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Physical review. B, Condensed matter

Surface spin relaxation of stabilized atomic hydrogen

René Ahn, J.P.H.W. van den Eijnde, C. J. Reuver, BOUDEWIJN J. VERHAAR, Isaac F. Silvera

Published Jul 1, 1982• 21 citations
Publisher

Abstract

We present a distorted-wave calculation of the spin relaxation of hydrogen atoms adsorbed at a superfluid helium surface, due to H-H collisions. Both the interatomic triplet potential and the dipole-dipole interactions are averaged over the bound state at the surface. The result is compared with experiment and with some alternate methods.

DOI
10.1103/physrevb.26.452

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arXiv:0902.4818•Journal of Experimental and Theoretical Physics Letters•Sep 1, 2009•2 citations
We present a distorted-wave calculation of the spin relaxation of hydrogen atoms adsorbed at a superfluid helium surface, due to H-H collisions. Both the interatomic triplet potential and the dipole-dipole interactions are averaged over the bound state at the surface. The result is compared with experiment and with some alternate methods.
The experimental realization of a thin layer of spin-polarized hydrogen H↓ adsorbed on top of the surface of superfluid (4)He provides one of the best examples of a stable, nearly two-dimensional (2D) quantum Bose gas. We report a theoretical study of this system using quantum Monte Carlo methods in the limit of zero temperature. Using the full Hamiltonian of the system, composed of a superfluid (4)He slab and the adsorbed H↓ layer, we calculate the main properties of its ground state using accurate models for the pair interatomic potentials. Comparing the results for the layer with the ones obtained for a strictly 2D setup, we analyze the departure from the 2D character when the density increases. Only when the coverage is rather small the use of a purely 2D model is justified. The condensate fraction of the layer is significantly larger than in 2D at the same surface density, being as large as 60% at the largest coverage studied.
A study is made of the interaction between hydrogen atoms and the surface elementary excitations of superfluid "He. Calculations for the sticking probability and for the energy and effective mass of a hydrogen atom bound to the surface are presented. As a first step in the calculations, we formulate the Hamiltonian describing a hydrogen atom interacting with the surface of "He in its ground state together with the interaction coupling to the surface elementary excitations (the ripplons). The derivation is based on the association of the surface ground state with a flat surface and the excited states with a sinusoidally varying height of the surface. The interaction potential is derived by summing a *He-H atom-atom pair potential over helium atoms below the surface. The atom-atom pair potential is chosen so that the derived surface potential is a Morse potential with parameters which are fitted to the effective surface potential derived by Mantz and Edwards for a hydrogen atom interacting with N-1 helium atoms. The energy and angle dependent sticking probability, S(E,θ), and the thermally averaged sticking probability, S(T), are calculated. Results are compared with the experimental value of S(T), S(T)=0.035±0.005, measured for the temperature range 0.18<T<0.27K. The possibility that a hydrogen atom bound above the surface may exhibit polaronic behaviour is investigated. The energy of the hydrogen surface "polaron" and its effective mass are calculated using perturbation theory. The hydrogen atom is found to be weakly coupled to the surface elementary excitations, and therefore the polaronic effects are weak. The contribution to these results from virtual transition to free states is emphasized.
We study three-body recombination in the gas of spin-polarized atomic hydrogen adsorbed on the surface of superfluid helium at temperatures from 45to130mK45\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}130\phantom{\rule{0.3em}{0ex}}\mathrm{mK}45to130mK. The two-dimensional gas is thermally compressed to densities up to $\ensuremath{\approx}4\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ using the ``cold spot'' method which makes the three-body process the dominant decay channel in the system. We measure the loss rate and surface density of atoms directly and independently and observe the former to be proportional to the third power of the latter. The result for the surface three-body recombination rate constant at 4.6T4.6\phantom{\rule{0.3em}{0ex}}\mathrm{T}4.6T, ${L}_{s}=2.0(7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{4}∕\mathrm{s}$, significantly reduces the discrepancy between the theory and earlier measurements where the surface density was inferred from the adsorption isotherm. We also measured the three-body rate constant on a 0.1% $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ film and found ${L}_{s}=1.3(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{4}∕\mathrm{s}$. This larger value is attributed to an increased delocalization of adsorbed hydrogen atoms in the direction normal to the surface.
We propose the explanation of a small yet finite frequency shift of a hyperfine transition in two-dimensional atomic hydrogen bound to the surface of superfluid helium at T < 0.1 K. The nonzero shift is caused, first, by the interaction between adsorbed atoms, which effectively reduces their binding energy to the helium surface by a value proportional to their density and, consequently, reduces the deviation of the hyperfine constant from the free-atom value. Second, the transition between the hyperfine states b and c is shifted owing to a difference in the interaction of the b and c atoms with the residual atoms in the state a that appear due to one and two-body nuclear relaxation. This shift is also linear in the density of the two-dimensional gas. The net effect of the two contributions qualitatively agrees with the experimentally observed value of the shift.