Second Born approximation to the elastic scattering of electrons and positrons by helium atoms

Abstract

A widely occurring error in the evaluation of the closure term in the simplified second Born approximation to electron- helium scattering is corrected. The corrected theory is applied to the elastic scattering of electrons and positrons by the 1 ¹S ground state of helium in the energy range 50 eV to 800 eV. The full second Born approximation, in which cross sections are calculated by squaring the modulus of the full second Born amplitude, and the third-order second Born approximation, in which the second Born cross section is only evaluated correct to third order in the interaction potential, are both shown to be poor. A modification of the second Born approximation first used in the original work of Massey and Mohr (1934) is adopted. This 'new' approximation gives special treatment to the coupling of the 1¹S state to itself. The results obtained are in much better agreement with experiment. Exchange effects are also taken into account in electron-helium scattering and appear to be important up to quite high energies. Positron-helium differential cross sections are found to be smaller and flatter than the corresponding electron cross sections.