Splitting of Potential Curves in the Two-Coulomb-Centre Problem

Abstract

Abstract. The quasiclassical expression for the exchange interaction ∆E of potential curves at the points of their quasicrossing in the two-Coulomb-centre problem is found. It can be used for the calculation of cross sections of charge exchange processes between hydrogen or hydrogen-like atoms and bare nuclei.

Semiclassical Treatment of High-Lying Electronic States of H2+

“…On the contrary, semiclassical, WKB-like methods for electronically bound energies and separation constants of H 2 + have also led to good agreement with quantum results, − and we chose to take that approach. Existing semiclassical treatments of H 2 + are either carried out for the general two-center Coulomb case or are refined for accurate treatment of the lowest-lying states, or both.…”

“…The analyses can be complicated because of the presence of a potential barrier between the two nuclei. Some authors go around the classical turning points in the complex plane to derive quantization conditions that include reflection just above the barrier, − , whereas others utilize uniform approaches to derive quantization conditions that account for the coalescence of the classical turning points at the barrier top. ,,− Whereas these refinements are essential for the lowest-lying states of H 2 + , for higher states, only very small portions of the PECs involve energies near the height of the barrier, and a simple treatment of the system can supplant more refined methods with little loss of accuracy.…”