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. 110 487 (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.