Electron capture into highly excited states in proton-hydrogen collisions

A new straightforward technique for the evaluation of the rearrangement-scattering amplitude for the process ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{H}\mathrm{}\left(\mathrm{nlm}\right)+{\mathrm{H}}^{+}$ has been presented in the continuum—intermediate-state approximation. We reduce the scattering amplitude to a closed analytical form. The asymptotic behavior of the capture cross sections with respect to $n$ has also been derived. It has been shown conclusively that the charge-exchange cross sections asymptotically obey the $n^{-3\mathrm{}}$ power law throughout the entire energy range of the projectile. It is found that the cross sections for capture into different angular momentum states can be calculated from the respective asymptotic cross-section values with the help of a simple scaling law. The present calculated results have been compared with the available experimental findings.