Nonvariational and nonadiabatic calculations on the hydrogen molecular ion and its µ – isotopes

Abstract

A nonadiabatic, nonvariational, and computationally inexpensive scheme to describe bound and continuum states of three-body molecular ions, including µ –-mesonic ions, is proposed. The method relies on treating perturbatively the nonadiabatic coupling between the Born–Oppenheimer (BO) particle states and nuclear motion terms, such that the appropriate expansion parameter is the mass ratio of the lightest particle in the system to that of the heaviest one. In practice, the method requires solving, numerically, a system of coupled inhomogeneous Schrödinger equations with effective potentials that depend on the "internuclear" separation, R, and allow for the mixing of BO states because of nonadiabatic terms in the Hamiltonian. The utility of our approach is clearly evidenced by the results of the numerical calculations carried out for rovibrational states of several lowest J in the H+2 and (ppµ–) molecules. These demonstrate that nonadiabatic eigenenergies and eigenstates, both of the bound and scattering type, for ordinary as well as µ-mesonic molecules can be directly and quite accurately calculated from the same principles in the entire range of R, without making use of the variational techniques that more sophisticated studies of this kind are usually based on. PACS Nos.: 31.15Ar, 31.15Pf