Electron capture by fast protons from helium, nitrogen, and oxygen: The corrected first Born approximation

The first Born approximation corrected for the boundary conditions is used to compute total cross sections for charge exchange in ${\mathrm{H}}^{+}$-He, ${\mathrm{H}}^{+}$-N, and ${\mathrm{H}}^{+}$-O collisions at intermediate and high energies. An independent-particle method is employed with a one-electron orbital for the target. Two sets of computation are presented in which the initial state of the active electron is described by the Roothaan-Hartree-Fock and hydrogenlike wave functions. These two approaches yield noticeably different results for the cross sections. Excellent agreement with existing experimental data is obtained at energies ranging from 50 keV to 50 MeV by using the Roothaan-Hartree-Fock wave function as a linear combination of normalized Slater-type orbitals.