Application of the Statistical Model to Nuclear Magnetic Relaxation in Solid Hydrogen

Abstract

The nuclear-spin relaxation of orthohydrogen molecules in solid ${\mathrm{H}}_{2}$ is due to the intramolecular dipole-dipole interaction modulated by the quadrupole-quadrupole interaction between $J=1$ molecules. Using the statistical method developed by Margenau and Anderson, we calculate the angular momentum correlation functions. In contrast to Moriya and Motizuki's result, where the Gaussian mode is used and relaxation times are found to be proportional to ${c}^{\frac{1}{2}}$ ($c$ is the concentration of orthohydrogen molecules in the solid), we obtain relaxation times proportional to ${c}^{\frac{5}{3}}$. Our result checks with the experimental data of Hardy and Gaines for $c<0.3$. In order to fit the experimental data for the entire range of concentration, a crystal field on the orthohydrogen molecules in the range 0.01-0.03\ifmmode^\circ\else\textdegree\fi{}K must be assumed.