Truncated Matching Potentials in the Classical Theory of Elastic Atomic Scattering

Abstract

Atomic collisions in the radiation damage of solids can be described by repulsive potentials for which the scattering integrals cannot generally be evaluated in closed form. However, the evaluation becomes possible when the actual interatomic potential is replaced by certain truncated power potentials which match the actual potential in value and in slope at the minimum distance. The usefulness and accuracy of such matching potentials are discussed and numerical examples are given for the scattering angle, the "time integral," and the energy transfer in the cases of an exponential potential and of an exponentially screened Coulomb potential. The agreement with the exact numerical solutions is surprisingly good.