On magnetic transitions and the interpretation of the partial wave parameter in the CS and IOS approximations in molecular scattering theory

Abstract

The recent discovery by Khare that choosing the CS partial wave parameter ? to be the initial orbital angular momentum, l_i, leads to a simple differential scattering amplitude for definite polarization transitions is examined in detail. It is found that the resulting scattering amplitude formula, which is a rotation of the usual McGuire–Kouri formula, predicts nonzero magnetic transitions in all frames except that whose Z axis always points in the final observation direction ?. A detailed comparison of l_i and l_f labeling is made and it is shown that both lead to nondiagonal approximations to the p‐helicity amplitude, T^J(jλ‖j₀m₀), and to differential scattering amplitudes which have the proper limiting behavior at small and large scattering angles. In addition it is shown that both l_i and l_f labeling yield identical results for all degeneracy averaged cross sections, including the general relaxation cross sections. Further, we show rigorously that if the quantization axis is along a direction perpendicular to the plane of the incident and final momenta, then the l_i and l_f labeled cross sections are identical. It is argued on the basis of available numerical results and on physical grounds that the l_i‐labeled CS is preferred over the l_f CS for calculating magnetic transitions quantized along the incident momentum. We further expect the l_f CS to be preferred for calculating magnetic transitions quantized along the final momentum. However, other ? choices may be better yet for magnetic transitions in general.