Electron Compton-like quasielastic scattering from $H2$⁠, $D2$⁠, and HD

A significant anomaly in the ratio of the cross sections for quasielastic scattering of $D2$ to $H2$ in a 50:50 mixture has been reported recently [Phys. Rev. Lett. 100, 043204 (2008)]. In particular, the interpretation of quasielastic scattering provided in that work predicts that the signals should be based on the elemental content and not on the molecular structure, and thus the spectrum for HD and that for the 50:50 mixture should be effectively the same, aside from minor line shape differences. In fact the signal from H in the mixture was low by 31(4)% (or that from D was correspondingly high) when compared to the signal from H in HD. Here, an attempt is made to explain this anomaly by scattering theory calculations based on the first Born and Born–Oppenheimer approximations. The relative contributions of translational, vibrational, and rotational excitations are computed for several temperatures. The computed signals are compared to the experimental spectra of HD and the 50:50 $H2/D2$ mixture and to pure $H2$ and $D2$⁠, which were reported previously. Good agreement is found for the spectral line shapes. The predicted peak positions are also found to be in good agreement with experiment except for a slight shift in the case of $D2$⁠. However the anomalous cross section ratio of $D2$ to $H2$ experimentally observed in the 50:50 mixture could not be explained by this approach.