Application of Fredholm theory to elastic scattering

Abstract

The Fredholm expansion method is used to evaluate the S-wave phase shifts for: (i) the elastic scattering of electrons by (a) the static potential of atomic hydrogen, (b) a hydrogen atom, with exchange taken into account by the use of symmetrized wave functions; (ii) the elastic scattering of particles by exponential and screened Coulomb potentials. It is found that, whereas the Born series often converges slowly, even at quite high impact energies, the Fredholm expansion usually converges fairly rapidly to the exact value of the phase shift. In the cases the authors have investigated the second Fredholm approximation is superior to the second Born approximation except sometimes at low impact energies. However, it should be noted that the first Fredhom approximation is usually much inferior to the first Born approximation at all impact energies and so should not be used.