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Physical review. B, Condensed matter

Three-body recombination in spin-polarized atomic hydrogen

L.P.H. de Goey, T. H. M. van den Berg, Norbert Mulders, Henk T. C. Stoof, BOUDEWIJN J. VERHAAR, W. Glöckle

Published Nov 1, 1986• 27 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.34.6183

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Physical review. B, Condensed matter•Dec 1, 1986•57 citations
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 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 ${L}_{s}^{\mathrm{eff}=2.7(7)\ifmmode\times\else\texttimes\fi{}{10}^{\mathrm{\ensuremath{-}}25}}$ cm4{\mathrm{cm}}^{4}cm4 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ 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.
We have nearly tripled the range of magnetic-field strength over which bulk three-body recombination has been studied in spin-polarized atomic hydrogen. Analysis of our data (8-20 T) shows for the first time a qualitative agreement with theoretical predictions for the field dependence of dipolar recombination. Our results for the three-body exchange recombination are over an order of magnitude lower than a previously published value, and thus in reasonable agreement with theory. We discuss the prospects for observing Bose-Einstein condensation in very high magnetic fields.
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.
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.
Three-body recombination in spin-polarized hydrogen has been observed. Doubly polarized hydrogen was compressed by a piston into a thin cell and the temperature and pressure were independently monitored. Measurements were carried out in the temperature range 0.3 to 0.45 K in a magnetic field of 8.0 T at densities up to 1.5\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018 ${\mathrm{cm}}^{\ensuremath{-}3}$. The results are in good agreement with the theory of Kagan, Vartanyants and Shlyapnikov.
We have studied relaxation and recombination processes in compressed, doubly polarized atomic hydrogen at temperatures from 0.13 to 0.60 K and magnetic fields from 3 to 9 T. The gas and surface dipole three-body recombination rate constants at a field of 7.6 T are measured to be, respectively, Lg{L}_{g}Lg​=8.9(8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}39}$ cm6{\mathrm{cm}}^{6}cm6 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and Ls{L}_{s}Ls​=1.2(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}24}$ cm4{\mathrm{cm}}^{4}cm4 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. They decrease slowly with field and Ls{L}_{s}Ls​ exhibits no significant angular dependence. The three-body recombination rate due to hyperfine mixing has also been measured. Electronic and nuclear relaxation rates have been measured; the b-c electronic relaxation rate constant in the gas is Gbc{G}^{\mathrm{bc}}Gbc=1.03(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$exp(-Ebc{E}_{\mathrm{bc}}Ebc​/kB{k}_{B}kB​T). The temperature and field dependence of the nuclear relaxation rate in the gas are observed to be in excellent agreement with recent theoretical calculations. Three-body surface recombination-rate measurements using $^{3}\mathrm{\ensuremath{-}}^{4}$He surfaces indicate that as little as one monolayer of 3He^{3}\mathrm{He}3He on the liquid 4He^{4}\mathrm{He}4He surface appreciably decreases the adsorption energy of atomic hydrogen. Densities achieved include 4.5\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018 atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.55 K (pure 4He^{4}\mathrm{He}4He walls), and 1.4\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018 atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.19 K (8 at. ? sup 3---He).