Partial-Wave Scattering by Non-Spherically-Symmetric Potentials. I. General Theory of Elastic Scattering

Abstract

A general method is developed to obtain the elastic-scattering cross section of an asymmetric potential V(r) = J2iVi( r )Pi(Pz*r) where we have expanded the potential as a sum of multipoles and tii is a unit vector along the 2/-pole axis. We assume that vi(r) is effectively zero beyond a cutoff radius R and we solve the resulting set of coupled differential equations in terms of a scattering matrix S. A general expression for the scattering amplitude /(k,k') is derived in terms of the elements of S and 3j symbols. Finally, as an example, we apply the method to the problem of calculating the total and momentum-transfer cross sections for a randomly orientated set of axially symmetric centers.

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