High-Temperature Expansion for the Orientational Specific Heat of SolidH2andD2

Terms up to order ${\left(\frac{\Gamma }{k_{B}T}\right)}^5$ in the high-temperature expansion of the orientational specific heat of ortho-para alloys of solid ${\mathrm{H}}_2$ or ${\mathrm{D}}_2$ are evaluated. Good agreement is obtained between theory and experiment using a Padé approximant and effective values of the quadrupolar coupling constant, $\frac{{\Gamma }_{\mathrm{eff}}}{{\Gamma }_0}=0.83\mathrm{}$ for ${\mathrm{D}}_2$ and $\frac{{\Gamma }_{\mathrm{eff}}}{{\Gamma }_0}=0.80\mathrm{}$ for ${\mathrm{H}}_2$, where ${\Gamma }_0$ is the value for a rigid lattice. These values agree with other determinations of ${\Gamma }_{\mathrm{eff}}$, whereas the $T^{-2\mathrm{}}$ approximation for the specific heat yields anomalously small values of ${\Gamma }_{\mathrm{eff}}$.