On the complex angular momentum theory of scattering

Abstract

A contribution to the theory of complex angular momentum techniques in the field of atomic and molecular collisions is given. The author derives a new, flexible representation of the scattering amplitude on the basis of realistic assumptions for the behaviour of the S-matrix in the complex angular momentum plane. The representation has the form of a sum of steepest-descent integrals, S-matrix residue terms and a symmetry-type background integral. The flexibility is due to the presence of two integer parameters which may be chosen conveniently so as to make the residue sums sufficiently convergent and to minimise the total number of important terms.