Lower vibrational transitions of the ³He⁴He ⁺ ion calculated without the Born-Oppenheimer approximation and with leading relativistic corrections

Very accurate variational calculations of the five lowest vibrational states of the ³He⁴He⁺ ion are carried out within a framework that does not assume the Born-Oppenheimer (BO) approximation, i.e., treating the two nuclei and three electrons forming the system on an equal footing. The non-BO wave functions are expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance. The wave functions are used to calculate the leading relativistic corrections. The approach reproduces the experimental ³He⁴He⁺ fundamental transition within 0.055 cm^-1 and similar accuracy is expected for the higher yet unmeasured vibrational transitions determined in the present calculations.