Proton—Hydrogen-Atom System at Large Distances. Resonant Charge Transfer and the1sσg−2pσuEigenenergies ofH2+

Abstract

The resonant charge-transfer reaction of a proton with a hydrogen atom is evaluated in the adiabatic approximation. Previous calculations of this cross section have used various approximations to the energy difference between the $1s{\sigma }_g$ and $2p{\sigma }_u$ states of the hydrogen molecule ion $\mathrm{H}_2^{}{}_{}{}^{+}$. This approximation is removed by solving the $\mathrm{H}_2^{}{}_{}{}^{+}$ Schrödinger equation for the eigenparameters required in addition to those previously available in the literature. The resulting energy differences, found for internuclear separations of $R\le 40.0a_0$, are used to test the accuracy of large $R$ estimates based on quasiclassical (WKB) and asymptotic arguments. The charge-transfer cross section calculated with the eigenergies is found to be, at most, a few percent different from earlier results based on approximate energy differences. Firsov's approximation and a recent modification by Smirnov are shown to be highly accurate when used with the eigenenergies.