An approximate solution to the scattering integral for general interatomic potentials

Abstract

An approximation of the scattering integral is derived by expanding the potential about the distance of closest approach and truncating the expansion so that the integral can be performed analytically. The results are improved by using the approximate integrand only in the region near the closest approach, and assuming zero potential for large distances. The analytical solution, which requires little computation time relative to other solution methods, is shown to yield sufficient accuracy for a wide range of particle energies and impact parameters, using both the Moliere and ‘‘Universal’’ potentials.