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 Ionization 24.59 eV I 3's __ 2-1° 3 3Pp 3D 33S 22.72 eV in 2 P 2 1.22 2 3P 2 I 20.96 2 S 20.61 E n erg y 2 3S 19.82 I s 1.1. Vi ' nw jiff ] ji r; vcfy 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.