The non-linear optical response of a medium can be used to explore the fundamental physical properties of molecules. In the present work, coherent anti-Stokes Raman spectroscopy is employed to investigate the intra-molecular interaction caused by the vibration-rotation coupling, whose effect is of great importance in the precise determination of spectroscopic strengths of very light molecules. More precisely, the coupling is defined by the so-called Herman-Wallis (HW) factor F = |<v,J|O|v',J'>|² / |<v,J|O|v',J'>|² where O is the operator responsible for the rovibrational molecular transition  [1]. Although the Herman-Wallis factor is well known, its calculation is not easy and, in the literature, either the correction is not considered at all, or different authors suggest different Q-branch HW factors in manifest disagreement with each other.

To gain more insight into the problem, an experiment based on vibrational CARS applied to H₂ molecules is illustrated [2]. Here, the measured spectroscopic strength for the line Q(7) is compared with the calculated line strengths obtained from different HW factors found in the literature. The idea behind this experimental proof is very simple. The spectra have been acquired from a flat flame produced in a Hencken burner fed with H₂ and air. Since the flame is very stable and works under adiabatic conditions, the flame temperature is well known and its maximum value is at stoichiometric condition. On the other hand, the acquired CARS spectra are temperature dependent and they can be fitted with theoretical spectra that incorporate the given temperature and, alternatively, the expressions of different HW factors. The conclusion of this analysis clearly shows that the experimental results help in the determination of the most reliable factor needed to define the non-linear Raman spectra of hydrogen.

[1] R. Herman and R. F. Wallis, J. Chem. Phys. 23, 637 (1955).

[2] M. Marrocco, Chem. Phys. Lett. 442, 224 (2007).

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