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

TL;DR

This paper presents an improved numerical method and a practical fitting formula for calculating the Mott cross section ratio for electrons and positrons scattering on nuclei with Z up to 118 across a broad energy range, achieving high accuracy.

Contribution

It introduces a new numerical solution and a fitting formula for the Mott cross section ratio, covering energies from 1 keV to 900 MeV for nuclei with Z up to 118, with high precision.

Findings

Average error below 1% for electrons at low energies.

Average error below 0.05% for positrons across all energies.

Applicable to nuclei with Z up to 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.