Direct inner-shell ionization of atomic ions by electron impact

We study the higher-subshells effect on the direct ionization from inner 1s, 2s, 2p, 3s, 3p subshells of ions charged 5+ and more. The cross-sections analysed are those calculated in the relativistic distorted-wave (RDW) approach. For removal of an electron from a certain nl-subshell of ions, belonging to a sequence of ionization stages, we found approximate scaling of the cross-sections. The scaled cross-sections differ from each other by less than 50%. The difference depends on the number of electrons, N, bound above the nl-subshell undergoing the ionization. With an increase in N the scaled cross-sections decrease for projectiles of near-threshold energy and increase for high-energy (non-relativistic) projectiles. Dependence of the scaled cross-sections on a target ion (its chemical element, charge and level) is weak. For use in applications, we approximated the direct inner-shell ionization cross-sections by a simple formula with nl-dependent coefficients