Analytical Solutions of the Boltzmann Transport Equation for Light Ion Reflection

Reflection of light ions from solids have been calculated in the low-energy region where large-angle multiple collisions dominate. Backscattering parameters are obtained as a solution of the Boltzmann equation in the transport approximation. The Laplace transformed equation, which has the form of a one-group transport equation for isotropic scattering, has been solved by using an accurate analytical approximation of Chandrasekhar's H-function. Universal curves as well as analytical results are presented for reflected energy spectra integrated over all ejection angles, particle and energy reflection coefficients, and total angular distribution of backscattered ions. Calculations have been done for different angles of incidence. For normal ion incidence and primary energies higher than 100 eV, the agreement between analytical theory and computer simulation data is satisfactory.