Importance of coupling for inelastic collisions between protons and hydrogen atoms

The importance of coupling for fast collisions between protons and hydrogen atoms is examined with the two-centred expansion in atomic eigenfunctions proposed by Bates (1958 a ). Cross-sections are evaluated for reactions H + + H (I s ) → H(I s ) + H + , H + + H( I s ) → H(2 s ) + H + , and H + + H(l a ) → H + + H(2 s ). The effect of a single intermediate state, either I s or 2 s , is considered. For the non-resonance processes, it is found that the cross-sections may be substantially increased by passage through intermediate state for incident energies less than about 10 keV, tending towards equality with decrease in relative velocity. Results obtained for the symmetrical resonance reactions are in good agreement with the two-state solutions of McCarroll (1961).

Theory of charge transfer in high energy collisions

A new theoretical treatment of charge exchange is developed from the Faddeev–Lovelace equations for three-body scattering, by means of the simplifications recently proposed by Dodd & Greider. Detailed consideration is given to the process of electron capture by protons in atomic hydrogen and a rigorous first-order expression for the scattering amplitude is subsequently derived. It is shown that the high-energy form of the total cross-section is indeed that given by the second Born approximation. It is further established that previous treatment of charge-exchange based on the impulse approximation and the continuum distorted wave approximation may be deduced from the present theory by making certain additional assumptions. These assumptions are of questionable validity except at very high energies.