Non-Born-Oppenheimer study of the muonic molecule ion 4Heμ^+

Accurate non-Born-Oppenheimer variational calculations of all bound states of the positive muon molecular ion 4Heμ^+ have been performed using explicitly correlated Gaussian functions in conjunction with the global vectors.All the energies obtained are accurate in the order of 10-6 Hartree(1 Hartree=27.2114 eV).Compared with the binding energies obtained from calculations based on the Born-Oppenheimer potential with the mass-weighted adiabatic corrections(Chem.Phys.Lett.110487(1984)),the largest relative deviation is up to 15%.By analyzing the average interparticle distances and possibility distributions of interparticle distances of this system,it is confirmed that the Born-Oppenheimer approximation is reasonable for this system and that 4Heμ^+ can be regarded as a system of positive muon bound to a slightly distorted helium atom.