = 0.33 (KVcm"1)"2sec"1 with an overall maximum uncertainty of 55$. The result of Section 5.5 that c< = 0.40 with an overall uncertainty of 40$ is In reasonable agreement with this estimate. Comparison with Results of Holt & Krotkov (1966) Holt & Krotkov (1966), in an experimental study of the excitation of the n = 2 levels In helium near threshold, electro statically quenched He 2^S atoms to separate the 2^S and 2JS states. Electron impact excitation took place in the atomic beam source chamber and the singlet metastables were quenched in the collimator region 118 (between the two beam defining slits.). Thus the electric field was applied to the metastables before they were formed into a beam. An experimental curve of metastable current as a function of electric field was obtained to which the function N = n0 erJp {-(7J ] was fitted, by adjusting the disposable parameters and Vg. Nq, the quantity of interest, was the initial singlet metastable component of the beam and Vg was a characteristic voltage. N/Nq was the fraction of singlet metastables, quenched by the application of the voltage V to the electric field quenching plates. Holt & Krotkov did not explicitly compare theoretical and experimental values of ok( ^ in their paper), Their experimental vaIue of Vq, implies o( = 0.76 (29% error) -1 -2 -1 The units of cK, are (KVcm ) sec To calculate this figure from the observed value of Vg, we used the most probable velocity (of a "v^" distribution) which these workers measured by magnetic deflexion of the triplet metastables in the beam. The result of the velocity measurement Is discussed further in Appendix 4. The maximum error was quoted to be 29%, i.e. 0^ = 0.76 ± 0.22 so that the theoretical value of (0.90 ± 0.04) lies within their error limits. The lowest value oMcompatible with these observations is 0.54, compared with the highest value consistent with the present work, 0.56; thus although a large difference exists between the results of the two measurements, within the estimated uncertainties they are 119 not entirely irreconcible. Holt & Krotkov comment that a further possible source of error was that charged oil films may have decreased the electric field, but that they were unable to prove or disprove this hypothesis. They do not say why the hypothesis was advanced but presumably it was to account for the difference between the observed and expected quenching. Discussion. The experimental value oft?s, obtained in the present work, was a factor of 2.2 lower than the theoretical value. One obvious possible cause of an apparently low value of<^from experiment 2 is that the metastable current, I, may have been partly due to irradiation of the metastable detector by resonance photons. This possibility Is discussed in Appendix 3, where it is shown that the photon contribution is not likely to exceed 6% of the metastable signal. Such independent experimental evidence as is available, however, indicates that this contribution would be less than 2%, It was concluded that resonance radiation did not play an important role, in the present work, for the following additional ressons: (I) There was no significant change Ino<(, with bombarding energy. The only direct experimental evidence (Dorrestein, 1942), Appendix 3, suggests that, in this range, the resonance radiation contribution Is reduced by a factor of two. (ii) There was an approximate agreement between the two measured values ofo< , and we have presented evidence ( §5.1, ^5.2 &$6.1>. 120 (ii) to show that resonance radiation does not contribute significantly to the photon detector signal. (iii) The results of the experiment described in Section 6.1 also indicate that resonance radiation did not contribute significantly to the metastable detector current. Thus the low value of o( , cannot be explained in terms of resonance radiation contributions to the metastable signal. If there is a systematic error in the experimental determination of(X, the approximate agreement between the separate determinations indicates an error common to both i.e. in the estimation of the electric field. It would be necessary for the field to be a factor of 1.5 less than estimated for the experimental results to be compatible with the theoretical results. It is difficult to advance an hypothesis to account for any systematic weakening of the field of sufficient magnitude to influence the experimental results. As previously mentioned, Holt & Krotkov suggested the possibility of a reduction in the field due to that charging of oil films on the field plates. However, for this to have any significant effect, the surface films would have to be able to maintain potential differences of the order of the applied potential difference, i.e. of the order of 10KV. If a film thickness of the order of microns is postulated, then the films would have to 121 have dielectric strengths in excess of 5 x 10^cm .V. This weakening of the field would be more effective In the Holt & Krotkov experiment than in the present experiment because, In the latter, lower applied potential differences were employed. It may be necessary in future experiments of this kind to monitor the field between the plates. Conclusion: The experimental results described in this Chapter indicate that the 21S level in helium decays in the presence of an electric field at a rate given by equation 3.15 viz. 2 w(F) = w + o(F o where 0^= 0.40 (KVcm ) sec is the experimentally determined quenching coefficient, and U) w = 770 sec'1 (single photon) 0 or (Z) w = 1210 sec"1 (double photon) 0 is the natural decay rate of the 21S state compared with the theoretical values of c< = 0.9 (KVcm"1 )“2sec_1 (§3.7) and -1 w = 46 sec (double photon) (§ 3.5) 0 The estimated uncertainties in the values of and w are o both ca 40$. 122 CHAPTER 6. ADDITIONAL EXPERIMENTS. Introduction: In this chapter, we briefly discuss additional exploratory experiments which have an indirect bearing on the results of Chapter 5. 6.1 RATIO OF THE He 21S AND 23S ELECTRON IMPACT EXCITATION FUNCTIONS. The results of Chapter 5 (Sections 5.1 and 5.2) indicated that the photon detector signal from the beam of metastable atoms, was primarily due to the radiative decay of the He 2^S atoms in the beam. Furthermore, from the results of Section 5.6 it was concluded that resonance radiation from the excitation region, did not contribute appreciably to the metastable signal (at the beam target). In this section, by examining the ratio of the "photon" signal and the "metastable" signal as a function of the exciting electron energy we obtain further evidence in support of the conclusions drawn from Chapter 5. Since the "photon" signal "C" was supposedly due to the decay of the 2^S state, and the "metastable" signal arose from the ejection of electrons by 2^S and 2^S atoms from the beam target electrode, the ratio of the cross sections for the excitation of the 2^S and 2JS states can be estimated from the ratio of the "photon" and "metastable" signals. The cross section ratio estimated in this way can be compared with the results of other workers. Agreement provides evidence in support of the conclusion that resonance radiation contributes negligibly to both signals. 123 Consider an electron beam, of energy E and current i travelling in the z direction and which crosses the atomic beam moving in the x direction. If, in the region where the two beams intersect, the atomic beam has an effective thlcknessAz, and a density Nx then the metastable flux is given by f = f + f t ...6.1 Bf i Nx q A z — s :_J. = BT j Nx A z e ...6.2 where ’fT is the total metastable beam flux, f and f+ are the separate 2^S and 2^S fluxes respectively. The total electron bombarding current, "i", will depend on the energy, and the fraction BT of the electron current which passes through the beam, will also depend on E. (In this experiment the fraction B? was not known, as the electron beam was not sufficiently well defined). From the discussion above, the "photon” signal C (E) is expected to be proportional to the flux of the 2^S atoms i .e. C(E) oC f (E) s C(E) \ f ...6.3 where the constant of proportionality k is a function of scaling factors, the solid angle subtended by the photon detector, the length of the metastable beam viewed by it, its efficiency and the natural decay rate of the 2^S state (c.f. equation 4.5). 124 The "metastabIeM signal, I, is related to the total metastable flux according to I = V e (f + f.) ...6.4 • m s t (c.f. equations 4.1 and 4.2) The ratio of the metastable signal to the photon signal, / is independent of the unknown current, Bi, through the beam, f + f. s t ...6.5 where ^ e ...6.6 1 m from equations 6.2 It f s ^s .. .6.7 thus 5+ 1 % ...6.8 Thus the values of 1/C were determined for a range of exciting energies, and corresponding estimates of q_^_/qs were obtained from them through equation 6.8. The empirical constant K, was implicitly evaluated by "normal- izing" the value of 1/C at 108 volts to coincide with the value of q^/q^ at 108 volts, obtained by Dugan et a I ( 1967). The agreement between the energy 125 dependence of q+/qs from the present experiment and the results of Dugan et al, is illustrated in Figure 6.1. The points represent values for q /q^. obtained from the present work on the smooth curve Is replotted from Fig. 5 of Dugan et a I (reproduced from their paper in Figure 6.1). Resume of Previous Work on Helium Metastable Excitation Functions. Total electron impact excitation functions for the two metastable states have been determined by the measurement of the total metastable flux by Dorresteln (1942), Shultz and Fox (1957) and Shultz (1959). Dorresteln was able to obtain separate excitation functions by monitoring the 2^S population through its optical absorption, making use of the optical excitation functions of Thieme (1932) for this purpose. Cermak (1966) obtained separate excitation functions by discrimination between the kinetic energies of electrons produced in the Penning ionization of argon by the two metastable species. Holt & Krotkov (1966) used an atomic beam technique to investigate the 2^S and 2^S cross sections near threshold. Their work is of particular interest to this investigation as they were able to separate the two states by electrostatic quenching of the 2^S state. The relative populations of the magnetic substates of the 2^S level were determined by magnetic beam deflexion and were related to the threshold polarization of the radiation emitted in the 2^P - 2^S transition. Dugan, Richards and Muschlitz (1967), used an atomic beam method to measure the relative electron impact excitation functions TV----"'j 2 4- J2r & Of i-o O'' Q, G" J0 I o' 20 30 40 50 ■ 60 Ao 80 SO ’ tOO MO >20 150 140 C sc ! f o n £ n * r g y (eV! Comparison of ratio of 2’S to 2WS excitation functions of DUGAN et al with that obtained in this work O this work. ----- solid curve, DUGAN et al. Fig. 6.1 126 of the helium metastable levels in the energy range 25-135 eV. Separation of the two metastable states was achieved by deflexion of the 2^S M. = ± 1 metastables in an inhomogeneous magnetic field. J In both Holt & Krotkov's work and the experiments of Dugan et al, excitation took place in the atomic beam source. Dugan et a I were able to estimate the Influence of resonance radiation on their results, by exploiting the large differences in scattering cross sections of self reversed resonant photons (~TTo0) and of metastables 2. -4 ('vIOOttoo). At post chamber pressures in excess of 10 Torr. the metastable beam was completely attenuated but the resonance photons were not. Resonance radiation was no problem in Holt & Krotkov’s work, because they were only concerned with excitation near the thresh olds. No energy selection of the electrons was employed in the work cited above. In general, the energies of the electrons had spreads in excess of 0.5eV. Dugan et a I measured the energy spread in their work to be 1eV. For sections 5.3 and 5.5 it was required to know the value of q^/q^. Values of q^/q were read from Fig. 5 of Dugan et al, and from a comparison between their measurements and those of Cermak (loc cit), we estimated an error of Ca 10% in q^_/qs. E Vqs 50 0.83 70 0.57 90 0.48±0.04 108 0.44 The appropriate values used in sections 5.3 and 5.5 are shown above in table 6.1 127 Cone I us ion: The points in Figure 6.2 were calculated on the assumption that resonance radiation did not contribute significantly to either the "photon’’ or "metastable" signals. The agreement between values of q_j_/qs from the present work and those of Dugan et a I constitutes corroborative evidence in support of the assumption of the negligible role of resonance photons, i.e. that the photon signal C(E) was proportional to the number of 2^S metastables in the beam 6.2 PRESSURE DEPENDENCE OF PHOTON SIGNAL. In ,§5.3 the helium pressure dependence of the photon detector signal was shown to be given by, processes are responsible for this pressure dependence. Collisions Between Metastables and Atoms. If a helium metastable collides with a helium atom in the ground state 5 different kinds of events are possible viz: (a) elastic scattering (b) excitation transfer (c) collisional deactivation (non radiative) (d) collision induced radiation (e) quasi molecule formation. (For further details see Hasted 1964 Ch. 13) Attenuation of Metastable Beam by Background Helium Gas - - ! Increasing Beam Density. x 1.67 x 10"13A (V) -P a . o o u MW u e i— -6 X 1.11 X 10 torr .0" Jl.. 7 5* 6 "7 9~~ 9 /O 7 2. Fig. 6.2 V 2 - x 1,67 x 10-1SA bp‘ 1 - /OO zoo *. -Si"® , , I .... 4 » J I x 10~12 torr2 Fig. 6.3 128 (a) Elastic scattering is discussed in the next section (6.3). Because it is highly anisotropic in the forward direction, scattered metastables may not contribute to the observed signal appreciably. Bernstein (1964) reports a e. dependence for low angle scattering, in the range o to 10°. An elastically scattered metastable would have to be deflected through angles >80° to be registered in the photon detector. (b) Excitation transfer: metastables in the atom beam, have a ““162 significant cross section (^5 x 10 cm'') for excitation exchange with helium atoms in the background gas, through which the beam passes. The resulting randomly moving metastables can contribute to the apparent photon signal and this process is thought to make the major contribution to the electron multiplier signal. (c,d,&e) Phelps & Phelps & Molnar loc cit §5.5) found, from studies of the afterglows of terminated helium glow discharges, that, the cross section for the binary destruction of He 2^S in collision with normal helium atoms was 3x10 ^cm^ at 300°K 3 -22 2 and that for 2 S was 1x10 cm . Because of the low cross sections of these processes they can be ruled out as possible sources of spurious photon signal. 129 (f) Resonance Radiation: On the basis of the results of Sections 5.2 and 6.1, the contribution of resonance radiation to the total "photon signal, was judged to be negligible. We shall assume for the present that its con tribution to the pressure dependent component of the photon signal, can also be neglected. Thus in what follows we assume that the major contribution to the pressure dependent "photon" signal was from excitation transfer collisions. From the pressure dependence (observed in Section 5.2) we I can estimate a value for the excitation transfer cross section for helium metastables in collision with helium ground state atoms. By comparing the value so obtained with the determinations of other workers, we can, in principle, test the above assumption. Estimation of Excitation Transfer Cross Section. In Section 4.8 we derived the relationship between the (pressure independent) photon signal, C , and the radiative decay rate, w , of the 2^S metastables in the beam. o C x-~> GT, f (x) _T1 (x) dx 4 IT v x^ s ...4.5 since f (x) is a slowly varying function of x (negligible attenuation) we may rewrite equation 4.5 woGT rro /1 (x) dx 4 tt V J ...6.9 130 To modify the above equation to include excitation transfer we introduce a term ’W’ which represents the number of excitation transfer events, per rnetastable, per second. W = NQ V where Q is an average excitation transfer cross section for singlet and triplet metastables, andVis the mean velocity of the metastable beam, through helium gas of density N cm ^ C (p) JCL (x) dx ,w + (f +f,)°1 wl- 4 rr V I { fs"l 1 o s t ' m 3 1 ...6.10 where f & f^ denote the average 2^S and 2^S metastable fluxes respectively, and is the electron ejection efficiency of (He) metastables incident on the photocathode of the photon detector. From equations 6.9 and 6.10 C (P) - C C (p)-C ^ W i m ( 1 + — ) V,, W( q. ...6.12 Comparing equation 5.7 _1_ 3C Co with equation 6.12 we finally obtain the expression for Q , RT W B 1m * V * ~ n + q+/qs) ...6.13 131 Calculation of Qx from equation 6.13, requires substitution of the experimental values for W , B, ^ . Unfortunately^^ is not known for a Cu Be surface, and we merely assume that from the data of Section 4.3 and 4.5 putting W = 770 sec ^ (from § 5.4) o s V = 1.26 x 10^cm sec ^ ( S Section 5.3) B = 0.005 x 10^ torr ^ (108eV) (Section 5.2) RT *• 1 Torr cm^ _3~10 16 and 1 + q^/q^ = 1*44 (Dugan et al 5 6.1) We finally obtain Q = 6.0 x 10 ^cm^ ...6.14 x The greatest uncertainty in this figure is in the value of 'V\XJ'V\\> which is of the order of 25%. In addition we have the uncertainties in the determination of w , and B, so that the overall uncertainty could be as high as 65%. Previous Measurements of the He (2^S - 1^S) and(2^S - 1^S) Excitation Transfer Cross Section. Richards & Muschlitz 1964, used an atomic beam method to study the dependence on angular resolution of the total cross sections for the scattering of helium metastables by normal helium. They obtained a lower 132 limit for the excitation transfer cross section of Q > 0 1A-16 2. x - 2 x 10 cm On the assumption of the isotropy of the distribution of helium metast ables produced by excitation transfer collisions, they obtained 1n-16 2 Q = 7 x 10 cm x No variation with electron bombarding energy could be detected, indicating that the excitation transfer cross sections for the singlet and triplet metastables are the Same. Colegrove, Schearer & Walters (1963) obtained a value of 5 x 10 cm"- for the triplet cross section at 400°K. Buckingham & Da Igarno (1952b)obtained a theoretical value for Q of 0.35 x 10 cm at 300°K, based on their calculations of the interaction potentials (ibid 1952a). The theoretical value for this cross section will be increased if the calculated height of the repulsive barrier of the interaction potential were reduced. Poshusta & Matsen (1963) obtain 0.139 eV for the height of the maximum in the triplet interaction compared with the 0.29eV of Dalgarno & Kingston loc cit. Cone I us ion: A comparison between the results in the present work and those of other workers indicates that the major contribution to the pressure dependent photon signal was from excitation transfer collisions. 133 6.3 ATTENUATION OF METASTABLE BEAM BY HELIUM GAS. In this section we examine the pressure dependence of the metastable signal, I. In the measurement of the lifetime in §5.3 it was necessary to operate at a pressure at which attenuation of the metastable signal by the background helium gas is negligible. In the present experiment the attenuation of the beam at higher pressures was measured and compared with the measurements of other workers. Attenuation by collisions with atoms other than helium was negligible (~1$) as the base pressure of the system was usually 2 x 10 Torr. On the other hand, the attenuation of the beam by background helium at a pressure of 9 x 10 "Torr was ~10%. The metastable beam is mainly attenuated by small ungle elastic scattering of the metastables by helium ground state atoms. The method used, was to increase the beam density and background gas density, by raising the source pressure. If the background gas density is sufficiently low , the attenuation of the beam by scattering will be negligible and the background pressure will be proportional to the beam density, provided the pumping speed remains constant; i.e. the metastable signal I, will be proportional to the background pressure. At low pressure this linear relationship was observed but as the helium pressure increased, scattering was manifested as a parabolic departure from linearity of the metastable signal as illustrated in Fig. 6.3. 134 A metastable beam of flux fo at the point x = o, v/hich traverses a thickness x of helium gas at a pressure Tp’ will be attenuated according to f = f e " ...6.15 x o where f is the beam flux at the point ’xT and 7 is the attenuation co-efficient 7s ...6.16 NQ, 21' where fN’ is the scattering gas density and is related to the pressure of helium by P = NRT Qm is the effective total cross section for the scattering of a metastable beam by helium and is in fact an average of the cross sections for the 2^S and 2^S metastables. Similarly Q . is an average cross section for the scattering of the helium metastable beam by atoms of the ? th. chemical species, present in a concentration of N. cm ^. Such scattering by atoms other than helium was negligible here because of the low base pressure. In this experiment the background helium pressure fpf arose solely from the admission of the atomic beam to the beam chamber, and hence the initial beam flux fo was proportional to the helium pressure fpf f = ap o r where ’a’ is a constant which depends on the excitation efficiency and the pumping speed. As the helium pressure ’pT is raised the metastable beam flux will depend on the pressure according to 155 f (p) ...6.17 x r fc O) j where Qm P ^ (p) M for small attenuation MtO x « l fx The dependence of the metastable signal on the pressure has the functional form f (p) = a(> - ...6.19 where b = RT Since the beam contained both 2^S and 2^S metastables, Qm represents an average scattering cross section for both the 2^S and 2^S metastables by normal helium, Q and Q, respectively, related to s ' Q by 0fn TTT ...6.20 where qs and are the electron impact excitation cross sections for the 2^S and 2"S states respectively. The energy dependence of the ratio qs/q^. was discussed in $ 6.1. ResuIts. Fig. 6.2 represents a plot of metastable current as a function of background helium pressure, taken on an X-Y plotter. The curve approximates to the anticipated form . 2 f (p) = ap - bp 136 and Qm was evaluated by measuring the quantities a and b a = Iim df p —*■ 0 .. .6.21 was determined from Fig. 6.2 b = ap - f(p) p2 ...6.22 2 2 was determined from Fig. 6.3, a plot of bp versus p . The measured values were a = (5.1 ±0.1) x 10^ torr ^ b = (6.9 ± 0.5) x 10^ torr ^ whence Q = (340 ± 30) TTa ^ m o Comparison with previous work. Previous work on the scattering of helium metastables by normal helium through small angles, is summarized below: Q. ( Tfa 2) Q (ira 2) min. ^t o s o (p Stebbings (1957) 170 ± 17 - 1° Hasted (1958) et a I 165 ± 17 - i° Richards & Muschlitz (1964) 110 ± 10 60 ± 6 1°221 t? V 80 48 3° J------Table 6.2 137 The present work was done with an electron bombarding energy of 80V corresponding to a ratio of q /q^ of 1.87 (Seej6.1). If we 2 assume Stebbings’ value of 170Tfao for Q^, we obtain from equation 6.20 Qs = Qm +qt ( Q - Q,). — Ym t qs Q = (430 + 40) TT a 2 ^S o which is a factor of ca 2.5 greater than the value of obtained by Stebbings. Another determination was made at a bombarding energy of 108 volts (qs/q_|. = 2.27) yielding a value of Q = (470 ± 40) TT a 2 s o The scattering path length was increased by removing the metastable detector to the end of the system (x = 37.5 cm) and the experiment repeated. The observed attenuation was three times the original, corres ponding correctly to the increase in the path length by this factor. D? scussion: Because elastic scattering is strongly favoured in the forward direction, it is necessary to have a high angular resolution to obtain an accurate total collision cross section. The angular resolution ^min is defined as the minimum angle through which an atom must be deflected to be regarded as having been scattered. If the scattering path is x and the width of the detector is a min artan _a_ 2x. 138 Stebbings (1957) on the basis of a private communication with Willmore, asserts that at an angular resolution of 1° there will be 6% error in the total cross section. The angular resolution in the present experiments was ca 0.8°. It is difficult to account for the large discrepancy between the results obtained here and those quoted in Table 6.X for Qs. However, a determination of Q+, to be described below gave fair agreement with other determinations. The (23S - 1^S) Total Scattering Cross Section. In an attempt to clarify the issues of the preceding Section, vie measured the attenuation by gas scattering of a beam containing triplet metastables only. This was achieved by exciting the metastables in a hot cathode glow discharge in the source chamber, (c.f. Stebbings 1957, Hasted 1958). A triplet beam was obtained in the main observation chamber, whose flux corresponded to a metastable signal of ca 5x10_13amp. The singlet metastables were eliminated by their rapid conversion to the triplet state by superelastic collisions with thermal electrons (See$5.4). That the beam consisted primarily of atoms in the 2JS state was evident from the small photon counter signal observed, with this mode of excitation; ca 3 counts sec ^ for a metastable signal of 5 x 10 ^3A ""6 (background helium pressure 3 x 10 Torr) compared with a typical photon signal of ca 200 counts sec ^ when a similar metastable signal was produced by the normal crossed beam arrangement. 139 With a fixed beam density, helium was admitted to the beam chamber (via a separate needle valve) and a linear decrease in the metastable signal was observed. For small attenuations, the triplet scattering cross section Q., may be obtained from the relation 't BI lx l. dp J where x is the length of the scattering path, whence we obtained 2 Qh (120 ± 20)iTa; The discrepancy between this value and that of Stebbings (1957) (Table 6.X0, can be attributed to the influence of resonance radiation. Under similar experimental conditions to those obtaining in this work, Hasted (1958) showed that resonance radiation could contribute up to 50% to the metastable signal. Hence, allowing for resonance radiation, there is fair agreement. It is possible that resonance radiation gave a spurious low value of Qc in the work quoted in Table 6.X, but the problem of reconciling the experimental results, remains. There is a need for further work on the small angle scattering of helium metastables. 140 6.4 TEST FOR DOUBLE QUANTUM DECAY. Lipeles e+ ai (1965) published the first experimental evidence for the existence of spontaneous double quantum emission. Coincidence counting of the photons simultaneously emitted during the decay of the He+ 2S± metastable level was employed (5 2.5). 2 In the present experiment one may be able to determine whether the He 2^S level decays by single or double quantum emission by using a Iithiumt fIuoride window. The transmission limit of a / good quality carefully prepared LiF window is 1050A°, so that 600.5A° photons would not pass through it, but photons with energies in the vicinity of the mode of the distribution A(y) (/\ ~ 1200$), Fig. 3.1^ 5 3.5) could pass through, albeit with considerable reduction in their number. The proposed method is as follows: One observes the photon signal for a given set of excitation conditions and then places the LiF window between the beam and the photon detector (electron multiplier). With the LiF window in place the photon detector would respond to a band of photons whose wave lengths were in the approximate range 1100$ to 1300$. The lower limit is imposed by the transmission of the window and the upper limit by the low quantum efficiency of the CuBe photo cathode for >1300$ (c.f. d iscussion i 4.6). A preliminary attempt at this experiment was made. A 3 mm thick 2cm diameter LiF window which could be swung into position with a bar magnet outside the vacuum system, was mounted in a shutter in 141 front of the photon detector. The photon signal was observed to decrease from ca 300 counts sec to the 1 count sec ^ (background count rate) when the window was closed. In this range we estimate by reference to Fig. 4.1 the nett photoelectric efficiency due to the effective participation of both photons, to be 6$. The number of photons in this range of wave lengths represents ca 20% of the number that would contribute to the two photon signal in the absence of a window, (estimated from Fig. 3.1). From the observations of Schneider (1956) on the transmission characteristics of LiF in the vacuum ultra violet we estimate the average transmission of a 3 mm thick window in this range of wave lengths to be ca 25$. Thus we would expect the introduction of the LiF window to reduce the double photon signal to betv/een two and three percent of its former value; in the present experiment double quantum decay of the 2^S level would have resulted in 6 to 9 c/s. On the assumption that the window was of good quality, this result indicates that the 2^S level decays primarily by single quantum emission. However, Schneider (loc cit) points out that the transmission of these windows is highly sensitive to surface contamination and it is intended, in future work, to measure the transmission of the window. 142 CHAPTER 7. CONCLUSION 7.1 Resume. !+ was anticipated that the He 2^S state would decay in the presence of an electric field F according to w (F) = w +o(Fi" (Equation 3.15) where w^ Is tha natural decay rate and o(\s the "quenching coefficient’’. (Section 3.7). In Section 5.1 we described experimental results In which the photon detector signal was proportional to the square of the electric field strength. The photon detector signal was able to be identified with the radiative decay of the He 2^S atoms In the beam, because the fractional change in photon signal for a given electric field was independent of the energy of the exciting electron beam. The results of Section 5.1 provided an experimental measure of the fractional change in lifetime of the He 2^S state l.e. = ot p2 /OJO A comparison between the experimental results and an estimate based on theoretical values of c< and w (from Chapter 3), revealed that the observed change in lifetime for a given field was a factor of 200 less than anticipated theoretically. In order to trace the source of the discrepancy it was necessary to determine the absolute change in lifetime, i.e. to measure the quenching coefficient,^, and/or the zero field decay rate, w , independently. To determine w it was essential to make an empirical 143 assessment of extraneous contributions to the photon detector signal, which could give an apparent (2^S - 1^S) transition rate in excess of the true value. In Section 5.3 it was argued that such spurious signals would 1 1 have a pressure dependence different from that of the (2 - 1 S| photon signal. An analysis of the pressure dependence showed that ca 80^ of the signal was independent of the background pressure, consistent with the same proportion of the photon detector signal being due to the radiative decay of the He 2^S atoms in the beam. Perhaps the most convincing evidence was that obtained in Section 6.1. A comparison of the ratio of the energy dependence of the ’’photon” and ’’metastabIer signals with published date on the ratio of the He 2^S and 2^S excitation functions, indicated that the photon detector signal was proportional to the 2'S population in the beam. By calibrating the photon detector ( j 4.6) and identifying the photon detector signal with the natural decay of the He 2^S level, we were able to obtain an experimental estimate of w . ( J 5.3). The result was ambiguous; the observed photon signal could have been due to a single quantum transitions corresponding to (,) -1 w = 770 sec o or double quantum transitions in which ,, (2) 101n -1 wq = 1210 sec but the double quantum decay mode was thought to be the more probable of the two. 144 We sought corroborative evidence for such a large decay rate by a reevaluation of some helium afterglow experiments of previous workers. By extrapolating the metastable destruction frequency data to zero pressure, we estimated the natural decay rate to be 720 sec ^ in good agreement with single photon value obtained from the photon counting experiment. However, because of the overall uncertainties in both estimates, this agreement could not be regarded as proof of the single photon decay mode. In a further attempt to determine whether the photon signal was from single or double quantum transitions, a lithium fluoride window was employed (56.4). The fact that the photon signal was completely eliminated by the window, was consistent with single photon (2^S - 1^S) transitions. Although the window was in all probability of good quality, this test was not definitive because the transmission of this particular window was not explicitly measured. Thus whilst there is some experimental evidence in support of the single photon decay rate, it is not irrefutable. By comparing the experimental value of w , with the fractional changes in lifetime caused by the electric field ( ?5.1) we estimated, = 0.33 (KVcm ^) ^sec ^ In Section 5.3, we described a direct determination of °^from the attenuation of the metastable flux by the electric field; c<= 0.40 (KVcm S ^sec ^ The value of c< obtained in this way is not dependent on a knowledge of w. The approximate agreement between the two values of provided an approximate confirmation of wq. 145 The uncertainties in the determination of w and <=< from o w , were ~ 50$, mainly because of the uncertainties in the published values for the quantum efficiencies of the photon and metastable detectors. The second determination of c< was Independent of these factors but because this determination depends on the measurement of small differences the uncertainties were estimated to be of the order of 40$. The values of c< and wq are in disagreement with the theoretical values discussed in ^ 3.5 and $ 3.7. 7.2 Discussion The experimental value of oC was a factor of 2.2. lower than the theoretical value. If there were a systematic error in the experimental value of Os, the approximate agreement between the two determinations indicates an error common to both f.e. In the determination of the electric field. It would be necessary for the field to be a factor of 1.5 less than estimated, for the experimental results to be compatible with the theoretical results. It is difficult to advance a hypothesis to account for any systematic weakening of the field. This question was discussed in Section 5.6 but we were unable to find any way in which the experimental value might be grossly in error. If the experimental value for is correct, the problem of determining where the theoretical value may be in error, arises. The calculated value of c< depends primarily on the magnitudes of the two oscillator strengths corresponding to the 1^S - 2^P and the 2^S - 2^P transitions. For the experimental result to be correct the two 146 oscillator strengths would have to be lower than theoretical estimates by 50%. Computed oscillator strengths rarely show Internal disagreement greater than twenty five percent. The fact that the oscillator strengths form a self consistent set satisfying the sum rules, further limits the possible discrepancies between theoretical and actual oscillator strengths. On the other hand neither of the two oscillator strengths mentioned above seems to have been measured. (Since the 2V excitation cross section is proportional to the (1^S - 2V) oscillator strength, one could infer from the discussion of Dorrestein's results in Appendix 3 that this oscillator strength is lower than expected). If the theoretical value of oL (Holt & Krotkov, 1966) (£3.7. of this thesis) has been overestimated, it is possibly because the negative contribution from the summation of terms with n > 2 was under estimated. The reason for this is that hydrogen matrix elements were used for terms with n > 5, and dipole matrix elements are highly sensitive to the form of the wave function used to calculate them. Although we were unable to reach a definite conclusion about the mode of decay of the 2^S level, either interpretation of the results of Chapter 5 represents a radical departure from theory. From a theoretical standpoint the two quantum decay mode is much more probable than the single quantum. On the other hand the experimental results indicated that the single photon decay process was the more probable. ] The assumption of a single photon transition, implies that the 2 S state is not a pure J = 0 state, that an intraatornic perturbation mixes 1 1 components of the 2 P wave function into the 2 S wave function. (c.f. Sections 2.1(d)). 147 An interesting parallel exists between the results of this research and the radiative decay of the metastable (2S±) level in the hydrogen atom, (described in Section 2.3). Fite, Brackmann, Hummer & Stebbings (1959) found that the 2SX metastable level in the hydrogen 2 atom decays by a single photon emission at the rate of 420sec ; theoretically it is expected to decay at the rate of 8.2sec ^ by double quantum emission. The aim of this particular experiment was to estimate an upper limit to the permanent electric dipole moment of the electron. The existence of such a dipole moment would mix the 2P, and2S± wave 2 2 functions and the single quantum decay rate of the 2SX state would provide 2 a measure of the mixing. The observed single quantum decay rate implied that the upper limit to the dipole moment of the electron was 10 ^e cm. -21 This limit has subsequently been reduced to 10 e cm. by a precision measurement of the dipole moment of the cesium atom. (Sandars & Lipworth$, 1964), (further details § 2.3). The single quantum decay rate of H2Sj, state remains unexplained. 2 Fite et a I emphasized that such a result should be accepted with reservations, as stray fields of the order of 0.5Vcm ^ could account for the observed decay rate, although they took pains to show that stray fields between (and normal to) the electrostatic quench plates were less than 0.2Vcm \ If we can accept the single quantum decay of the H2SX 2 level as being due to a perturbation within the atom, such a phenomenon is interesting in light of the conclusions relating to the decay of the helium 2 S level. On the other hand the differences between the two cases are perhaps greater than the similarities; whilst an external field 148 of 0.5Vcm ^ could cause the observed single photon decay of the hydrogen rnetastable level, an external field of the order of 40KVcm ^ would be required to cause the observed decay rate of the helium level. If we assume that the 2^S level is decaying by single quantum emission due to an intrinsic electric perturbation, then from the relation 2 Aw = cAF (Equation 4.7) this perturbation produces the same effect on the 2^S state as an external field of ^ 44KVcm ^ (where we have used <=< = 0.4 and Aw = w o = 770secl. Such a field will cause a Stark shift of ~ 7 x 10 '’em ^ (Bethe & SaI peter (1957) § 56) tahich is 7p of the He 2^S Lamb Shift. (0.106cm \ Suh & Zaidi, 1966). Since the limit of spectroscopic resolution is ~ 0.05cm \ it can be seen that an electric perturbation which could account for the observed (single quantum) decay rate would have no other observable consequences, provided its influence was confined to the vicinity of the nucleus. An electron in the 2^S state of helium, has a high probability of being close to the nucleus, because the 2^S level is low lying but principally because it is a zero angular momentum state. It Is conceivable that a (hypothetical) anomaly in the electron-nucleus or electron- electron interactions might profoundly influence the decay rate of the metastable level without measureably Influencing any other atomic properties. It Is for similar reasons that the Lamb Shift, which arises from the zero point vibrations of the radiation field in the vicinity of the nucleus, Is largest for the metastable states In hydrogen and he Iium. 149 Artura, Novick & Tolk, of the Columbia Radiation Laboratory (New York) are at present engaged in an investigation of the metastability of the He+2S± state. An 2 examination of the rate and mode of decay of this state provides a critical test for the presence of any parity violating inter actions which would reduce the lifetime and cause single photon decay. Before further speculation about the decay of the He2^S state is warranted, it is necessary in future work to measure the lifetime by another more precise means and to make a definitive determination of the mode of decay. The most obvious and direct way to determine the lenqhh lifetime, is to measure the decay/of a metastable beam. The single or double photon nature of the decay could be established by: (i) further experiments with lithium fluoride windows, (ii) an analysis of the energy distribution of the associated photoelectrons. (iii) coincidence counting of the simultaneously emitted photons in double quantum transitions (c.f. Lipeles, Novick & Tolk, 1965 § 2.5). 150 APPENDIX 1 DETERMINATION OF (x)dx An atomic beam travelling along the x axis emits (f) photons per second per unit length of the beam. Assuming the emission from each element of the beam (dx) to be Isotropic, the problem is to determine how many photons per unit time will pass through a rectangular slit, whose plane is parallel to the beam axis to strike a detector behind the slit. The slit has a width W, small compared with its length x^, and is distant from the beam. The detector, behind the slit, is distant y^ from the beam and has a diameter of(x2 - x^). Fig. A.1.1.) f(x) W o V ...A 1.1 (c.f. equation 4.4) Number of photons emitted from element dx per second will equal (j)dx the number of photons passing through the length of the £|Jt dL which subtends a solid angle dJL at dx will be dn = (j)dx d-fl- & d Si = 4tT 6 SI = Wd9 = WdBsin0- R .'..dn = (j)W sln0 d© dx 4tt y. ...A.1.2 To find the total number of photons reaching the detector, we first integrate over the appropriate range of angles S , for each element Photon Deteotor Field of View, Fig, A.1,1 151 To find the total number of photons reaching the detector, we first integrate over the appropriate range of angles 9, for each element dx, and second integrate over x. From the figure, it is evident that the range of 9, is different over the range of x between x and xo, than from x to x.. o 4 Accordingly we have n <$ W Lo where V t Yz. X-X 0^ — toyrz 1 a4 == tew 1 V. X - ...A.1.3 integrating over 0 fl ~ 4>W ...A.1.4 152 From the equation A. 1.3 connecting 9 and x -X4 rt= AmL f Oc-Xi______DC-Ji 2. doc ~XI r._ X-^3 \ 4ry, Lv/S-X,)2-* J(x- OCo l7 +■ ilz ) integrating over x this becomes Try, {lifx + J If So finally, we have the total flux of photons reaching the detector given by +j(vJt.)+£ +](*o-*3f+tf -(J‘x*-*J+!£+-J(x4-Xsf+tf +^ ■3^ • • *A • X • ft i.e. from equations A. 1.1. and A. 1.5. we have f*7. J2[x)df< W. j - (|r-«V¥ y. A 1.6. 153 So I Id Angle Factor In the Lifetime Experimentsj 5.3) r *’: In the photon counting experiment (S 5.3) the dimensions were as foilows W = 0.32 cm sz 3.5 ± 0.1 Vi zz 12.7 ± 0.5 ^2 0.9 X1 = =z 3.5 X2 zz 4.3 X3 which from the geometry Fig. A.1.1 corresponds to X zz 4.6 o zz 5.4 x4 Substitution of these values into equation A.5 gives [2 j _f2.(x) dx = (0.091 ± 0.002)cm X1 (corresponding to an average solid angle of 0.017 sterad.) 154 (b) Experiment 1 - Correction Factor ( § 5.2) In the quenching experiment, the detector viewed ca 8 cms of the beam, but the field plates were only 4.4cms long. We need to determine the appropriatec correction factor^’, to the value of Sq ini 5.1. The length of beam which lies between the field plates is i n the range x < x rx ' \ q % = J Jl(x) dx f ^Jl (x) dx 4 o substituting xq = x^ = x^ into equation A.1.5 R^Vi+ /fcTvTt +y^3)l+y,ztJxf+'ii y The appropriate dimensions were = 1cm = 6.3cm X1 *1 >- = 3.5cm CM = 12.2cm X2 X X 1! K C = 4.4cm W = 0.7cm q 3 which from Fig. A.1.1 implies x = 5.3cm o x^ = 8 cm Substitution of these values into equation A.1.5 gives y'= 0.59 155 APPENDIX 2. ELECTRON IMPACT DEFLECTIONS. Electron bombardment energies of ca 100 volts were used to produce metastables. Since the momentum of a 100 eV electron is approximately equal to the momentum of a thermal helium atom, the excitation of a helium atom may result in it suffering a large deflection from the original beam direction. However, inelastic scattering cross sections are largest when the exciting electron is deflected through small angles and the majority of the metastables are deflected siightly. We shall not, in what follows, attempt to calculate the shape of the metastable beam, but merely estimate the expected limits of the deflections, by finding the relation between the angle through which the electron is scattered (p ) and the resulting atomic deflexion. Consider a beam of electrons of energy E (mass m) moving in the z direction and intersecting a thermal beam of atoms of mass M moving in the x direction. If the electron is deflected through an angle ±p in the x - z plane and ±% in the z - y plane and increases the internal energy of the atom by En, we can calculate the direction of the metastable momentum (See Fig. A.2.1) Prom the conservation of linear momentum we may write: p + P = p^ + P^ ...A.2.1 where unprimed and primed symbols refer to the momenta before and after collision respectively. Deflection of Atoms by Electron Impact. Atom Beam Fig. A.2.1. F = initial a to: direction, P' J? 156 i H = JZmE , I > ) = /j»(E -e„) = Jz n kT |p| • magnitude of atom momentum after collision. Case I Scattering In the x - z plane: Resolving In the x direction: ------i ------— JznkT • Px+j2m(e-En') si a (3 Similarly In the z direction ______/ ______JJrnE * (E-Em) 'OS $ ta/n (M „ _P^— Px w • ELzJEIL Ja~Zr ±fT-c„.s~ji. where (f Is the angle through which the metastable Is scattered In the x - z plane. I.e. if . w' -./ £ ___. tosg v/~f *T ± ’ /e -E A. . S^n/3, . . •.A.2.2 157 Case 2 The electron Is scattered through an angle ±y in the y - z plane, causing the metastable to be deflected up or down In the y - z plane through an angle ±Q . _ ^3 ~ J 2. rr\ (E- E n ) Son ^ tasn$= J 2 m (E-E n) Sun X Jznk T J C^'En) • S in V Fig. A.2.2 is a plot of equation A.2.2 with E = 100 V and En = 20V. We can assess the likely ranges of values of (p & G, from a knowledge of the inelastic differential cross sections for the scattering of electrons by helium. Mohr & Nicoll (1932,1933) in a comprehensive series of experiments investigated elastic and inelastic differential scattering between 10° and 155°, in helium and a variety of other atoms. Fig. 52 of Massey & Burhop (1952) p. 96, shows that the scattering cross section falls off rapidly with scattering angle. Although the distribution for the excitation of the metastable states will differ from that shown, the differences at energies ^100 eV between elastic and -inelastic differential scattering cross sections, are slight. •4- O -40 Tr Atomic Deflexion in the x - z plene as a function of electron scattering angle, for an incident electron energy of lOOeV (equation A. 2.2.) Fig, A, 2. 2 158 Most of the metastables produced will be deflected by electrons which have been scattered through less than 20°. From Equation A.2.2 for - 20° < |3 < 20° (p < 9° and from equation A.2.3 for - 20° < y -12 0 © <•' 10? for 10OeV bombardment energy. Whilst cross beam electron bombardment introduces some spatial indefiniteness in the resulting metastable beam, we conclude that the majority of metastables are deflected only slightly from the ground state beam direction. 159 APPENDIX 3 -He (rJp - 11S) RESONANCE RADIATION. (a) Role of Resonance Radiation. Although electron bombardment after collimatlon of an atomic beam (crossed beam excitation) has the advantage of discriminating against resonance radiation, In this experiment, such radiation could possibly contribute significantly to the metastable signal, depending on the magnitude of the 2^P excitation cross section. Several observations on the optical excitation functions of helium have been reported, but the 2 P cross section has not been measured. The lack of this information makes the assessment of the role of resonance radiation in the present experiment, somewhat uncertain. If an electron current I in the Z direction passes through the atomic beam whose density is N and widthAZ, the flux of metastables will be f m = —'o N AZ (q + q.'t ) e where qs and q^ are the electron impact excitation cross sections for the 2^S and 2^S states respectively. In practice not all the metastables produced, reach the detector, because of the momentum recoil during excitation. If we denote the fraction of metastables which reach the detector by ^ , the flux incident on the detector will be given by fm ■ >e's. N where'y Is the electron ejection efficiency for metastables striking the beam target. Similarly the contribution to the metastable current due to resonance radiation will be given by 1=^7 SI 'o NAZq P / P ~TW~4n m e— KP ...A.3.2 Jl represents the solid angle subtended by the detector at the point of excitation. 'rJ is the photoelectric yield of the metastable * detector for these photons. qp is the effective cross section for the production of photons whose wave lengths are ^ 584$, corresponding to transitions from the n^P levels to the ground state * n = 2 ...A.3.3 where q^ is the cross section of the level nV (we consider only nV states^ as cross sections for levels not optically coupled to the ground state are much smaller). From the paper of Massey & Mohr (1933) we estimate that q2 * ^ 65$ qp+ ...A.3.4 Hence the fractional contribution of the photons to the metastable signaI is given by n * 111 = ^2. -V I ___L_ 1 ^ 4ir ^ (qs + qt) Dorrestein (1942) effectively measured the quantity o/ q * 1P HP 1.2 (at 100v) 161 Magnetically collimated electrons were used to excite helium atoms, and the metastables diffused outwards to a cylindrical electrode where they were detected by their electron emission. The detector responded, as in the present experiment, to helium resonance radiation. The detector signal arising from He (n P - 1 S) photons was distinguished from the 5 metastable signal by modulating the primary electron beam at 2 x 10 c/s. At this frequency the photon signal was modulated but the metastable signal was not. The detector surface material was undegassed platinum. Taki ng (roughly estimated from the argument in Appendix 2. J2. ^ 0.005 (footnote Section 4.3) 4 TT and substituting the above result of Do(-restein into equation A.3.5, we obtain (i / 0.02 (at lOOeV) ...A.3.6 Thus from Dorrestein's results, the photon contribution to the metastable signal in the present experiment, is less than 2$. At 50eV the contrib ution Is ca 4$. (b) The 2V Cross Section Dorrestein (loc cit) compared the observed photon signal with the cross section for excitation of resonance photons, expected from the theoretical calculations of Massey & Mohr (1933). From the requirement that the theoretical and experimental cross sections agree, he deduced that the photoelectricyield of undegassed platinum for helium resonance radiation ( A 6 5848) is 8$. He also deduced a value of 24$ for 162 ^7 (He 23S). / m l.e. ^ = 0.33 However Hasted & Mahadevan (1958) have subsequently made absolute measurements ofn^ and'vjm (helium resonance radiation and helium 23S atoms on an undegassed platinum target). (Section 4.4 and 4.6): they obtained 'TJ = 0.26 and /Vi = 0.19 I P yyj_2: = 0.73 ± 20$. ... , "I™ , ,, . . cross section (65$ 2^P, equation, which suggests that the actual n A.3.4.) is a factor of 2.2 less than the theoretical value. Dorrestein's result is also in conflict with the form of the 2^P cross section indicated by trends in the optical excitation functions; (Zapesochyni, 1967). Even if we allow for the possibility that Dorrestein’s result was in error, by this factor of 2.2, then 6$ ...A.3.7 Cone Iusion. Thus we conclude on the basis of the only available experimental dateu (Dorrestein loc cit) that resonance radiation contributes anta less than 2$ to the metastable signal (Equation A. 3.6). Taking into account the possibility that the apparent disagreement with theory is erroneous, resonance radiation still contributes less than 6$ to metastable current (at 100eV bombarding energy). (Equation A.3.7). 80 Volt Fig. A.3.1. '* Fier DOKEESTETM (l<>42) Folium Excitation Function: x total effect; ° G^-Qct of 2"S and 2 S me ta stabler; D °rfeot oi" (n*F - llS) photons. 163 APPENDIX 4 DISTRIBUTION OF VELOCITY IN THE ATOMIC REAM. (a) In the source of an atomic beam system the distribution of molecular velocities can be described by the Maxwell distribution function. If dN is the number of molecules In the velocity Interval v, v+ dv and N is the total number of molecules 2 r 2 dN = f(v) dv = 4 ( v \ exp j - I V ?dv N cTf? [ c ) Lie]) ...A.4.1 C = J2kT/M Because the probability of a molecule emerging from the source slit is proportional to v, the distribution function for the velocities in a molecular beam is similar to a Maxwell velocity distribution function, but is multiplied by another factor of "v,T. The "v^M distribution function is given by 1 ( v )dv = 2_ / v expj —/v~ l(dv U c ( c L j 2yj Ramsey (1956) p.20. ...A.4.2 where i(v) dv is the beam intensity from molecules whose velocities Iie between v + v + dv. It Is claimed (Kusch & Miller, 1955, Lichten,1956) that electron bombardment In the beam before or after its formation, reduces the velocity distribution function of the excited species to a Maxwell velocity distribution. The reason for this is presumably because the probability of excitation is inversely proportional to the atomic speed. 164 Holt & Krotkov (1966) similarly expected the velocity distribution of their metastable beam to be Maxwellian. They found instead that the velocity distribution of the beam resembled a "v"1" distribution. The most probable velocity and the form of the distribution were deduced from observations of the deflexions of 2^S atoms in inhomog= eneous magnetic fields. Another unexpected result was that the most probable velocity of the distribution depended on the source chamber pressure. Holt & Krotkov explained the departure from a Maxwell velocity distribution as being due to the existence of temperature gradients in the source chamber and the velocity dependence of the elastic scattering cross sections of atoms. Neither of these effects were present in the work reported here. The Maxwell distribution will therefore be assumed (b) In the derivation of equation 4.14 forc metastables in the beam, all had the same speed v. Rewriting equation 4.14, with ^denoting the value ofc Since the exponential factor contributes ca % we can for the present purpose put it equal to unity so that AL ° the value of o(, for a Maxwellian distribution of velocities in the beam is given by < = J f(v) d where f (v) is the Maxwell distribution function (equation A.4.1) 165 co where V = \ v f(v)dv J o is the mean velocity of the beam related to the most probable velocity, C, by 1.13C (1.26 ± 0.03) x 10"" cm sec ^ for helium atoms at (20 ± 5) C. (c) The question arises as to whether the electron impact excitation of atoms to metastabie states causes the resulting metastable beam to have an energy distribution other than thermal. The kinetic energy transfer T^ for a massTv^ and energy Eq incident on a mass rr)„ and scattered through an angle^, the k.e. transferred to 's given by \ = 4 m. m0 0 V S2 E Sin2 ©/, (m^ + m2) o 2 for < <. 0^2 K.E. ^4 m1 E Sin2 9 /0 — o 2 m2 Typically the electron has an incident energy of 100eV and is scattered through ft 20°, and here ^ = j____ m0 4x1837 1 z which gives K.E. 5S 0.0016eV compared with the mean thermal energy of beam kT — 0.025eV. 166 Thus excitation of the metastables by electron impact, introduces a further uncertainty of ca 4$ in the mean atomic beam speed and we take for our final estimate, 1,5 -1 (1.26 ± 0.07) x 10 cm sec A IENDIX 5 Bavaria 0-100 KV Supply CALIBRATION Fig. A.5.1. 168 ACKNOWLEDGEMENTS. I would like to thank my supervisor, Dr. K.M. Burrows for his interest and encouragement throughout this investigation and for his advice and criticism, which were of great value during the writing of this thesis. Also I would like to thank Mr. E. Harting for his thorough reading of the draft, Professor E.P. George for his valuable help and Mr. J. Gardener for his interest and generous assistance. I am grateful to Mr. J. Morrow whose skill and ingenuity made possible some of the more difficult construction tasks, and Rosaleen Webster, who undertook the arduous task of typing this thesis. Finally I want to acknowledge the tireless assistance of my wife, Linda, with the myriad details involved in the compilation of this thesis. 169 BIBLIOGRAPHY. CHAPTER 1 . Bethe, H.A. Handbook der Physik, 2A_, p.452-455 (1933) Dalgarno, A. Mon. Not. R . Astr. Soc. 131, p.311-313 (1966) Fite, W.L. Brackmann, R.T. Hummer, D.G. Phys. Rev. 116, p.363 (1959) S+ebbings, R.F. Lamb, W.E. Jnr. Retherford, R.C. Phvs. Rev. 79, p.4 (1959) Sel1 in, i.A. Phys. Rev. 136, p.5A A1245-1253 (1964) Schiff, B Pekeris, C.L. Phys. Rev. 134, A638 (1964) CHAPTER 2. Abe 1 la, 1 ,D. Phvs. Rev. Letters. 9, p.453 (1962) Alburger, D.E. Parker,R.D. Phys. Rev. 135, B294 (1964) Ama1di, E. Rend. Li nee 19, p .588 (1934) Bakker, C.J. Segre, E. Zeits f. Physik 79, 655 (1932) Bakker, C.J. Proc. Amst. Acad. 35. p.589 (1933) Bartels, S Zeits. f. Phvsik 73, 3-4 p.203-215 (1931) Bethe, H.A. Handbook der Phvsik 24, p.452-455 (1933) Bethe, H.A. Phys. Rev. 72, p.339 (1947) Borisoglebskii, L.A. Uspekh. fiz. Nauk 66, p.603 bovieT i^nys . uspekhi. j_, p.zn U95«; 170 Bowen, I .S. Astrophys. J. 67, p.1 (1928) Breit, G. Teller, E. Astrophys. J. 9J_, p.215 (1940) Brinkman, H.C. Dissertation - Utrecht (1932) Comm ins, E. GampeI, L. Lipeles, M. Bull. Am. Phys. Soc. 1_, (1962 Novick, R. Shultz, G. Condon, E.U. "The Theory of Atomic Spectra” Shortley, G.H. Cambridge Edition (1963) Da I garno, A. Mon. Not. R. Astr. Soc. 131, p.311-313 (1966) Datta, S. Proc. Roy. Soc. A101, p.539 (1922) Dewey, J.M. Phys. Rev. 28, p.1108 (1926) Dewey, J.M. Phys. Rev. 30, p.770 (1927) Dushman, S. D.Van Nostrand (1941) Epstein, Ann.d . Physik. 50, p.189 (1916) Fite, W.L. Brackman, R.T. Hummer, D.G. Phys. Rev. 116, p. 363 (1959) Stebbings, R.F. Foster, J.S. Phys. Rev. 23, P- 293 and 667 (1 ‘ Foster, J.S. Proc. Roy. Soc. Hi, p .47 (1927) Foster, J.S. Proc. Roy. Soc. 122, p.599 (1929) Foster, J.S. Proc. Roy. Soc. A117, p. 137 (1927) Foster, J.S. Proc. Roy. Soc. HI, p.133 (1931 ) Foster, J.S. Proc. Roy. Soc. A122, p.599 (1929) Foster, J.S. Proc. Roy. Soc. A131 , P.142 (1931) 171 Fujioka, Y. Scient. Pap. J0_, p.99 (1929) Garstang, R.H. "Atomic and Molecular Processes" D.R. Bates - Ed. Academic Press (1962) Goldemberg, J. Torizuka, Y. Phys. Rev. 129, p.2580 (1963) Goudsmit, S. Bacher, R.F. Z. Physik 66, p.13 (1930) Hal 1, J.L. Robinson, E.J. Phys. Rev. Letters 14, p.1013 (1965) Branscomb, L.M. Harrison, M.F.A. Dance, D.F. Dolder, K.T. R.S.I. 36, p.10 1443- 1447 (1965) Smith, A.C.H. Jacquinot, P. Bochard, J. C.R. Acad. Sci. Paris 216, p.581 (1943) Janssons, L. Acta. Phys. Pol on. 4_, p.281 (1935) Jenkins, F.A. Segre, E. Phvs. Rev. 55, p.52 (1939) Kaiser, W. Garnett, G.B. Phys. Rev. Letters 7, p.229 (1961) Kipper, A.Y. Pub. Astrom. Obs. Tartu 32, p.63 (1952) Koch, J. Ann. d. Phys. 48_, p. 98 (1915) Kramers, Det.Kal.Danske. Videnskabernes. Selskabs.Skrifter 8, p.111 and 278 (1919) Kramers, Heisenberg. Zeits.f.Physik 31, p.681 (1925) Kusch, P.R. Phvs. Rev. 101, p.627 (1956) Kuhn, H. Zeits.f.Physik 61, p.805 (1930) Lamb, W.E.Jnr. Retherford, R.C. Phys. Rev. 72, p.241 (1947) 172 Lamb, W.E.Jnr. Re+herford, R.C. Phys. Rev. 79, p.4 (1950) Lamb, W.E.Jnr. Skinner, M. Phys. Rev. 78, p.539 (1950) Lamb, W.E.Jnr. Rep. Progr. Phys. H, p-19 (1951) Lipeles, M. Novic k, R. Phys. Rev. 15, p. 17 (1965) Tolk, N. McLennan, J.C. Shrum, G.M. Proc. Roy. Soc. A108, p.501 (1925) McMahon, D.H. Soret, R.A. Phys. Rev. Letters 14, p.1060 (1965) Franklin, A.R. Mayer, M.G. Nature 17, p .932 (1929) Mayer, M.G. Ann. Phys. 9, p.273 (1931) Meissner, K.W. Graffunder, W. Ann. d. Phys. 84, p. 1009 (1927) Mi 1ianczuk, B. Acta. Phys. Pol on 111, p.123 (1934) Mi 1 ianczuk, B. Acta. Phys. Pol on . 3, p.123 (1934) Mi 1 ianczuk, B. Acta. Phys. Pol on . 4, p.65 (1935) Mi 1iyanchuk, V.S. Dokl. Akad. Nauk. USSR 68, p.41 (1949) Mitchell, A.C.G. ’’Resonance Radiation and Excited Atoms" Zemansky, M.W. Cambridge Edition (1934) Mrozowski, S. Zeits. f. Phys. 108, p. 204 (1938) Mrozowski, S. Rev. mod. Phys. 16, p. 153 (1944) Opechowski, W. Zeits. f. Physk. 109, p. 485 (1938) Paschen, Back Physica 1, p. 261 (1921) Pau1i, W. Math. Phys. M.tt. d .dan. Gessd.wiss. 7, p.3 (1925) 173 Phelps, A.V. Molnar, J.P. Phys. Rev. 89, p.1202 (1953) Phelps, A.V. Phys. Rev. 99, p.1307 (1955) Rayleigh Lord. Proc. Roy. Soc. A117, p.294 (1927) Rojansky, Van Vleck Phys. Rev. 32, p.327 (1929) Rojansky, Phys. Rev. 33, (1929) Rubinowicz, T. Zeits. f. Phys. 61_, p .338 (1930) Rubinowicz, T. Zeits. f. Phys. 65_, p .662 (1930) Sal peter, E.E. Phys. Rev. 112, p.1642 (1958) Salwen, H. Phys. Rev. 99, p.1274 (1955) Sandars, P.G.H. Lipworth, E. Phys. Rev. Letters 13, p.24 and 718 (1964) Seaton, M.J. Rep. Proq. Phys. 23, p.313 (1960) SchwartzchiId, Ber. Akad. Wiss. Berlin. 548 (1916) Segre, E. Rend. Li nee. 19, p.595 (1934) Segre, E. Wick, G.C. Proc. Amst. Acad. 36, p.3 (1933) Sel1 in, 1.A. Phys. Rev. 136, 5A - A1245-1253 (1964) Shapiro, J. Breit, G. Phys. Rev. 113, p.179 (1959) Shenstone, A.G. Proc. Roy. Soc. A219, p.419 (1953) Spitzer, L. Greenstein, J.L Astrophys. J. 114, d.407 (1951) Stark, J. Ann. d. Phys. 48 p.210 (1915) Stark, J. Ann. d. Phys. 56 , p.577 (1918) Steubing, W. Redepening, W. Ann. d. Physik 24 , p.161 (1935) 174 Sombursky, S. Zeits. f. Physik 68, p .774 (1931) Sombursky, S. Zeits, f. Physik 76, 3-4 p.266-267 (1932) Takamaine, T. Werner, W. Naturwiss 14, p .47 (1926) Van Gee 1, Zeits. f. Physik 51., p.51 (1928) Vavilov, S.1. (1950) (Borisoglebskii, L.A. - 1958) Zwaan, Zeits. f. Physik 51, p.62 (1928) CHAPTER 3. Bethe, H.A. Sal peter, E.E. Handbook des Physik 35 (1957) Breit, G. Teller, E. Astrophys. J. 91, p .215 (1940) Dalgarno, A Mon. Not. R. astr. Soc . J_31_, p .311 -313 (1966) Dirac, P.A.M. Proc. Roy. Soc. A114 , p.243 and 710 (1927) Gabriel, A.H. Heddle, D.W.O. Proc. Phys. Soc. A258 p.124 (1960) Green, L.C. Johnson, N.C. Phys. Rev. 139, 2A , A373-378 (1965) Kolchin, E.K. Green, L.C. Johnson, N.C. Kolchin, E.K. Astrophys. J. 144, 1 p.369 (1966) Heitler, W. MThe Quantum Theory of Radiation” 3rd. Ed. Clarendon Press, Oxford (1954) Holt, H.K. Krotkov, R. Phys. Rev. 144, 1 p.82-93 (1966) McConneII, J. "Quantum Particle Dynamics" North Holland Publishing Co. (1960) 175 Schiff, L.I. "Quantum Mechanics” McGraw Hill Book Company (1955) Spltzer, L. Greenstein J L. Astrophys. J. 114, p.407 (1951) CHAPTER 4. Allen, J.S. R.C.I. 18, p.747 (1947) Baldwin, G.C. Friedman, S. R.S.I. 36, p.1:16 (1965) Breit, G. Teller, E. Astrophys. J. 91, p.215 (1940) Da I garno, A. Mon. Not. R. Astr. Soc. 131, p.311-313 (1966) Die Itz Rev. Sci. Instr. 36, 12 1700 (1965) Dorrestein, R. Keninkl. Ned.Akad.Wetenschap.Proc. 41, Smit, J.A. p. 725 (1938) Dorrestein, R. Physica 9_, p.433 (1942) Dugan, J.L.G. Richards, H. . J. Chem. Phys. 46, 1 p.346-351 (1967) MuschIItz, E E.Jr. Fraser, R. "Molecular Rays" Cambridge Edition (1931) Hagstrum, H.D. Phys. Rev. 89, p.244 (1953a) Hagstrum, H.D. Phys. Rev. 21, p .543 (1953b) Hagstrum, H.D. Phys. Rev. 96, p.325 (1954a) Hagstrum, H.D. Phys. Rev. 96, p.336 (1954b) Hasted, J.B. "Physics ef Atomic Collisions," Butterworth Ed. (1964) Hasted, J.B. Mahadevan, P Proc. Roy. Soc. A249, p.42 (1958) Hasted, J.B. J. AppI. Phys. 30, p.22 (1959) Hinteregger, H. Watanabe, K. J. Opt. Soc. Am. r 43, p. 604 (1953) Hinteregger, H. Phys. Rev. 96, p. 538 (1954) Holt, H.K. Krotkov, R. Phys. Rev. 144, p. 82 (1966) Hughes, V. Tucker, G. Rhoderick, E. Phys. Rev. 91, p. 4 (1953) Weinreich, G. Isaak, G.R. Nature, 189, p. 373 (1960) Jackson, D.A. Kuhn, H. Proc. Roy. Soc. A148, p. 335 (1935) Lombard, F.J. Ma rtin, F. R.S.I. 32, p. 200 (1961) MacLennan, D.A. Phys. Rev. 148, p. 218-223 (1966) Phelps, A.V. Phys. Rev. 99, p. 1307 (1965) Phelps, A.V. Phys. Rev. 110, p. 1362 (1958) Sholette, W.P. Muschlltz,E.E.Jnr. J. Chem. Phys. 36, p.12 (1962) Stebbings, R.F. Proc. Roy. Soc. (London) A241 , p.270 (1957) Tusting, R.F. Kerns, Q.A. 1.R.E. TRans. Nucl. Sci. NS-9 Knudsen, H.K. No. 3 118 (1962) Varherin, L.J.Jnr. Phys. Rev. 91, p.859 (1953) Walker, W.C. Wainfan, N. J. App. Phys. 26, p. 1367 (1955) Weissler, G.L. Weinreich, G. Hughes, V.W. Phys. Rev. 95 p.6 (1954) Weissler, G.L. Hdbck der Physik 22 (1956) CHAPTER 5. Breit, G. Teller, E. Astrophys. J. 91, p.215 (1940) Dugan, J.L.G. Richards, H.L. J. Chem. Phys. 46, 1 p.346-351 (1967) MuschIitz,E.E.Jnr. Holt, H.K. Krotkov, R. Phys. Rev. 144, 1 p .82-93 (1966) McDaniel, E.W. "Col Iisiong Phenomena in Ionized Cases" John Wi1ey & Sons. (1964) McLennan, D.A. Phys. Rev. 148, 1 p.218-223 (1966) Meissner, K.W. Graffunder, W. Ann. Physik 84, p.1009 (1927) Mitchell, A.C.G. "Resonance Radiation and Excited Atoms’1 Zemansky, M.W. Cambridge Edition (1934) Phelps, A.V. Molnar, J.P. Phys. Rev. 89, p.1202 (1952) Phelps, A.V. Phys. Rev. 99, p.1307 (1955) Ramsay, N.F. "Mol ecular Beams" Oxford Uni .Press (London) (1956) Richards, H.L. MuschIitz,E.E.Jnr. J. Chem.Phys. 41, 2 p.559-565 (1964) CHAPTER 6 Bernstein, R.B. "Atomic Collision Processes” North Holland Publishing Company (1964) Buckingham, R.A. Dalgarno, A. Proc. Roy. Soc. (London) A213, p.327 (1952a) Buckingham, R.A. Dalgarno, A. Proc. Roy. Soc. (London) A213, p.506 (1952b) 178 Cermak, V. J.Chem. Phys. 44 P.3774 (1966) Co legrove, F.D. Schearer, L.D. Bu11.Am.Phys.Soc. 8, p. 112 (1963) Walters, G.K. Da 1garno,A. Kingston, A.E. Proc. Roy. Soc. (London) A71 , p.1053 (1958) Dorrestein, R Physica 9, p.433 (1942) Dugan, J.L.G. Richards, H.L. J.Chem.Phys. 46, 1 p.346-351 (1967) Muschlitz,E.E.Jr. Hasted, J.B. Mahadevan, P. Proc.Roy. Soc. (London) A249, p.42 (1958) Hasted, J.B. "Physics of Atomic Colli soons1! Butterworth Ed. (1964) Holt, H.K. Krotkov, R. Phys. Rev. 144, p.82 (1966) McDaniel, E.W. "Collision Phenomena in Ionized Gases" John Wiley & Sons. Inc. (1964) Phelps, A.V. Molnar, J.P. Phys. Rev. 89, p.1202 (1953) Phelps, A.V. Phys. Rev. 99, p.1307 (1955) Poshusta, R.D. Matsen,F.A. J.Chem. Phys. 32 p.307 (1963) Richards, H.L. Muschlitz,E.E.Jr. J.Chem. Phys. 41 , 2 p.559-565 (1964) Rothe, E.W. Rol , P.K. Bernstein, R.B. Phys. Rev. 130, p.2333 (1963) Shulz, G.J. Fox, R.E. Phys. Rev. 106, p. 1179 (1957) Shulz, G.J. Phys. Rev. 116, p. 1141 (1959) 179 Stebbings, R.F. Proc. Roy. Soc. A241, p.270 (1957) Thieme, 0 Z. Phys. 78, p.412 (1932) CHAPTER 7 Bethe, H.A. Salpeter, E.E. Handbook der Physik. 35 (1957) Holt, H.K. Krotkov, R. Phys. Rev. 144, 1 p.82-93 (1966) Fite, W.L. Brackmann,R.T. Hummer, D.G. Phys. Rev. 116, p.363 (1959) Stebbings, R.F. Green, L.C. Johnson, N.C. Kolchin, E.K. Phys. Rev. 139 2A A373-378 (1966) Saunders, P.G.H. Lipworth, E. Phys. Rev. Letters, 13 24 p.718 (1964) Schiff, B. Pekeris, C.L. Phys. Rev. 134 A638 (1964) Suh, K.S. Zaidi, M.H. Proc. Roy. Soc. A291, p.94-105 (1966) APPEND 1C IES Dorrestein, R. Physica 9 433 447 (1942) Hasted, J.B. Mahadevan, P. Proc. Roy. Soc. A249, p.42 (1958) Holt, H.K. Krotkov, R. Phys. Rev. 144, 1 p.82-93 (1966) Kusch, P. Mi Iler, R.C. Phys. Rev. 99, p.1314 (1955) 180 Lees, Thieme, Proc. Roy. Soc. A137, p. 133 (1932) Litchen, W. Chem. Phys . 26, p.2 (1956) Massey, H.S.W. Mohr, C.B.U. Proc. Roy. Soc. A140, p.613 (1933) Massey, H.S.W. Burlop, E.H.S. "Electronics and Ionic Phenomena” Clarendon Press, Oxford (1952) Mohr, C.B.O. Nicol1 Proc. Roy. Soc. A138 229 469 (1932) Mohr, C.B.O. Nicol1 Proc. Roy. Soc. A142, 320 647 (1933) Ramsay, N.F. "Molecular Beams" Oxford Uni. Press (1956) Zapesochnyi, I.P. Sov. Phys. Dbklady 11 11 p .961 (1967)