Charge transfer in proton—hydrogen-molecule collisions

Abstract

Charge transfer into a number of excited $s$ states of atomic hydrogen by proton impact on hydrogen molecule has been studied for both gerade and ungerade transitions of the molecular ion for the energy range 50 keV to 5 MeV. Using a contour integral representation of the hydrogenic wave function, the molecular Brinkman-Kramers amplitude has been expressed in a closed form, while the molecular Jackson-Schiff amplitude involving proton-proton interactions has been reduced to a one-dimensional integral over the real variables. Just as in the case of ground-state formation of hydrogen atoms, molecular effects play a significant role in the case of excited-state capture of an electron; and a hydrogen molecule cannot be regarded as a pair of independent hydrogen atoms at any energy in the considered range. The cross sections at a particular energy satisfy the inverse ${n}^{3}$ law approximately. The charge transfer involving the gerade transition of the molecular ion is the most important process; although, depending on the choice of the molecular wave function, there is a 10-28% chance of the charge-transfer process involving the ungerade transition.