Very accurate quantum mechanical calculations of the pure vibrational spectrum of the ${\mathrm{HeH}}^{+}$ molecular ion are reported and compared with newly obtained pure vibrational transitions extracted from the available experimental data. The calculations are performed without assuming the Born-Oppenheimer approximation regarding separability of the nuclear and electronic motions and include the first order relativistic mass-velocity and Darwin corrections. For the two lowest transitions, whose experimental energies are established with the highest precision, the calculated and the experimental results show very good agreement.

• Received 4 January 2006

DOI:https://doi.org/10.1103/PhysRevLett.96.233002