Coulomb effect on elastic electron scattering by hydrogen atom and hydrogen-like ions in their metastable 2s state in the 511–770 KeV energy range

This paper reports on a study investigating the elastic scattering of hydrogen atoms in their metastable state (2S-2S) when subjected to electron impact, with a focus on the Coulomb effect within an energy range spanning from 511keV to 770keV. The analysis employs semi-relativistic wave functions to depict the hydrogen states. The validity of using Darwin wave functions is confirmed by ensuring that the condition Zα<<1 is met, where α represents the structure constant. Both incident and scattered free electrons are described using Dirac spinors. Notably, the semi-relativistic calculations converge with those of the non-relativistic case at low electron velocities. Additionally, in the presence of the Coulomb effect, the electron wave function is approximated by a Dirac function modulated by the confluent hypergeometric function. The paper presents the relativistic differential cross-section (RDCS) as a function of the final scattering angle for various energies of the incident electron, revealing intriguing insights into diffusion probabilities in specific directions. Moreover, the impact of the atomic number Z on the elastic scattering of hydrogen atoms and hydrogen-like ions by electron impact under the influence of the Coulomb effect is thoroughly examined.