Inelastic collision of fast charged particles with arbitrary levelled hydrogen-like atoms

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Abstract
In collision of the charged particles with neutral atoms when the relative incident momentum is some ten times or more larger than the momentum of the target electron, the inelastic cross section can be expressed in terms of the incident energy and two atomic parameters, called the Bethe coefficients. In the case of the total inelastic cross section of the hydrogen-like atoms in a given initial state these coefficients in the forms of sums and integrals have been found, and for the first seven principal quantum numbers they are evaluated numerically. For these quantum numbers as the initial states a table of the Bethe coefficients for all possible excitations, ionizations and the total inelastic cross sections is given. An asymptotic formula for the total inelastic cross section for arbitrary large excited states is also given. A table published by Bethe and Salpeter (1957) for the electric dipole matrices between hydrogen-like states does not have the proper normalization. This normalization has been performed and a new table for these matrices is presented.