Abstract
Fano obtained a relation between the tetradic collision operator W (z) in the Liouville representation and the transition operator T which is the solution of the Lippmann–Schwinger equation in scattering theory. Fano’s formula involves a convolution integral over the entire energy range. In this paper we propose an alternate for the relation, which does not include such a convolution integral and is more algebraic. We obtain the formula by suitably rewriting the ’’Lippmann–Schwinger equation’’ for W (z) and thereby obtaining a set of coupled integral equations. We discuss the formula obtained by Snider and Sanctuary in the light of Fano’s and the present formulas.
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