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Measurement Science and Technology

Solid angle and lens corrections for light-polarization analysis in atomic scattering experiments

Ian Humphrey

Published Jan 1, 1999• 5 citations

Abstract

Although it is a routine matter to correct for the systematic effects of a finite solid angle and the polarizing effects of a light-collection system in atomic collision studies, the methods for conducting such corrections are rarely (if at all) presented. It is the intention of the present work to present explicit formulae for the general case and explicit results for some popular experiments. No experimental results are presented. Integration over the solid angle of a conical light-collection system and the polarizing effect of a lens will be discussed. Three sample cases for which the solid-angle integration can be performed analytically are presented: a standard J = 1 J = 0 (or P S) electron-photon coincidence experiment; a laser-mediated stepwise coincidence experiment (laser-excited J = 1 J = 2 and spontaneous J = 2 J = 1); and an uncorrelated 3 P 0,1,2 3 S 1 light-polarization measurement (such as is commonly used to establish electron spin polarization). For most realistic cases, the total effect is very small and, furthermore, the lens, with some important exceptions, only marginally modifies the result of a pure solid-angle integration. The effect of internal absorption within the lens is considered and shown to be negligible. In-plane Stokes' measurements, such as of P 4 (or the stepwise P 190 parameter), are most seriously affected by these corrections.

DOI: 10.1088/0957-0233/10/5/310

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Although it is a routine matter to correct for the systematic effects of a finite solid angle and the polarizing effects of a light-collection system in atomic collision studies, the methods for conducting such corrections are rarely (if at all) presented. It is the intention of the present work to present explicit formulae for the general case and explicit results for some popular experiments. No experimental results are presented. Integration over the solid angle of a conical light-collection system and the polarizing effect of a lens will be discussed. Three sample cases for which the solid-angle integration can be performed analytically are presented: a standard J = 1 J = 0 (or P S) electron-photon coincidence experiment; a laser-mediated stepwise coincidence experiment (laser-excited J = 1 J = 2 and spontaneous J = 2 J = 1); and an uncorrelated 3 P 0,1,2 3 S 1 light-polarization measurement (such as is commonly used to establish electron spin polarization). For most realistic cases, the total effect is very small and, furthermore, the lens, with some important exceptions, only marginally modifies the result of a pure solid-angle integration. The effect of internal absorption within the lens is considered and shown to be negligible. In-plane Stokes' measurements, such as of P 4 (or the stepwise P 190 parameter), are most seriously affected by these corrections.

The density matrix parametrization of collisionally excited atomic ensembles is generalized to account for a projectile spin. The elements are related to the ``generalized Stokes parameters'' of Andersen and Bartschat [J. Phys. B 27, 3189 (1994)], determined in scattered-projectile--polarized-photon coincidence experiments after impact excitation by spin-polarized electrons. The well-established orientation propensity rule for unpolarized electron beam experiments is not valid for spin-resolved collisions.

In an electron-polarized photon coincidence experiment the Stokes' parameters P 1 , P 2 , P 3 and P 4 have been determined for four Ne * (3p) to Ne * (3s) transitions at a fixed electron energy of 50 eV and in the electron angular scattering range 30 degrees -70 degrees . The results indicate a tendency towards positive values for P 3 at the lowest scattering angles studied and a strong tendency towards zero and even negative values for P 4 . In all cases a drop in the total polarization degree between 30 degrees and 50 degrees electron scattering angle is observed, indicating that there is a decrease of coherence at these scattering angles.

We present a parametrization in terms of Stokes parameters for the scattering from a P state to a P state for atomic collisions in a beam experiment. The classic approach to a `complete scattering experiment', well known for S-state-to-P-state transitions, is generalized by a systematic combination of optical preparation of specific initial P states with Stokes parameter analysis of the radiation pattern from the final P state. The anisotropy of the initial and final state provides the possibility of extraction of a complete set of nine parameters describing the reaction at the level of five independent scattering amplitudes. We discuss the minimum number of experiments required to obtain a complete set of parameters in the cases of scattering angle-integrated and scattering angle-differential measurements. Relations to collision parameters for the reverse process are derived. Finally, effects due to fine and hyperfine depolarization, as well as inclusion of electron spin polarization, are treated.

The density matrix parametrisation of collisionally excited atomic ensembles is generalised to account for projectile and target spin polarisations. The density matrix elements, containing spin-resolved alignment and orientation parameters, can be determined by measurements of the 'generalised Stokes parameters' introduced by Andersen and Bartschat (1994) to describe scattered-projectile-polarised-photon coincidence experiments. Focusing on electron impact excitation of light alkali-type targets and mercury, the present experimental status of such experiments is reviewed, in particular with regard to the 'perfect scattering experiment' whereby all independent scattering amplitudes are determined.

In this paper, we specifically examine the consequences of a finite scattering geometry on ''in-plane'' coherence experiments, i.e. polarization correlation or superelastic scattering experiments in which the incidence vector of the detected photon or the laser 'photon lies in the nominal scattering plane (/phi//nu/ = 0). The ''in-plane'' experimental configuration is adopted in order to give direct information about spin-orbit coupling effects. We show that a finite scattering geometry can give rise to severe distortion in the dependence of the coincidence or superelastic scattering signal intensity on the photon polarization and that this distorted behavior can be misinterpreted as arising from spin-orbit coupling effects. 11 refs., 3 figs.