Reflection coefficient of low-energy ions as a universal function of the scaled transport cross section

Multiple collision theory of heavy ion ranges in an infinite medium has been used to calculate the reflection coefficient from the penetration profile, by a method first described by Bottiger et al. Interaction with target electrons has been neglected and nuclear collisions have been described by the power cross sections. Calculations are restricted to low reduced ion energies e0≤0.1 and to target/ion mass ratios μ≤10, when electronic stopping is much less than the nuclear stopping. The Gaussian approximation of the penetration profile and the reflection coefficient are found in a form of simple analytic formulas. Furthermore, the penetration profile was constructed by using Edgeworth expansion and moments of the distribution up to the fourth order, and the reflection coefficient was determined from the profile. Good agreement between the analytical results and the reflection coefficient obtained from Edgeworth expansion was found, for target atom/ion mass ratios μ≥1.3. It is shown that the reflection coefficient is a universal function of the scaled transport cross section. The scaling is fulfilled for v≥2, when ion reflection is determined by large-angle multiple collisions, and breaks down for v<1 i.e. μ<1, when scattering angles are small. Results are compared with TRIM computer simulation data.