We determine the rate of b+b+b surface dipole recombination for hydrogen atoms adsorbed on a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ film. The calculation is based on the Kagan mechanism adapted to a 2(1/2-dimensional initial state. We find a rate constant $L_s^{\mathrm{eff}=2.7\mathrm{}\left(7\right)\mathrm{}\times {10}^{\mathrm{-}25}}$ ${\mathrm{cm}}^4$ ${\mathrm{s}}^{\mathrm{-}1}$ at B=7.6 T and T=0.4 K, which is roughly a factor of 6 smaller than the experimental results. The magnetic-field dependence also disagrees with experiment. A scaling approach, although leading to the correct order of magnitude, is discussed and shown to be unsatisfactory. The reliability of some of our approximations is estimated. We conclude that the dipole-exchange mechanism is probably responsible for the discrepancies with experiment.

• Received 4 April 1988

DOI:https://doi.org/10.1103/PhysRevB.38.11500