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Physical Review A

Theory of angular-correlation experiments in electron scattering, including fine structure

Gregory A. Parker, Thomas M. Miller, Massoud Mahgerefteh, David E. Golden

Published Apr 1, 1984• 2 citations
Publisher

Abstract

A theory of electron-impact excitation of atoms in which fine structure is included as a perturbation is presented in detail. Hyperfine structure is included in the target atom but neglected in the electron-atom interaction. Expressions for electron-photon angular-correlation parameters and scattering cross sections are derived in terms of products of complex scattering amplitudes, with emphasis on electron-sodium excitation. Examples are given in which zero-field quantum beats may be observed in electron-photon angular-correlation and differential-cross-section measurements. Some of the interference terms are only observable in angular-correlation experiments. Examples are also given of partial cross sections for electron-impact excitation of state-to-state hyperfine levels in terms of direct- and exchange-scattering amplitudes plus additional terms due to the inclusion of fine-structure effects. The expressions given allow a comparison between the various possible scattering experiments.

DOI
10.1103/physreva.29.1770

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A theory of electron-impact excitation of atoms in which fine structure is included as a perturbation is presented in detail. Hyperfine structure is included in the target atom but neglected in the electron-atom interaction. Expressions for electron-photon angular-correlation parameters and scattering cross sections are derived in terms of products of complex scattering amplitudes, with emphasis on electron-sodium excitation. Examples are given in which zero-field quantum beats may be observed in electron-photon angular-correlation and differential-cross-section measurements. Some of the interference terms are only observable in angular-correlation experiments. Examples are also given of partial cross sections for electron-impact excitation of state-to-state hyperfine levels in terms of direct- and exchange-scattering amplitudes plus additional terms due to the inclusion of fine-structure effects. The expressions given allow a comparison between the various possible scattering experiments.
Electron-photon angular-correlation parameters are given for the 2P^{2}P2P states of sodium which include both fine and hyperfine effects. These expressions contain interference terms between scattering amplitudes which are only observable in angular-correlation experiments and give rise to zero-field quantum beats in the excitation of the 2P32^{2}P_{\frac{3}{2}}2P23​​ state. By neglecting fine structure, partial cross sections for the $^{2}P_{J}(F,{M}_{F})\ensuremath{\leftarrow}^{2}S_{\frac{1}{2}}(F=2,{M}_{F}=2)$ excitations are given in terms of direct and exchange-scattering amplitudes.
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.
Three techniques are described from which the scattering parameters A and X can be measured in electron-photon coincidence studies of the 32P state of sodium. The relative sensitivity of the angular correlation and polarized photon techniques is discussed for states which have significant hyperfine structure in the excited state. The phenomenon of zero field quantum beats is described in the framework of the electron impact excitation of sodium. It is shown that the amplitude of the beat pattern depends on the parameter it. The use of the beat pattern to determine A is discussed.
Abstract The dipole radiation emitted by an atom excited by a unidirectional electron beam has a nonuniform angular distribution which is simply related to the percentage polarization P of the radiation emitted perpendicular to the beam. P was first calculated using the OppenheimerPenney (O.-P.) theory. In this theory the probability of excitation of an upper quantum state and the probability of subsequent emission of a polarized photon from such a state are considered independently. P is finally expressed in terms of the cross-sections QM for excitation of states of definite component of angular momentum along the direction of the electron beam. In general, P is dependent on detailed numerical calculations of QM j, but the selection rule A = 0 removes this dependence at threshold. In the O.-P. theory allowance may be made for fine structure and hyperfine structure, but the theory is ambiguous when the f.s. or h.f.s. separations are comparable with the line width. A theory is therefore developed which is based on the calculation of the probability of a polarized photon being emitted by the complete system of atom + electron. The ambiguity of the O.-P. theory is removed by integration over line profiles, but the expressions reduce to O.-P. expressions when the f.s. or h.f.s. separations are much smaller or much larger than the line width. The Lyot line of hydrogen is an intermediate case for which the line widths and the h.f.s. separations are comparable. Assuming the validity of the Born approximation, a simple expression is obtained which allows the QM to be calculated from the angular distribution of the scattered electrons. Theoretical predictions are compared with experimental results. For the Na£) lines the predicted polarization is small enough to escape experimental detection. Polarizations observed by - Skinner & Appleyard in 1927 for various Hg lines rise to maxima with decreasing electron energy, and then tend to values close to zero at threshold. These experimental results at low energies appear to be inexplicable in terms of the reactions considered, but if the polarization curve above the maximum is extrapolated to threshold, the theory and experiment are found to be in reasonable agreement. Further experimental work is thought to be desirable
We report the first observation of zero-field quantum beats in the electron-impact excitation of an atomic state. The effect has been observed in electron-photon coincidence experiments on the 32P3^{2}P32P state in sodium. The beats arise from the influence of the hyperfine structure in the J=32J=\frac{3}{2}J=23​ level of the excited state.