Quantum Theory of Raman Scattering in Solid Ortho-Hydrogen and Para-Deuterium. I

Abstract

A ·reformulation of the theory of libration waves is presented to study the first-order Raman scattering of solid o-H2 and p-D2, basing on the unshielded electric quadrupole-quad­ rupole interaction and assuming Pa3 structure to be the lowest energy configuration of J=1 molecules. An accurate estimation of the zero point effect is given, in agreement with the previous result obtained by perturbation method. The k=O libration modes relevant for the first order processes are studied exactly. It is shown that the ratios of three excitation ener­ gies with k=O agrees fairly with the low-lying three Raman spectra observed by Silvera, Hardy and McTague for o~H2 and p-D2• The predicted value of F=6e 2 Q 2 /25a 5 is in a good agreement with the other measurements for p-D2, while a considerable discrepancy appears for o-H2• The theoretical intensity ratio agrees fairly with the measured result, assuming the sample to be polycrystalline. The angular dependence of the scattering cross section is given for the right angle scattering by single crystal. It is pointed out that a strong angular de­ pendence of the scattering cross section due to the lowest mode excitation may be used to set the orientation of single crystal o-H2 and p-D2 to be possibly prepared in future. It is also pointed out that the remaining two Raman spectra observed are possibly due to the second order scattering.