Asymptotic theory of the strongly asymmetric two-Coulomb-center problem

Abstract

Asymptotic expansions for the wave functions and energy spectrum of the two-Coulomb-center system (${Z}_{1}$,e,${Z}_{2}$) are derived in the region R\ensuremath{\gg}1 (R being the distance between Coulomb charges ${Z}_{1}$ and ${Z}_{2}$) for the strongly asymmetric case ${Z}_{1}$\ensuremath{\ll}${Z}_{2}$\ensuremath{\sim}R, with use of the comparison-equation method. The energy splitting \ensuremath{\Delta}(R) of adiabatic molecular states having the same symmetry is calculated asymptotically exactly. For the particular system (p,e,${Z}_{2}$), \ensuremath{\Delta}(R) is calculated at the potential-curve pseudocrossings for 5\ensuremath{\le}${Z}_{2}$\ensuremath{\le}26, and the results are compared with those obtained with use of either other asymptotic expansions or numerical solution of the eigenvalue problem for this system.