Exact Calculation of the Second-Order Born Terms for Proton-Hydrogen Electron-Transfer Collisions

The four second-order terms in the Born series for the proton-hydrogen electron-transfer problem are analytically reduced from six-dimensional to three-dimensional integrals. No mass approximations are made. This permits an accurate numerical calculation of the total cross section to second order. Numerical results are given from 0.1 to 2.5 MeV. The complete second-order cross section reduces the first-order results by 30% from 1 to 2.5 MeV. The various first- and second-order Born approximations for this problem are discussed.