A semiempirical method for describing the cross-section of elastic scattering of low-energy electrons on an atom

A semiclassical method for describing cross-sections for elastic scattering of electrons with energies above $1$ eV on an atom is proposed. The idea of the method is to calculate the screening length, taking into account the effect of the electron density distribution in the atom and its polarization by the field of the incident particle, taking into account the delay of the induced dipole moment vector relative to the field strength vector. Analytical expressions are obtained for calculating the screening length, which contain empirical constants. An algorithm for finding constants is described. In the electron energy range of $0.1$–$1$ eV, the cross-sections obtained from the phase theory and the method proposed in this study are matched. Comparisons of the cross-sections obtained by this method with the experimental and theoretical results of various authors are presented.