Coulomb Scattering of Dirac Particles

Abstract

The expressions for the Coulomb scattering amplitudes $F$ and $G$ up to ${\alpha }^4$ terms ($\alpha =\frac{Z}{137}$) for arbitrary $q=\frac{\alpha }{\beta }$ are given. These expressions are used to evaluate the cross section $\frac{d\sigma }{d\Omega }$ and the asymmetry function $S$ at small angles. The behavior of $F$ and $G$ as well as $\frac{d\sigma }{d\Omega }$ and $S$ near $\theta =180\mathrm{}°$ is also discussed. The approximation is then extended to a screened potential by introducing a cutoff parameter $e^{-\mu n}(\mu \ll 1)$ in the partial-wave series. The scattering amplitudes and $\frac{d\sigma }{d\Omega }$ and $S$ are compared with the corresponding Coulomb case.