Rotational level spacings in HD from vibrational saturation spectroscopy

The R(1), R(3) and P(3) ro-vibrational transitions in the (2-0) overtone band of the HD molecule are measured in Doppler-free saturation using the technique of NICE-OHMS spectroscopy. For the P(3) line, hitherto not observed in saturation, we report a frequency of $203\,821\,936\,805\,(60)$ kHz. The dispersive line shapes observed in the three spectra show strong correlations, allowing for extraction of accurate information on rotational level spacings. This leads to level spacings of $\Delta_{(J=3)-(J=1)}= 13\,283\,245\,098\,(30)$ kHz in the $v=0$ ground state, and $\Delta_{(J=4)-(J=2)}= 16\,882\,368\,179\,(20)$ kHz in the $v=2$ excited vibration in HD. These results show that experimental values for the rotational spacings are consistently larger than those obtained with advanced ab initio theoretical calculations at 1.5$\sigma$, where the uncertainty is determined by theory. The same holds for the vibrational transitions where systematic deviations of 1.7-1.9$\sigma$ are consistently found for the five lines accurately measured in the (2-0) band.