Lowest vibrational states of He4 He+3: Non-Born-Oppenheimer calculations

Very accurate quantum mechanical calculations of the first five vibrational states of the He4 He+3 molecular ion are reported. The calculations have been performed explicitly including the coupling of the electronic and nuclear motions [i.e., without assuming the Born-Oppenheimer (BO) approximation]. The nonrelativistic non-BO wave functions were used to calculate the α2 relativistic mass velocity, Darwin, and spin-spin interaction corrections. For the lowest vibrational transition, whose experimental energy is established with high precision, the calculated and the experimental results differ by only 0.16 cm-1.