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Physical review. B, Condensed matter

Compression of spin-polarized hydrogen bubbles to thermal explosion

T. J. Tommila, E. Tjukanov, M. Krusius, S. Jaakkola

Published Nov 1, 1987• 16 citations
Publisher

Abstract

We have compressed spin-polarized atomic hydrogen gas in small, \ensuremath{\gtrsim}${10}^{\mathrm{\ensuremath{-}}6}$-${\mathrm{cm}}^{3}$ bubbles to densities higher than ${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ using a liquid${\mathrm{\ensuremath{-}}}^{4}$He piston at temperatures from 0.3 to 0.7 K and in magnetic fields from 4.5 to 7.5 T. A best fit to the compression sweeps is obtained by fixing the binding energy of the adsorbed H atom on the liquid $^{4}\mathrm{He}$ surface to 1.15 K, which then yields the third-order dipolar recombination rate constants ${K}_{\mathrm{bbb}}^{v}$=2.7(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}39}$ ${\mathrm{cm}}^{6}$/s for the gas phase and ${K}_{\mathrm{bbb}}^{s}$=8(2)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}25}$ ${\mathrm{cm}}^{4}$/s for the adsorbed surface layer. Because of inadequate transfer of the recombination heat to the surrounding He bath, the compression sweeps terminate in a spontaneous thermal explosion of the H\ensuremath{\downarrow} bubble. The pressure at the onset of the explosive recombination event is investigated as a function of ambient temperature, bubble volume, and magnetic field. Qualitative agreement with a simple thermally activated explosion model is found.

DOI
10.1103/physrevb.36.6837

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We have compressed spin-polarized atomic hydrogen gas in small, \ensuremath{\gtrsim}10\ensuremath−6{10}^{\mathrm{\ensuremath{-}}6}10\ensuremath−6-cm3{\mathrm{cm}}^{3}cm3 bubbles to densities higher than 1018{10}^{18}1018 cm\ensuremath−3{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}cm\ensuremath−3 using a liquid\ensuremath−4{\mathrm{\ensuremath{-}}}^{4}\ensuremath−4He piston at temperatures from 0.3 to 0.7 K and in magnetic fields from 4.5 to 7.5 T. A best fit to the compression sweeps is obtained by fixing the binding energy of the adsorbed H atom on the liquid 4He^{4}\mathrm{He}4He surface to 1.15 K, which then yields the third-order dipolar recombination rate constants Kbbbv{K}_{\mathrm{bbb}}^{v}Kbbbv​=2.7(7)\ifmmode\times\else\texttimes\fi{}10\ensuremath−39{10}^{\mathrm{\ensuremath{-}}39}10\ensuremath−39 cm6{\mathrm{cm}}^{6}cm6/s for the gas phase and Kbbbs{K}_{\mathrm{bbb}}^{s}Kbbbs​=8(2)\ifmmode\times\else\texttimes\fi{}10\ensuremath−25{10}^{\mathrm{\ensuremath{-}}25}10\ensuremath−25 cm4{\mathrm{cm}}^{4}cm4/s for the adsorbed surface layer. Because of inadequate transfer of the recombination heat to the surrounding He bath, the compression sweeps terminate in a spontaneous thermal explosion of the H\ensuremath{\downarrow} bubble. The pressure at the onset of the explosive recombination event is investigated as a function of ambient temperature, bubble volume, and magnetic field. Qualitative agreement with a simple thermally activated explosion model is found.
Doubly polarized hydrogen has been produced up to densities of 2\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ with the use of a compression technique. Samples were compressed up to five orders of magnitude into small bubblelike volumes under a column of liquid helium. This technique enabled us to study the volume decay of a bubble at almost constant gas density for minutes. The analysis of the volume decay of such a bubble is discussed. A bulk three-body recombination process was observed with rate constant C3{C}_{3}C3​=[7(2)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}39}$ cm6{\mathrm{cm}}^{6}cm6 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, as well as bulk electronic b\ensuremath{\rightarrow}c relaxation with rate constant Gbcv{G}_{\mathrm{bc}}^{v}Gbcv​\ensuremath{\downarrow}=[12(4)]\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}16}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. The nature of the three-body process is analyzed with a set of extended rate equations. The samples were very delicate and rapid compressions could result in explosions.
A new technique enabled the authors to compress doubly polarized hydrogen by up to five orders of magnitude and study the sample in very small volumes at constant density up to 2\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018/cm3{\mathrm{cm}}^{3}cm3. The first determination of the bulk three-body dipolar recombination rate was made, ${{K}_{V}}^{3\mathrm{b}}=4(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}39}$ cm6{\mathrm{cm}}^{6}cm6 ${\mathrm{s}}^{\ensuremath{-}1}$. The authors also identified a new process, bulk electronic dipolar $b\ensuremath{\rightarrow}c$-state relaxation with rate constant ${{G}_{V}}^{\mathrm{bc}}\mathrm{exp}(2{\ensuremath{\mu}}_{\mathrm{B}}\frac{B}{{k}_{\mathrm{B}}}T)=8(4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\ensuremath{-}1}$. Samples were very delicate and too rapid a compression could result in an explosion.
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).
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 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 describe experiments where two-dimensional (2D) atomic hydrogen gas is compressed thermally at a small ``cold spot'' on the surface of superfluid helium and detected directly with electron-spin resonance. We reach surface densities up to $5\ifmmode\times\else\texttimes\fi{}{10}^{12}{\mathrm{cm}}^{\ensuremath{-}2}$ at temperatures $\ensuremath{\approx}100\mathrm{mK}$ corresponding to the maximum 2D phase-space density $\ensuremath{\approx}1.5.$ By independent measurements of the surface density and its decay rate we make a direct determination of the three-body recombination rate constant and get the upper bound ${L}_{3b}\ensuremath{\lesssim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}{\mathrm{cm}}^{4}/\mathrm{s}$ which is an order of magnitude smaller than previously reported experimental results.