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Physical Review A

Theory of Atomic Photon-Particle Coincidence Measurements

J. H. Macek, D. H. Jaecks

Published Dec 1, 1971• 233 citations
Publisher

Abstract

The theory of measurements in which photons are detected in delayed coincidence with a scattered particle is developed in a form specifically applicable to atomic collisions. Equations are obtained which relate the measured coincidence rate to excitation amplitudes. These equations incorporate the polarization of the radiation, the fine and hyperfine structure of the atomic levels, the coherence of the radiation, and the time dependence of the radiation intensity. A semiclassical model for certain transitions is introduced to illustrate new features of coincidence measurements. The $\mathrm{Ly}\ensuremath{-}\ensuremath{\alpha}$ transitions in hydrogen and $^{1}P\ensuremath{\rightarrow}^{1}S$ transitions in He are treated in detail to illustrate the general theory.

DOI
10.1103/physreva.4.2288

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The theory of measurements in which photons are detected in delayed coincidence with a scattered particle is developed in a form specifically applicable to atomic collisions. Equations are obtained which relate the measured coincidence rate to excitation amplitudes. These equations incorporate the polarization of the radiation, the fine and hyperfine structure of the atomic levels, the coherence of the radiation, and the time dependence of the radiation intensity. A semiclassical model for certain transitions is introduced to illustrate new features of coincidence measurements. The Ly\ensuremath−\ensuremathα\mathrm{Ly}\ensuremath{-}\ensuremath{\alpha}Ly\ensuremath−\ensuremathα transitions in hydrogen and 1P\ensuremath→1S^{1}P\ensuremath{\rightarrow}^{1}S1P\ensuremath→1S transitions in He are treated in detail to illustrate the general theory.
A brief review is given on development of electron-photon coincidence studies from electron impact of atoms. The theory of electron-photon correlations is outlined in detail in terms of cross sections of excited atoms and excited state charge clouds. The state of a target atom is determined by the various orientation and alignment parameters and the multipole moments of the excited atom. General considerations, such as coherence effects in impact excitation, the influence of fine and hyperfine structures in correlations are taken into account. The relationship between scattering amplitudes (including their phases) and target parameters is worked out for singlet and doublet transitions.
Measurements have been made of the polarization of characteristic radiation of excited states, formed in charge exchange collisions, in delayed time coincidence with the neutral particles formed and scattered during the collision. Such information directly provides ratios of populations of orbital magnetic sublevels and phase differences between scattering amplitudes. This relative phase data, in conjunction with an appropriate model of the collision process, has provided insights into the evolution of the electronic charge distribution during the collision process. These techniques are also being applied to ion-molecule charge transfer collisions.
The results of electron-photon coincidence experiments have given a new insight into the excitation of atoms by electron impact. This article reviews the way in which this new experimental technique has provided an exacting and fundamental test for the theory of the excitation process. The basic experimental method is first described, and a comprehensive treatment of excitation of the n 1 P states of helium is given. The extension of the technique to the study of excitation of the n=2 states of atomic hydrogen is then presented. Coincidence measurements also provide information on the role of spin in the collision, and this subject is treated in detail for excitation of heavy atoms by both unpolarised and spin-polarised beams of electrons. Finally, the electron-photon coincidence method permits observation of the time evolution of excited atomic states, and this review describes the attempts made to observe quantum beats in the radiative decay.
We present linear and circular polarization measurements of $3^{1}P\ensuremath{-}2^{1}S$ (501.6 nm) photons detected in delayed coincidence with electrons inelastically scattered from the 31P3^{1}P31P level of helium. Vector polarization and coherence parameters of the coincident radiation provide direct experimental evidence of the coherent nature of the excitation process. Atomic orientation is obtained directly from the circular polarization measurements. Analysis of the data also yields $\ensuremath{\lambda}$ and $\ensuremath{\chi}$ parameters for 31P3^{1}P31P excitations, which are compared with previous data and theory.