Electron and positron atomic elastic scattering cross sections

A method was developed to calculate the total and differential elastic-scattering cross sections for incident electrons and positrons in the energy range from $\text{0.01}\text{eV}$ to $\text{1}\text{MeV}$ for atoms of Z=1–100. For electrons, hydrogen, helium, nitrogen, oxygen, krypton, and xenon, and for positrons, helium, neon, and argon atoms were considered for comparison with experimental data.First, the variationally optimized atomic static potentials were calculated for each atom by solving the Dirac equations for bound electron states. Second, the Dirac equations for a free electron or positron are solved for an atom using the previously calculated static potential accomplished (in the case of electrons) by “adjusted” Hara's exchange potential for a free-state particle. Additional to the exchange effects, the charge cloud polarization effects are considered applying the correlation-polarization potential of O'Connell and Lane (with correction of Padial and Norcross) for incident electrons, and of Jain for incident positrons.The total, cutoff and differential elastic-scattering cross sections are calculated for incident electrons and positrons with the help of the relativistic partial wave analysis. The solid state effects for scattering in solids are described by means of a muffin-tin model, i.e. the potentials of neighboring atoms are superpositioned in such a way that the resulting potential and its derivative are zero in the middle distance between the atoms. The potential of isolated atom is calculated up to the radius at which the long-range polarization potential becomes a value of −10⁻⁸.