Asymptotic approach to the quantum mechanical problem of the three Coulomb centers

Abstract

The asymptotic properties of the solution of quantum-mechanical three Coulomb centers problem eZ1ZZ are studied. Within the framework of the perturbation theory the asymptotic formulas for energies of eZ1ZZ system are obtained at large separation L between interacting fragments. Asymptotic for one-electron three-center wave function of the hydrogenlike atomic ion in the vicinity of two Coulomb centers Z + Z are constructed. As the applications of obtained results the leading term of the asymptotic of exchange interactions between hydrogen-like molecular ion eZZ with nuclei of different elements are calculated.