Effects of Librational Anharmonicity in the Solid Hydrogens

Abstract

We compare the results of the recently published anharmonic theory of librons to the best available data on the libron Raman frequencies. This allows us to deduce a refined estimate of the effective value of the intermolecular quadrupolar coupling constant ${\Gamma }_{\mathrm{eff}}$ for solid ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. The effect on the librons of virtual transitions to the ($J=3\mathrm{}$) rotational state is included with the result that ${\Gamma }_{\mathrm{eff}}$ is decreased. Our estimate from the optical data is then ${\Gamma }_{\mathrm{eff}}=0.72\mathrm{}\pm 0.04 \mathrm{and} 0.58\pm 0.03$ ${\mathrm{cm}}^{-1\mathrm{}}$ for ${\mathrm{D}}_2\mathrm{}(x=1\mathrm{})\mathrm{}$ and ${\mathrm{H}}_2\mathrm{}(x=1\mathrm{})\mathrm{}$, respectively, at zero pressure, where $x$ denotes the mole fraction of $J=1\mathrm{}$ molecules. We also use the anharmonic density of states to analyze specific heat and ${\left(\frac{\partial P}{\partial T}\right)}_V$ data from which we obtain the average libron energy as a function of $x$. For $D_2\mathrm{}(x=1\mathrm{})\mathrm{}$ the result is ${\Gamma }_{\mathrm{eff}}=0.70\mathrm{}\pm 0.04$ ${\mathrm{cm}}^{-1\mathrm{}}$. Measurements of the conversion-induced pressure change in ${\mathrm{H}}_2$ give ${\Gamma }_{\mathrm{eff}}=0.56\mathrm{}\pm 0.03$ ${\mathrm{cm}}^{-1\mathrm{}}$. Both these determinations are in good agreement with the results from optical data for librons. Furthermore, it is found that there is no significant difference between ${\Gamma }_{\mathrm{eff}}\mathrm{}(x=1\mathrm{})\mathrm{}$ and ${\Gamma }_{\mathrm{eff}}$ determined from pair spectra in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ with $x\ll 1$. The anharmonic density of states is also used to interpret the infrared absorption sideband spectrum for the creation of a vibron plus libron(s). The part of the spectrum which we attribute to one-libron processes has a width in agreement with this model and as expected there are two-libron processes resulting from cubic anharmonic libron-libron interactions. Incoherent-neutron-scattering data is also consistent with the anharmonic-libron spectrum.