Energy Distribution of Energetic Atoms in an Irradiated Medium. II. Single Species Case: Application to Radiation Damage Calculations

Abstract

Collision densities are calculated for a homogeneous time-invariant system of energetic and thermal atoms of a single species. It is assumed that the rapidly moving atoms emanate from a monoenergetic source and undergo only binary elastic collisions with thermal atoms. For a class of interaction potentials whose differential scattering cross sections are independent of the energy of the incident atom, the collision density is found to vary as 1/E near the source energy, and as 1/E2 at lower energies. For hard-sphere scattering, the 1/E2 functionality extends over the entire energy range from zero to the source energy; as the degree of scattering anisotropy increases, the 1/E2 range contracts, and the 1/E variation covers an increasingly broad interval. Analytical expressions are obtained for the collision densities in both regions. Similar conclusions are reached for a less restricted class of interaction potentials, and the results applied to the calculation of the number of displaced atoms produced by a primary energetic atom.