Statistical model of an atom in electron scattering calculations

The parameters describing scattering of electrons by atoms, which usually involve multiple integration of the atomic potentials, may be severely affected by the accuracy of these potentials. In the present work an iterative procedure is proposed providing a sequence of solutions of the Thomas-Fermi equation with increasing accuracy. Such a sequence makes it possible to establish the sensitivity of a given parameter to the accuracy of the atomic potential, and consequently to determine the accurate value of this parameter. Based on the present solutions, the differential scattering cross-sections for the Thomas-Fermi atom are calculated, and are found to deviate from the literature data.