A double resonance two-photon spectroscopy scheme is discussed to probe jointly rotational and rovibrational transitions of ensembles of trapped HD
+ ions. The two-photon transition rates and lightshifts are calculated with the two-photon tensor operator formalism. The rotational lines may be observed with sub-Doppler linewidth at the hertz level and good signal-to-noise ratio, improving the resolution in HD
+ spectroscopy beyond the 10
−12 level. The experimental accuracy, estimated at the 10
−12 level, is comparable with the accuracy of theoretical calculations of HD
+ energy levels. An adjustment of selected rotational and rovibrational HD
+ lines may add clues to the proton radius puzzle, may provide an independent determination of the Rydberg constant, and may improve the values of proton-to-electron and deuteron-to-proton mass ratios beyond the 10
−11 level.
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