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Physical review. B, Condensed matter

Spin-exchange and dipole relaxation rates in atomic hydrogen: Rigorous and simplified calculations

Henk T. C. Stoof, J. M. V. A. Koelman, BOUDEWIJN J. VERHAAR

Published Sep 1, 1988• 216 citations
Publisher

Abstract

We calculate the magnetic field and temperature dependence of the rates for all two-body spin-exchange and dipolar transitions among hyperfine levels in cryogenic H gas by means of the coupled-channels method. A description of this method and its practical application is presented. A simple interpretation of the rates is given, in some cases with associated simple closed-form formulas, based on the degenerate-internal-states approximation.

DOI
10.1103/physrevb.38.4688

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ESR on spin-polarized atomic hydrogen at temperatures below 0.5 K

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•Jan 1, 2010•1 citation
We calculate the magnetic field and temperature dependence of the rates for all two-body spin-exchange and dipolar transitions among hyperfine levels in cryogenic H gas by means of the coupled-channels method. A description of this method and its practical application is presented. A simple interpretation of the rates is given, in some cases with associated simple closed-form formulas, based on the degenerate-internal-states approximation.
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).
A calculation is presented of the relaxation rate ${{T}_{1}}^{\ensuremath{-}1}$ between the lowest two hyperfine states of a dilute gas of H atoms in high magnetic field at low temperatures. Dipole-dipole interactions dominate ${{T}_{1}}^{\ensuremath{-}1}$, leading to long relaxation times at low temperatures (${{T}_{1}}^{\ensuremath{-}1}\ensuremath{\approx}{10}^{\ensuremath{-}2}{n}_{\mathrm{H}}{T}^{\frac{1}{2}}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ at $H\ensuremath{\approx}100$ kG). The recombination rate due to wall collisions is much greater than ${{T}_{1}}^{\ensuremath{-}1}$ and can lead to a depletion of the lowest hyperfine state from thermal equilibrium and an effective recombination rate equal to ${{T}_{1}}^{\ensuremath{-}1}$.
An experiment for studying a gas of atomic hydrogen at temperatures between 0.9 K and 1.3 K is described. The field dependence of the recombination rate of H atoms into H₂ molecules and the spin-exchange cross-section are investigated. Atoms are produced in situ in a low temperature discharge and are confined in a pyrex cell. The walls of this cell are covered with a film of superfluid ⁴He for preventing recombination. The detection and the study of the hydrogen atoms is done using the technique of pulsed magnetic resonance between the lowest two hyperfine levels of the 1s hydrogen atoms. The frequency is about 765.5 MHz and corresponds to a shallow minimum in the difference between the lowest two hyperfine levels, which occurs at 6481 kGauss. A simple model is also derived for explaining the field dependence of the recombination in the presence of a relatively large ⁴He density. In fact, due to the vapour pressure, the helium density will be above 10¹⁸ atoms/cm³ in the range of temperatures in which we are interested, while the density of hydrogen atoms will be about 10¹¹ -10¹² atoms/cm³. The relaxation mechanism assumed is spin-exchange. The parameters of the model are fit to the existing data. It is found in particular that the asymptotic behavior of the hyperfine populations depends sensitively on the initial populations.
Spin-polarized atomic hydrogen (H↓) gas at low temperatures (<0.5 K) has been studied using Electron Spin Resonance (ESR) techniques which allow direct measurements of the densities of H atoms in each of the two lower hyperfine states (a and b). It has been demonstrated that ESR can be made to yield accurate and detailed information about the decay of H↓ densities in time. Crucial to the analysis of the data is the ability to confine the sample of H↓, gas inside the liquid ⁴He coated microwave cavity where the magnetic field and temperature are well known. Measurements of K[sub aa] and K[sub ab], the two surface recombination rate constants, and their ratio γ=K[sub aa]/K[sub ab] have been made and from these results the binding energy of H on liquid ⁴He has been extracted. Also reported are the results of the first detailed study of the one-body surface relaxation rate which we find is due to microscopic magnetic impurities in the cell walls. Theoretical calculations of the two-body dipole-dipole relaxation rate of H↓ in the gas and on the surface are also presented.