Energy Distribution of Energetic Atoms in an Irradiated Medium

A set of coupled linear integral equations for the energy distributions of rapidly moving atoms in an irradiated medium composed of many species is investigated. It is assumed that only binary collisions occur in which an energetic atom interacts with a thermal atom. Solutions are obtained for the case of two species where scattering is isotropic in the center of mass system and all collision cross sections have the same energy dependence. When the mass m₁ of species 1 is much less than m₂ the collision densities have the form ${\mathrm{f(E)=aE}}^{\text{−2}}{\mathrm{+bE}}^{{\text{−2+4(c}}_1{\mathrm{+c}}_2{\mathrm{)m}}_1{\mathrm{/m}}_2}$ , where c₁ and c₂ are related to the collision cross sections. When m₁ = m₂, then ${\mathrm{f(E)=aE}}^{\text{−2}}{\mathrm{+bE}}^{{\text{−1/(1+c}}_1{\text{)−1/(1+c}}_2)}$ . Similar solutions are found for intermediate mass ratios.