Herman-Wallis factor to improve thermometric accuracy of vibrational coherent anti-Stokes Raman spectra of H2

The Herman-Wallis factor is a molecular parameter that measures the influence of centrifugal force on the intensity of spectral lines. Understandably, the effect is significant for very light molecules that necessarily have large couplings between vibrational and rotational degrees of freedom. Although known, the conceptual basis of the Herman-Wallis factor are nevertheless not clearly established in the literature. Over the years, different approaches have been proposed to explain the corrections to spectral line-strengths and, recently, an experimental study has demonstrated that Q-branch Raman transitions of H2 are highly sensitive to the theoretical model employed to determine the Herman-Wallis factor. In this paper, this fact is used to analyze the consequences on thermometry based on coherent anti-Stokes Raman scattering (CARS) designed to probe H2 molecules in combustion studies. It is found that the different Herman-Wallis factors lead to relative thermometric disagreements from several tens up to hundreds of degrees. This analysis could explain why H2 CARS thermometry has been considered less reliable than thermometric predictions based on CARS of more common molecules such as N2, O2 and others. In particular, it is remarked that unreliable expressions of Herman-Wallis factors have been used so far to interpret Q-branch H2 CARS experiments.