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

The recent discovery by Khare that choosing the CS partial wave parameter l-bar to be the initial orbital angular momentum, l/sub 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 R. A detailed comparison of l/sub i/ and l/sub f/ labeling is made and it is shown that both lead to nondiagonal approximations to the p-helicity amplitude, T/sup J/(jlambdavertical-barj0m0), 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/sub i/ and l/sub 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/sub i/ and l/sub f/ labeled cross sections are identical. It is argued on the basis of available numerical results and on physical grounds that the l/sub i/-labeled CS is preferred over the l/sub f/ CS for calculating magnetic transitions quantized along the incident momentum. We further expect the l/sub f/ CS to be preferred for calculating magnetic transitions quantized along the final momentum. However, other l-bar choices may be better yet for magnetic transitions in general