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

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.