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({β}mω²{d}²/2)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.