Mott differential cross section by light nuclei using Monte Carlo simulation

Abstract

The interactions of high speed $e^{ - }$ and $e^{ + }$ by an atomic nucleus have provided the accurate knowledge about nuclear dimensions and charge allocation. For two light nuclei (${}_{2}^{4} {\text{He }}$ and ${}_{6}^{12} {\text{C}}$), the ratio of differential Mott to differential Rutherford cross sections $\left( {\frac{{d\sigma_{{{\text{Mott}}}} }}{{d\sigma_{{{\text{Retherford}}}} }}} \right)$ was calculated in the energy range $5 {\text{keV}} - 10 {\text{MeV}}$ and through scattering angles from $15^\circ$ to $180^\circ$. In the present investigation, Mott differential cross section evaluated by the following relationships: Mott–Born, McKinley–Feshbach, and Rutherford equations. The first one which was modified with the three vital correction parameters namely for spin $\left( {f_{{{\text{spin}}}} } \right)$, finite recoiled nucleus $\left( {f_{{{\text{recoil}}}} } \right)$, and the finite nuclear size $\left( {f_{{{\text{size}}}} } \right)$. Monte Carlo simulation was used to accomplish all the calculations. The results were in good agreement in comparison with results for others studies.