Multipole relaxation and transfer rates in the impact approximation: application to the resonance interaction

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Abstract
A theoretical treatment of the relaxation and transfer of atomic multipole moments due to interatomic collisions is presented, applicable to systems of emitters and perturbers with any angular momenta. Expressions are obtained for the rate constants, within the impact approximation, in terms of the elements of the scattering matrix evaluated as a function of impact parameter for an emitter-perturber collision. Processes in which the total electronic excitation energy is not conserved are excluded and collisions are assumed to occur isotropically. Explicit evaluation of rate constants has been carried out using the first-order dipole-dipole (resonance) interaction, assuming the classical straight line path approximation. Four special cases have been treated by numerical integration of the Schrodinger equation in the interaction representation. These are: Jg (ground state angular momentum)=0, Je (excited state)=1; jg=1/2, Je=1/2; Jg=1/2, Je=3/2; Jg=1, Je=1. The (1/2, 1/2) rate constants are shown to be simply related to those for the (0, 1) case. Within the context of the various approximations, numerical accuracy is expected to be better than 1%.