Cross sections and rate coefficients for inelastic interactions of heavy particles

The existing analytical inelastic cross-sections for direct atom-atom ionizing collisions of Firsov (1959), Fleischmann et al. (1972), and Drawin (1968) are discussed. General analytical expressions for direct ionization cross-sections in atom-atom collisions are derived. The main advantage of the present cross-sections is their generality, simplicity, and overall accuracy, which is acceptable in most applications and is better than the overall accuracy of the cross-sections of Firsov, Fleischmann et al., and Drawin. The atom-atom interaction is considered as a superposition of all the pairwise interactions between the test particle and all the electrons of the outer nl shell of the target atom. Such a picture of atom-atom collision is acceptable at low- and medium-impact energies because then the electrons of the outer shell of the target atom are most likely the ones that get ionized. At high-impact energy, the picture becomes inaccurate because of strong overlapping of the atomic shells.