Theory of nuclear spin-lattice relaxation of spin-polarized hydrogen on liquid-helium-coated surfaces due to magnetic particles in the substrate

A theory is presented for the nuclear spin-lattice relaxation rate 1/T1 for electron-spin-polarized H atoms on or near a liquid-He-coated surface due to magnetic particles in the substrate below the He film. The H-atom motion is assumed to be free-particle-like for atoms on the surface, while atoms in the gas are assumed to be reflected elastically by the surface. 1/T1 is found to exhibit a minimum at low temperatures due to two competing tendencies. 1/T1 decreases with decreasing temperature because lower thermal velocities give a smaller density of fluctuating magnetic fields at the NMR frequency ω. However, at lower temperatures, the atoms spend more time on the surface so that &, where β=1/kBT and EB is the binding energy of H to liquid He. For atoms on the surface, the dominant frequency dependence of 1/T1 is given approximately by exp[-3(βmω2d2/2)1/3] which predicts a very strong dependence of the relaxation on ω. For atoms reflected by the surface, the dependence is ω-4, which agrees with the classical calculation of Purcell as reported by Kleppner, Goldenberg, and Ramsey.