CoulombTMatrix and Electron Capture by Protons Passing through Hydrogen

Abstract

Using Nutt's expression for the two-particle off-shell Coulomb $T$ matrix, and neglecting multiple-scattering terms in Faddeev's expansion for the transition matrix, an expression for the charge-exchange amplitude in proton-hydrogen scattering is derived. The results of numerical calculations are compared with the corresponding results of Brinkman and Kramers, of Jackson and Schiff, and of Drisko. An analytical expression for the total cross section at high energies is obtained from our formalism. In the high-energy limit, our results approach the Brinkman-Kramers formula.