Calculations of inner-shell ionization by electron impact with the distorted-wave and plane-wave Born approximations

A method is described for computing total cross sections for the ionization of inner shells of atoms and positive ions by impact of electrons and positrons with arbitrary energies. The method combines the relativistic plane-wave Born approximation (PWBA) with a semirelativistic version of the distorted-wave Born approximation (DWBA). Formal expressions for the longitudinal and transverse generalized oscillator strengths (GOSs) of closed shells are derived. Tables of GOSs for K shells and for L and M subshells of neutral atoms have been calculated for a discrete grid of energy losses and recoil energies. A suitable interpolation scheme allows the easy evaluation of PWBA ionization cross sections from these GOS tables. The difference between the total ionization cross sections that result from the DWBA and the PWBA (considering the longitudinal interaction only) has been calculated numerically for projectiles with kinetic energies up to 16 times the ionization energy of the active shell. In this energy range, ionization cross sections with the accuracy of a distorted-wave calculation are obtained by simply adding this difference to the cross section resulting from the conventional PWBA. For higher energies, the cross section is obtained by multiplying the PWBA cross section by an energy-dependent scaling factor that is determined by a single fitted parameter. Numerical results are shown to agree with experimental data, when these are available.