Calculations of Total Cross Sections for Scattering from Coulomb Potentials with Exponential Screening

Abstract

Momentum transfer cross sections and total cross sections are calculated for scattering from the potential energy function $V=\left(\frac{Z_1{Z}_2{e}^2}{r}\right)\exp (-\frac{r}{a})$. Here the first factor is the Coulomb term and the exponential factor contains a screening length $a$. The cross sections are obtained by integrating the differential cross section over all angles using a classical calculation or a Born approximation calculation according to whichever is valid. The validity criteria are discussed as they depend on the de Broglie wavelength of the scattered particle. In certain cases the Born approximation solution is valid at small angles and the classical solution is valid at large angles. Graphs and tables are presented showing the results as functions of suitable parameters.