Exactly Solvable Model Mimicking the H2 Molecule in the Limit of Large Nuclear Masses

摘要

Avoiding the limitations of the Born–Oppenheimer approximation remains an issue of continuing importance in molecular physics. If we take the H2 molecule as a prototype, then one uses, in some sense, the ratio of electron mass m to nuclear mass M as an expansion parameter, sometimes cited to be explicitly (m/M)1/4. Here, we employ a model of such a two-electron diatomic molecule set up by Makarewicz [Am. J. Phys. 54 (1986) 178] to study the exact ground-state wave function obtained by treating electrons and nuclei on the same footing, Of course, to obtain such a wave function analytically means adopting model force laws, both for confinement and for the interelectronic interaction. From the exact wave function and ground-state energy, contact is finally established with the large nuclear mass limit.