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Physical review. B, Condensed matter

Surface three-body recombination in spin-polarized atomic hydrogen

L.P.H. de Goey, Henk T. C. Stoof, J. M. Vianney, J. M. V. A. Koelman, BOUDEWIJN J. VERHAAR, Jook T. M. Walraven

Published Dec 1, 1988• 8 citations
Publisher

Abstract

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 ${L}_{s}^{\mathrm{eff}=2.7(7)\ifmmode\times\else\texttimes\fi{}{10}^{\mathrm{\ensuremath{-}}25}}$ ${\mathrm{cm}}^{4}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ 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.

DOI
10.1103/physrevb.38.11500

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We determine the rate of b+b+b surface dipole recombination for hydrogen atoms adsorbed on a 4He^{4}\mathrm{He}4He film. The calculation is based on the Kagan mechanism adapted to a 2(1/2-dimensional initial state. We find a rate constant Lseff=2.7(7)\ifmmode×\else\texttimes\fi10\ensuremath−25{L}_{s}^{\mathrm{eff}=2.7(7)\ifmmode\times\else\texttimes\fi{}{10}^{\mathrm{\ensuremath{-}}25}}Lseff=2.7(7)\ifmmode×\else\texttimes\fi10\ensuremath−25​ cm4{\mathrm{cm}}^{4}cm4 s\ensuremath−1{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}s\ensuremath−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.
We calculate the surface dipolar recombination rate Ls{L}_{s}Ls​ for spin-polarized hydrogen adsorbed on 4He^{4}\mathrm{He}4He surfaces at temperatures in the 0.2- to 0.6-K regime and for magnetic fields up to 30 T. For a magnetic field of 7.6 T normal to the surface and 0.4 K we find ${L}_{s}=1.3(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}$ cm4{\mathrm{cm}}^{4}cm4 ${\mathrm{s}}^{\ensuremath{-}1}$ increasing by 10%/T in the range of experimental interest. The anisotropy with the direction of the magnetic field is considerably smaller than in the case of the surface dipolar relaxation.
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.
In view of the failure of the Kagan dipole mechanism to explain the magnetic field dependence of the H+H+H recombination rate in spin-polarized atomic hydrogen, we consider an additional process, the so-called dipole-exchange mechanism. Two simple approaches to estimate its consequences turn out to be promising but the question of the role of different and higher-order processes remains open. We therefore turn to in principle, an exact approach to the three-body recombination, including all possible processes. The first numerical results of the approach are presented.
We present results of a calculation of the volume rate constant Lgeff{L}_{g}^{\mathrm{eff}}Lgeff​ of dipole recombination in H\ensuremath{\downarrow}?, in which the bbb incoming state is determined exactly by means of the Faddeev formalism. Inclusion of all three-particle correlations in the initial state does not resolve the discrepancies between Kagan's approach and experiment. As a first step towards an exact determination of the outgoing atom-molecule state, we present a calculation in which all three-particle collision aspects are taken into account, except for rearrangement. This leads to values for Lgeff{L}_{g}^{\mathrm{eff}}Lgeff​, which are a factor of 5 smaller than experiment, while the B dependence of the rate constant still shows a slowly increasing behavior. On the basis of this state-of-the-art calculation, we thus localize the cause for the existing discrepancies in rearrangement processes.
The study of spin-polarized atomic hydrogen in the three-dimensional gas phase has been extended into a new regime of magnetic field strength. Analysis of decay data for B=10--20 T reveal for the first time the characteristic peak in the three-body dipolar-decay rate constant as predicted by Kagan, Vartanyants, and Shlyapnikov (Zh. Eksp. Teor. Fiz. 81, 1113 (1981) [Sov. Phys.---JETP 54, 590 (1981)]). Beyond 17 T we observe a rapid falloff of the three-body-decay rate constant. We also determine a value for the three-body-exchange rate constant which is in accord with the calculation of Kagan et al. In contrast to the picture which was emerging from previous studies at more moderate fields, the data presented here suggest that existing theories are capable of describing the decay of the system in the very-high-field limit. The new picture which is emerging suggests that Bose-Einstein condensation may be achievable at somewhat higher fields which are currently available at high-magnetic-field facilities.