On quantal rotational rainbows

Abstract
The structure of rotational rainbows for the excitation of homonuclear molecules out of the ground state by atoms is examined. The authors assume that the energy sudden approximation (ESA) is valid but not the centrifugal sudden approximation (CSA). In these circumstances the classical differential cross section is known to have a step at the maximum value of the classically accessible angular momentum transfer, and logarithmic singularities elsewhere, rather than a single square root singularity as when the CSA is also valid. The authors have investigated how quantal effects alter this picture and in particular have tried to ascertain when the effects due to the breakdown of the CSA become apparent. They conclude that when analysing such cross sections it is important to use a quantisation axis along the apse, (Pf-Pi), where Pi(Pf) is the initial (final) momentum of the incident atom. They find that both interference effects and transitions out of the m=0 state play important roles, and that when the m=2 state is classically accessible the CSA is no longer valid.