Hyperfine transitions in the first overtone mode of hydrogen deuteride

Beyond the metrology and computational challenges associated with molecular hydrogen, key data are expected to assess the physics of simple molecular systems, and even the new physics beyond the standard model. To assist the deciphering of Doppler-free spectra obtained at very high accuracy ($\ensuremath{\sim}{10}^{\ensuremath{-}9})$, we report on hyperfine transitions of HD in the lowest vibrational levels of the ground electronic state. Using the spin-rotation, nuclear spin-spin, and quadrupolar hyperfine couplings determined by means of high-level quantum-chemical calculations, the hyperfine energy levels and the associated line intensity have been obtained by using tensorial momentum algebra. To illustrate our purpose, the hyperfine line intensity of two specific transitions (${P}_{1}$ and ${R}_{1}$) belonging to the first overtone of HD is reported and commented on. The calculated stick spectra emphasize the experimental challenge (in terms of sensitivity and of spectral resolution) associated with the spectral analysis, because the lines can be apart by less than 10 kHz.