Polarizabilities, light shifts and two-photon transition probabilities between J=0 states of the H2+ and D2+ molecular ions

We present the computation of the two-photon transition matrix element between vibrational states of H-2(+) or d(2)(+) of S-1(e) symmetry (i.e. two J = 0 vibrational levels of the 1s sigma (g) electronic ground state). The method uses very accurate fully non-adiabatic wavefunctions of the non-relativistic problem. It is first applied to the calculation of the static polarizabilities; our results for the ground state are in excellent agreement with the literature, with an improved accuracy. The method is applied to the evaluation of the two-photon transition probabilities and light shifts. We also discuss the feasibility of a two-photon spectroscopy experiment in H-2(+).