The Second Born Approximation in Inelastic Collisions of Electrons with Atoms

Abstract

The second approximation in Born's theory of collisions is worked out for the excitation of the 2p state of hydrogen and of the 21P state of helium from the corresponding ground states by electron impact. The method is not applicable to electron energies too close to the threshold. The correction introduced by the second approximation, which reduces the intensity of the small angle inelastic scattering and the total inelastic cross section by an amount increasing as the electron energy decreases, is of the correct sign and about the right magnitude, in the energy range to which it is applicable, to provide an explanation of the discrepancies between calculated and observed cross sections for excitation of optically allowed transitions.