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Effective reduced mass for the interaction of two ground state hydrogen atoms in a non-adiabatic Heitler-London approximation

The relative motion of two ground state hydrogen atoms is considered in the framework of the resonating group method and using the Heitler-London electronic basis. It is shown that, with correct simultaneous account for boundary conditions and indistinguishability of electrons, the effective reduced mass involved in the relative motion of atoms may be written as 1/2 (M+1+ delta M) where M is the proton mass in atomic units. The correction delta M, which is obtained as a function of the internuclear distance R, is different in sign and amplitude for the singlet and triplet states, it is of the order of unity at R=3 au and goes exponentially to zero as R increases.