Vibration–rotation interactions in H₂, HD and D₂: centrifugal distortion factors and the derivatives of polarisability invariants

We report the correction factors for centrifugal distortion in Raman intensities for pure rotation (O0- and S0-branch) and vibration–rotation (O1- and S1-branch) transitions in the ground electronic state of H₂, HD and (Formula presented.). These factors are presented for 52 selected excitation wavelengths and for the initial rotational states, (Formula presented.). This data is useful in applications of intensity calibration of spectrometers and the spectroscopy of flames. The classical treatment of centrifugal distortion involved the expansion of polarisability anisotropy (γ) over the internuclear distance, while assuming the diatomic molecule behaves as a harmonic oscillator. Here, this approximation of polarisability invariants as a Taylor series expansion is tested, revealing that truncation up to the second-order derivatives of mean polarisability ((Formula presented.)) and polarisability anisotropy (γ) gives faithful representations, yielding accurate expectation values with error (Formula presented.), for the ground rovibrational state and for the fundamental transition.