Cross sections for ionization of K, L and M shells of atoms by impact of electrons and positrons with energies up to 1 GeV: Analytical formulas

Analytical formulas are presented for the easy calculation of cross sections for ionization of K, L and M shells of neutral atoms by impact of electrons and positrons with kinetic energies up to 1 GeV. Each formula contains a number of parameters that are characteristic of the element, the active electron shell and the projectile particle. The values of these parameters were determined by fitting the cross section values in an extensive database that was calculated recently by means of a composite algorithm that combines the distorted-wave and plane-wave Born approximations. Tables of parameter values are given for all elements, from hydrogen ( Z = 1 ) to einsteinium ( Z = 99 ) . The proposed analytical expressions yield ionization cross sections that agree with those in the numerical database to within about 1%, except for projectiles with near-threshold energies.