The K-shell ionisation of atoms by relativistic protons

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Abstract
The K-shell ionisation is investigated using an extension of the first-order time-dependent perturbation-theory treatment of Moller (1932) taking Dirac plane waves for the description of the incident and scattered protons and the Darwin approximation for the relativistic wavefunctions of the K-shell atomic electrons and the ejected electron. The differential cross sections delta 2 sigma / delta k delta q and d sigma /dk, where k is the wavenumber of the ejected electron and hq is the momentum change of the proton, are calculated. The double differential cross section for collisions in which a change of spin of the atomic electron occurs is less sharply peaked for small q, and has a broader overall distribution with respect to q, than the double differential cross section for collisions without spin change, although being much less in magnitude than the latter for small q. This leads to total K-shell ionisation cross sections sigma with significant contributions coming from collisions with spin change of the atomic electron for large atomic numbers at high energies of impact.

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