We investigate the leading systematic effects in ro-vibrational spectroscopy of the molecular hydrogen ions H2+ and HD+, in order to assess their potential for the realization of optical clocks that would be sensitive to possible variations of the pr
oton-to-electron mass ratio. Both two-photon (2E1) and quadrupole (E2) transitions are considered. In view of the weakness of these transitions, most attention is devoted to the light shift induced by the probe laser, which we express as a function of the transition amplitude, differential dynamic polarizability and clock interrogation times. Transition amplitudes and dynamic polarizabilites including the effect of hyperfine structure are then calculated in a full three-body approach to get a precise evaluation of the light shift. Together with the quadrupole and Zeeman shifts that are obtained from previous works, these results provide a realistic estimate of the achievable accuracy. We show that the lightshift is the main limiting factor in the case of two-photon transitions, both in H2+ and HD+, leading to expected accuracy levels close to 5 10-16 in the best cases. Quadrupole transitions have even more promising properties and may allow reaching or going beyond 10-16.
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum polarizati
on correction to the binding energy of muonic and pionic molecules, both in a first-order perturbative treatment and in a nonperturbative approach. The first resonant states lying below the n=2 threshold are also studied, by means of the stabilization method with a real dilatation parameter.
We present an accurate computation of the g-factors of the hyperfine states of the hydrogen molecular ion H2+. The results are in good agreement with previous experiments, and can be tested further by rf spectroscopy. Their implication for high-preci
sion two-photon vibrational spectroscopy of H2+ is also discussed. It is found that the most intense hyperfine components of two-photon lines benefit from a very small Zeeman splitting.
We present the computation of two-photon transition spectra between ro-vibrational states of the H2+ molecular ion, including the effects of hyperfine structure and excitation polarization. The reduced two-photon matrix elements are obtained by means
of a variational method. We discuss the implications of our results for high-resolution spectroscopy of H2+.
