Energy levels and two-photon transition probabilities in the HD+ion

We present a fully exact non-relativistic calculation of the energies and wavefunctions of the J = 1 states of the HD + molecular ion. The energies are obtained with a very high accuracy of 10 −14 au, representing, for most levels, an improvement by several orders of magnitude over previous calculations. We compute the static polarizabilities of the J = 0 states, which are in agreement with the literature, with an improved accuracy, as well as the two-photon transition probabilities and light shifts between J = 0 states. Finally, we extend our study to transitions between higher J states, using an approximate expression of the transition probability, and discuss the feasibility of a two-photon spectroscopy experiment in HD + .