Electron Capture by Protons passing through Hydrogen

A variational method is applied to the problem of electron capture by protons from the ground state of hydrogen atoms. The problem is treated as a simplified one-body problem, viz. that of an electron in the Coulomb field of two protons, the proton-proton interaction being neglected. The numerical results of our theoretical calculations at low incident proton energies are in good agreement with the recent experimental findings of Fite, Brackmann and Snow. At low incident proton energies our theoretical results agree closely with those of Dalgarno and Yadav, though the methods of approach are different. Further, our results may, with suitable approximations, be easily reduced to those of Brinkman and Kramers or of Bates and Dalgarno and Jackson and Schiff.