Single-electron Born approximations for charge transfer from multielectron atoms to protons

The Born approximation, including the internuclear interaction, is used to compute cross sections for the transfer of one electron from a multielectron atom to an incident proton. When the full internuclear interaction is included, the results lie far above high-energy experinental $K$-shell data for $p$+Ar. However, when only enough internuclear interaction is used so that the total projectile-target interaction goes to zero asymptotically in accord with plane-wave functions actually used, fair agreement at high energies is obtained. The latter form of the Born approximation is compared to data on $K$-shell capture from helium as well as argon, in addition to the simpler approximation of Oppenheimer and of Brinkman and Kramers (OBK), where no internuclear interaction is included. The OBK results typically lie a factor of 2 to 8 above the data, while our Born results are within a factor of 2 of most of the existing high-velocity $K$-shell data, i.e., with an accuracy comparable to more sophisticated calculations.