Charge Transfer Processes Involving Highly Excited Hydrogen Atoms. I. The Born Amplitude in a Closed Form

Abstract

The Born cross sections for the charge transfer processes involving highly excited hydrogen atoms are expressed in closed forms for s-s and s-p transfers. In the calculation of the transition matrix elements, we have made use of the sum rules of the atomic wave functions in the momentum space derived from the Coulomb Green function. The momentum transfer effect of the electron is important and cannot be neglected throughout the energy range where the Born approximation is valid. We have also obtained an approximate expression for the cross section σ(n→n′) averaged over the initial azimuthal and magnetic quantum numbers and summed over the final ones. The averaged cross section satisfies a scaling law in the resonance case n=n′, that is, σ_n(E)=n⁴σ_1s(n²E). Applications will be given in the subsequent paper.