Spin relaxation of spin-polarized atomic hydrogen adsorbed on a surface

A calculation is presented of the relaxation rate, $T_1^{-1\mathrm{}}$, in a dilute gas of spin-polarized H atoms residing on a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ film. Included in this treatment is the large spatial extent of the surface wave function. A surprising result is that the complete anisotropy of $T_1^{-1\mathrm{}}$, in which $T_1^{-1\mathrm{}}$ is zero for the magnetic field perpendicular to the surface as expected for a purely two-dimensional calculation, survives this general three-dimensional treatment.