Calculation of double differential cross sections (DDCS) for H(3S) ionization using Bethe and Lewis Integrals

Calculations have been made for the double differential cross section (DDCS) for the ionization of metastable hydrogen atoms in the 3S state by electron and positron impact at energies of 150 eV and 250 eV. The authors implemented the second Born approximation to the multiple scattering theory as their model, evaluated the corresponding analytical expressions using Bethe and Lewis integrals, and numerically computed them using MATLAB. The generated DDCS captures the features of both recoil and binary fragmentation and, at the same time, provides an overall qualitative consistency with earlier studies, although some differences can be found between them at certain emission angles. The present work, therefore, supplies new theoretical reference levels for ionization investigations in hydrogen-like systems, now that no experimental data are available for the metastable 3S state.