Theory of Nuclear Magnetism of Solid Hydrogen at Low Temperatures.

Systematic studies of the nuclear magnetism of solid ortho-para hydrogen mixtures at low temperatures are presented. The formulation of the nuclear spin-lattice relaxation time T_1 for the case of the local ordering in the orientational "glass" phase of ortho-para hydrogen mixtures is given. The temperature dependence of T_1 is discussed. A strong dependence on the position of the NMR isochromat in the line shape is found and this is in good agreement with the experimental results of a group of physicists at Duke university, provided that the cross-relaxation is taken into account. The relaxation is found to deviate considerably from an exponential recovery. The orientational degrees of freedom of ortho hydrogen molecules in terms of density matrices and the irreducible tensorial operators associated with unit angular momentum are described. The range of allowed values for the orientational order parameters is determined from the positivity conditions imposed on the density matrix. A theory of solid echoes and nuclear spin stimulated echoes following a two-pulse RF sequence and a three-pulse sequence in the quadrupolar glass phase of solid hydrogen is developed. The stimulated echoes can be used to compare a "fingerprint" of the local molecular orientations at a given time with those at some later time (less than T_1) and thereby used to detect ultra -slow molecular re-orientations.