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Canadian Journal of Physics

Interference effects between electron exchange and the spin–orbit interaction

Wilhelm Raith, G. Baum, M. Tondera

Published Nov 1, 1996• 0 citations
Publisher

Abstract

In accordance with predictions made in 1974, recent measurements demonstrated that the elastic e–Cs scattering is richer in physics than a simple addition of Mott scattering and nonrelativistic exchange would provide. Now it is time to take a closer look at the general analysis of Burke and Mitchell and think about further experiments that will stimulate improvements in calculations and lead to a deeper understanding of the underlying physics.

DOI
10.1139/p96-803

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In accordance with predictions made in 1974, recent measurements demonstrated that the elastic e–Cs scattering is richer in physics than a simple addition of Mott scattering and nonrelativistic exchange would provide. Now it is time to take a closer look at the general analysis of Burke and Mitchell and think about further experiments that will stimulate improvements in calculations and lead to a deeper understanding of the underlying physics.
This report discusses the progress made on the research program on collision studies using optically state selected beams. The objective of this work is to stimulate deeper theoretical understanding of the electron-atom interaction by providing more complete experimental measurements on colliding systems. In particular we concentrate on effects dependent on the electron and atomic spins. Recent years have seen a rapid growth in the number and complexity of experiments which include spin analysis. The additional information provided by such experiments has contributed greatly to our ability to model numerically collisions between electrons and atoms. Those measurements have typically been on systems where one of the incident particles has zero spin. Hence, one could derive no direct information about the exchange interaction. In our measurement, both collision partners have non zero spin so that we see directly the effects of the exchange as well as the spin-orbit interaction. Indeed, our experimental observable, the asymmetry in a scattering rate when the incident spins are parallel versus antiparallel, is directly related to the ratio of the collision cross sections for scattering via the triplet versus the singlet spin state. 19 refs., 12 figs.
An analysis of spin-polarization in low energy elastic scattering electrons by one electron s-state atoms is carried out allowing both for electron exchange and relativistic effects. First the collision matrix is written in terms of the asymptotic form of the solutions of the radial equations. Then arguments, based on the invariance of the Hamiltonian under time reversal, space rotation and space reflection are used to write down the most general form of this matrix. It is found that it can be expressed in terms of six independent amplitudes. Then expressions for the observable quantities, including the spin polarization of the electron and of the atom after the collision are derived. Finally, the analysis is specialized to the case where spin-polarization effects are caused by a spin-orbit interaction and these effects are considered in the neighbourhood of cusps and resonances in electron alkali atom scattering.
Recent experiments using polarized electron beams have shown that spin exchange effects for elastic collisions with O2{\mathrm{O}}_{2}O2​ and NO are much smaller than for Na atoms. We report calculated spin-flip differential cross sections for elastic collisions of polarized electrons with O2{\mathrm{O}}_{2}O2​ in agreement with experiment. In general, we can attribute the large variation of the spin-flip differential cross sections to resonances and interference effects. Such features arising from interference, however, may be washed out in the molecular case due to the average over orientations. Calculations with oriented O2{\mathrm{O}}_{2}O2​ molecules show strong exchange effects as for Na.