Effect of correlated hyperfine theory errors in the determination of rotational and vibrational transition frequencies in HD+

Abstract

We revisit the problem of separating the purely rovibrational and hyperfine contributions to observed rovibrational transition frequencies. The separation of hyperfine frequency shifts played an essential role in recent works in which the value of the proton-electron mass ratio was determined from Doppler-free rovibrational spectroscopy and high-precision theory of the molecular ion. Here, we present an alternative approach to removing theoretically computed hyperfine shifts from a limited set of observed rovibrational transition frequencies, based on a least-squares adjustment. The adjustment facilitates a quantitative study of the effect of correlations between the uncertainties of lower- and upper-state hyperfine energies on the derived value of the rovibrational transition frequency. We find that correlations may lead to significant shifts of the extracted rovibrational transition frequencies. In addition, we propose and demonstrate a method to quantify the additional shift and uncertainty, which is of importance to other applications of the spectroscopic data, such as the determination of fundamental physical constants.