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

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 3P0,1,2 3S1 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 P4 (or the stepwise P190 parameter), are most seriously affected by these corrections.