Magnetic field effects in the transitions of the HD+ molecular ion and precision spectroscopy

We analyse the effects of an external magnetic field on the ro-vibrational, rotational and radiofrequency transitions of the HD+ molecular ion-an important systematic effect in precision spectroscopy of HD+, which is of interest for metrology of the fundamental constants. The effects of an external magnetic field on the ro-vibrational, rotational and radiofrequency (hyperfine) transitions of the HD+ molecular ion are considered, for one-photon and, where relevant, two-photon transitions. The hyperfine structure of the spectrum lines is taken into account. Particular attention has been devoted to those transitions which are most insensitive to the magnetic field and its orientation with respect to the polarization of the radiation field. We identify experimentally accessible two-photon transitions that exhibit no Zeeman shift, one-photon and two-photon transitions that provide symmetrically split doublets, and one-photon transitions that show only a very weak quadratic Zeeman shift. The importance of the spin-stretched states is emphasized. The results can be used to determine the most suitable transitions given the experimental conditions.