Theoretical study of nuclear-spin—lattice relaxation in solidH2

Nuclear-spin-lattice relaxation in solid mixtures of ortho and para hydrogen is studied as a function of the $o-{\mathrm{H}}_2$ concentration $c$. Equations of motion for the dynamical two-point angular momentum correlation functions are first obtained by the method of Blume and Hubbard. These equations are then impurity averaged by the Sung-Arnold method to obtain equations valid in the low-$c$ regime. Numerical solutions to the latter equations are then used to obtain the nuclear-spin—lattice relaxation time $T_1$ as a function of $c$. The resulting $T_1$ displays the experimentally observed $c^{\frac{5}{3}}$ behavior at small $c$ and its magnitude is shown to agree favorably with experiments at 10 K over the concentration range $0\le c\le 0.5$.