Doubly differential cross sections for K-shell ionization by e± impact∗

The single ionization of inner-shell bound electrons by lepton impact is a fundamental atomic process of particular interest. Recently, essential progress has been achieved in fragmentation experiments due to developments in many-particle imaging techniques, so-called reaction microscopes [1]. The measurements of the multiply differential cross sections become now feasible. We have deduced the universal scaling behavior for the doubly differential cross sections of the single K-shell ionization of hydrogen-like ions with moderate values of the nuclear charge Z by electron and positron impact [2]. The study is performed to leading order of non-relativistic perturbation theory with respect to the electron-electron interaction. Accordingly, it is assumed that 1/Z ≪ 1 and αZ ≪ 1, where α is the fine-structure constant. The projectile is characterized by the energy E = p/(2m) and the asymptotic momentum p, while the scattered particle is characterized by the energy E1 = p1/(2m) and the momentum p1. The consideration is performed within the near-threshold energy range I 6 E ≪ m, where I = m(αZ)/2 is the K-shell ionization potential and m is the electron mass (~ = 1, c = 1). The differential cross section for the single ionization of a K-shell electron can be cast into the following form