Classical Calculation of Differential Cross Section for Scattering from a Coulomb Potential with Exponential Screening

TLDR

The screened Coulomb potential \(V=(Z_{1}Z_{2}e^{2}/r)\exp(-r/a)\) models the interaction between two colliding atoms, incorporating electron screening through the length \(a\). Classical orbital calculations are shown to provide valid results for ions of several keV scattering from atoms, and the resulting impact parameters and differential cross sections for all scattering angles are computed and tabulated across a wide range of screening parameters.

Abstract

The potential energy function considered is $V=(\frac{{Z}_{1}{Z}_{2}{e}^{2}}{r})\mathrm{exp}(\ensuremath{-}\frac{r}{a})$, which approximately represents the potential between two atoms in collision taking into account the screening of the atomic electrons. Here the first factor is the Coulomb potential and the exponential factor contains a screening length $a$. It is shown first that a classical orbital calculation should give valid results under certain conditions in problems where ions with energies of many thousands of electron volts scatter from atoms. Calculated values of the impact parameters and differential cross sections are presented for all angles of scattering. These quantities are tabulated for a wide range of parameters corresponding to various degrees of screening.