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 $\ensuremath{\rho}$, of solid ortho-${\mathrm{H}}_{2}$ in its rotationally disordered state. For $\ensuremath{\rho}$ greater than about 1.1 times the zero-pressure density ${\ensuremath{\rho}}_{0}$, conversion is shown to result from a one-phonon process. This rate is proportional to ${(\frac{\ensuremath{\rho}}{{\ensuremath{\rho}}_{0}})}^{\frac{10}{3\ensuremath{-}2\ensuremath{\gamma}}}$, where $\ensuremath{\gamma}$ is the Gr\"uneisen 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 $1.0\ensuremath{\le}\frac{\ensuremath{\rho}}{{\ensuremath{\rho}}_{0}}\ensuremath{\le}1.7$, we extract the phonon spectral function and compare it to a theoretical spectrum calculated in a simple harmonic approximation.

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