Theory of ortho-para conversion in solid hydrogen at high densities

An expression is derived for the ortho-para conversion rate, as a function of density $\rho$, of solid ortho-${\mathrm{H}}_2$ in its rotationally disordered state. For $\rho$ greater than about 1.1 times the zero-pressure density ${\rho }_0$, conversion is shown to result from a one-phonon process. This rate is proportional to ${\left(\frac{\rho }{{\rho }_0}\right)}^{\frac{10}{3-2\gamma }}$, where $\gamma$ is the Grüneisen constant for solid ${\mathrm{H}}_2$, times a phonon spectral function which depends on the density as a parameter. Using the data of Pedroni et al. for the density dependence of the conversion rate for $1.0\le \frac{\rho }{{\rho }_0}\le 1.7$, we extract the phonon spectral function and compare it to a theoretical spectrum calculated in a simple harmonic approximation.