Non-Born–Oppenheimer study of the muonic molecule ion 4He μ+*

Abstract

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 4He μ+ can be regarded as a system of positive muon bound to a slightly distorted helium atom.