Spectral density functions for aJ=1quadrupolar solid: Application to solidH2

Integral equations for the dynamical two-point angular momentum correlation functions of a $J=1\mathrm{}$ quadrupolar solid are derived by the use of a diagrammatic technique which was previously developed for dense magnetic systems. For comparison to experiments on solid mixtures of ortho and para hydrogen, a simple scheme, valid in the high-concentration limit, is used to impurity average these equations. The averaged equations are then solved numerically to obtain the spectral functions for solid ${\mathrm{H}}_2$ self-consistently for the first time. The resulting spectral functions are then used to compute the nuclear spin-lattice relaxation time of solid ${\mathrm{H}}_2$ as a function of the ortho-molecule concentration and this is shown to agree well with experiments at 10 K and over a concentration range of $0.5\le C\le 1$. Finally, a formula is derived which expresses the differential inelastic-neutron-scattering cross section in solid ${\mathrm{H}}_2$ in terms of the calculated spectral functions. If the neutron wave vector and scattering angle are specified, one can then predict the scattering cross section from the numerical results for the spectral functions.