Direct calculation of the scattering amplitude without partialwave analysis
Abstract
Two developments in scattering theory are reported. We show, in a practical way, how one can calculate the scattering amplitude without invoking a partialwave expansion. First, the integral expression for the scattering amplitude f(θ) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wave function that appears in the integral expression for f(θ) is obtained by solving the Schrödinger equation with the finite element method. As an example, we calculate electron scattering from static hydrogen (the Hartree potential). With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.
 Publication:

Physical Review A
 Pub Date:
 June 2001
 DOI:
 10.1103/PhysRevA.63.062714
 Bibcode:
 2001PhRvA..63f2714S
 Keywords:

 34.10.+x;
 02.70.Dh;
 General theories and models of atomic and molecular collisions and interactions;
 Finiteelement and Galerkin methods