A proof of detailed balancing for the impact parameter method

Abstract

It is shown that the impact parameter method is consistent with detailed balancing even though only a finite number of states is included in the expansion set. Both atomic and molecular eigenfunction expansions are discussed. Conditions on the coupling coefficients are given which are sufficient for probability conservation and detailed balancing. It is emphasized that in the case of nonorthonormal expansions the matrix of coupling coefficients should not be Hermitian symmetric. The averaging processes used by Rapp and Francis and by Bates and Williams to symmetrize this matrix are shown not to be necessary for detailed balancing and to be inconsistent with the proper expression of probability conservation. Alternatives to the averaging process are suggested.