Anisotropic particle spectra and momentum sharing in multicomponent collision cascades

Abstract

Sigmund’s analytical sputtering theory has been used to explain various Monte Carlo simulations given by Urbassek and Conrad. It has been demonstrated that only Sigmund’s theory can predict all the simulation results. The present author has shown that all the transport equations describing the statistics of linear random collision cascades are suitable for a complete use of the exact scattering cross-section of power potential (V∝r−1/m) interaction collisions. Asymptotic expansions of an anisotropic particle flux (L=0,1) are derived here for an arbitrary multicomponent medium. Several new explicit expressions are further reported for various statistical distribution functions. Asymptotic formulae for energy and momentum sharing are presented. The correction terms in asymptotic expansions of isotropic solutions (L=0) are evaluated for a binary target by the use of both scattering cross-sections [dσ]p=C0dT/T and [dσ]z=σdT/Tm. It has been shown that [dσ]z greatly enlarges the range of validity of the asymptotic solutions as compared to [dσ]p. In some cases, [dσ]z can even yield exact solutions. As usual, the electronic stopping is ignored in the analysis.