An expression for the Mott cross section of electrons and positrons on nuclei with Z up t0 118

Abstract

In the present work, an improved numerical solution for determining the ratio,$\mathcal{R}^{\rm Mott}$, of the unscreened Mott differential cross section (MDCS) with respect to Rutherford's formula is proposed for the scattering of electrons and positrons on nuclei with $1\leq Z \leq 118$. It accounts for incoming lepton energies between 1\,keV and 900\,MeV. For both electrons and positrons, a fitting formula and a set of fitting coefficients for the ratio $\mathcal{R}^{\rm Mott}$ on nuclei are also presented. The found average error of the latter practical interpolated expression is typically lower than 1% also at low energy for electrons and lower than 0.05% for positrons for all nuclei over the entire energy range.