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Resonant recombination of atomic hydrogen and deuterium at low temperatures

M. W. Reynolds

Published Jan 1, 2010• 1 citation
Publisher

Abstract

The contents of this thesis include several experiments and a theory, the unifying theme of which is resonant recombination of atomic hydrogen (H) and deuterium (D) at low temperatures. Measurements of the interaction of H and D with the liquid helium (l-⁴He) wall coating used in low-temperature experiments are also included. Atomic hydrogen and deuterium were studied by ESR in a field of 41 kG at temperatures below 1 K, in a second generation of experiments on an existing apparatus. The binding energy of H on l-⁴He was measured, by direct observation of the physisorbed atoms, to be E[sub B]= 1.00(5) K. Extensive meaurements of recombination rate constants were made. Resonant recombination of H via the (v, J) = (14,4) level of H₂ was observed and identified. Atomic deuterium was also observed to recombine in a resonant process. At low temperatures, resonant recombination is possible due to the predissociation of weakly bound molecular levels by the intra-atomic hyperfine interaction. The theory of resonant recombination of H and D due to hyperfine predissociation is developed in detail. In order to keep the development self-contained, it is presented as appendix D of this thesis. The theory is combined with our ESR data in order to predict the magnetic-field dependence of resonant recombination of D. It is shown that observation of the threshold magnetic fields for resonant recombination will permit accurate measurement of the dissociation energy of the (v, J) = (21,0) and perhaps (21,1) levels of the D₂ molecule. An apparatus was constructed to study atomic deuterium by hyperfine magnetic resonance at temperatures near 1 K. The D atoms were produced from D₂ of 99.65% isotopic purity by an RF discharge in a bulb coated with a film of superfluid l-⁴He. Magnetic resonance in a field of 39 G on the longitudinal β-δ transition at its minimum frequency of 309 MHz was used to observe the atoms. The experiment was designed with the capability of measuring the recombination rate as a function of magnetic field for fields up to 30 kG by moving the sample between the 309 MHz resonator and a superconducting solenoid. A number of preliminary experiments were made using this apparatus. It was discovered that the D atom density decays away exponentially in time. The decay rate was measured as a function of temperature and found to follow an Arrhenius (thermally-activated) form, with an activation energy of about 15 K. No second-order decay was seen, permitting an upper bound to be placed on the D-D recombination rate. The exponential decay of the D atom density was due to the penetration by the atoms of the l-⁴He film coating their container. Our measurement of the temperature dependence of the density decay rate gives the energy required to dissolve a D atom in l-⁴He, Es[sub s] ≃ 14 K. This is the first experimental determination of this quantity. The longitudinal relaxation time T₁ for the β-δ transition was found to be too short to be due to D-D spin-exchange. It was conjectured that the sample was contaminated with substantial amounts of H, spin-exchange in H-D collisions causing the short T₁. Measurements in an existing 1420 MHz apparatus showed directly, by magnetic resonance on the hydrogen zero-field transition, that H atoms were, in fact, present. By varying the H concentration, we were able to show that the decay of the D density by was not due to recombination of H with D. Several attempts to substantially reduce the H impurity have failed. The penetration of the l-⁴He film is undoubtedly one reason why the D is so susceptible to contamination by H, since the film is permeable to D but not to H. For use in interpreting these experiments, the effects of spin-exchange relaxation on hyperfine resonance in mixtures of H and D were calculated.

DOI
10.14288/1.0085029

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The contents of this thesis include several experiments and a theory, the unifying theme of which is resonant recombination of atomic hydrogen (H) and deuterium (D) at low temperatures. Measurements of the interaction of H and D with the liquid helium (l-⁴He) wall coating used in low-temperature experiments are also included. Atomic hydrogen and deuterium were studied by ESR in a field of 41 kG at temperatures below 1 K, in a second generation of experiments on an existing apparatus. The binding energy of H on l-⁴He was measured, by direct observation of the physisorbed atoms, to be E[sub B]= 1.00(5) K. Extensive meaurements of recombination rate constants were made. Resonant recombination of H via the (v, J) = (14,4) level of H₂ was observed and identified. Atomic deuterium was also observed to recombine in a resonant process. At low temperatures, resonant recombination is possible due to the predissociation of weakly bound molecular levels by the intra-atomic hyperfine interaction. The theory of resonant recombination of H and D due to hyperfine predissociation is developed in detail. In order to keep the development self-contained, it is presented as appendix D of this thesis. The theory is combined with our ESR data in order to predict the magnetic-field dependence of resonant recombination of D. It is shown that observation of the threshold magnetic fields for resonant recombination will permit accurate measurement of the dissociation energy of the (v, J) = (21,0) and perhaps (21,1) levels of the D₂ molecule. An apparatus was constructed to study atomic deuterium by hyperfine magnetic resonance at temperatures near 1 K. The D atoms were produced from D₂ of 99.65% isotopic purity by an RF discharge in a bulb coated with a film of superfluid l-⁴He. Magnetic resonance in a field of 39 G on the longitudinal β-δ transition at its minimum frequency of 309 MHz was used to observe the atoms. The experiment was designed with the capability of measuring the recombination rate as a function of magnetic field for fields up to 30 kG by moving the sample between the 309 MHz resonator and a superconducting solenoid. A number of preliminary experiments were made using this apparatus. It was discovered that the D atom density decays away exponentially in time. The decay rate was measured as a function of temperature and found to follow an Arrhenius (thermally-activated) form, with an activation energy of about 15 K. No second-order decay was seen, permitting an upper bound to be placed on the D-D recombination rate. The exponential decay of the D atom density was due to the penetration by the atoms of the l-⁴He film coating their container. Our measurement of the temperature dependence of the density decay rate gives the energy required to dissolve a D atom in l-⁴He, Es[sub s] ≃ 14 K. This is the first experimental determination of this quantity. The longitudinal relaxation time T₁ for the β-δ transition was found to be too short to be due to D-D spin-exchange. It was conjectured that the sample was contaminated with substantial amounts of H, spin-exchange in H-D collisions causing the short T₁. Measurements in an existing 1420 MHz apparatus showed directly, by magnetic resonance on the hydrogen zero-field transition, that H atoms were, in fact, present. By varying the H concentration, we were able to show that the decay of the D density by was not due to recombination of H with D. Several attempts to substantially reduce the H impurity have failed. The penetration of the l-⁴He film is undoubtedly one reason why the D is so susceptible to contamination by H, since the film is permeable to D but not to H. For use in interpreting these experiments, the effects of spin-exchange relaxation on hyperfine resonance in mixtures of H and D were calculated.
In this thesis we describe the results of two sets of experiments on spin-polarized atomic hydrogen at temperatures below 1 K using a 115 GHz heterodyne ESR spectrometer. First, we have made measurements of the rates of the two-body recombination processes in spin-polarized atomic hydrogen gas and spin-polarized atomic deuterium gas in a 41 kG field. In the second set of experiments, we examined the ESR absorption line associated with the spin-polarized atomic hydrogen atoms adsorbed on surfaces of liquid helium. In hydrogen, a comparision of the measured recombination rates in 41 kG with the corresponding rates measured in different magnetic fields showed that an additional recombination process is activate for the conditions of these experiments. We demonstrate that this is due to a resonant recombination process via the (v,J) = (14,4) level of molecular hydrogen. In spin-polarized deuterium, we found that the recombination rate are much larger than the analogous rates in hydrogen, and therefore that atomic deuterium gas is much less stable than the hydrogen system under comparable conditions. We report the first observation and study of doubly spin-polarized deuterium, a gas in which both the deuteron and electron spins are aligned. At temperatures near 0.1 K, the absorption line of doubly spin-polarized H atoms changes drastically as a peak appears on both sides of the peak associated with the bulk atoms. We have shown that these new peaks are due to the atoms which are adsorbed onto the surface of the liquid helium film that coats the walls of the microwave cavity. The geometry dependent non-zero average magnetic dipolar field due to aligned spins on a planar surface results in a shift of the position of the ESR absorption lines. The lineshapes of the side peaks are very unusual and are best described as ramp-like. Even after extensive attempts to explain this lineshape, we still do not know what mechanism is responsible.
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.
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.
In this thesis three experiments with atomic hydrogen (H) at low temperatures T<1 K are presented. Experiments were carried out with two- (2D) and three-dimensional (3D) H gas, and with H atoms trapped in solid H2 matrix. The main focus of this work is on interatomic interactions, which have certain specific features in these three systems considered. A common feature is the very high density of atomic hydrogen, the systems are close to quantum degeneracy. Short range interactions in collisions between atoms are important in gaseous H. The system of H in H2 differ dramatically because atoms remain fixed in the H2 lattice and properties are governed by long-range interactions with the solid matrix and with H atoms. The main tools in our studies were the methods of magnetic resonance, with electron spin resonance (ESR) at 128 GHz being used as the principal detection method. For the first time in experiments with H in high magnetic fields and at low temperatures we combined ESR and NMR to perform electron-nuclear double resonance (ENDOR) as well as coherent two-photon spectroscopy. This allowed to distinguish between different types of interactions in the magnetic resonance spectra. Experiments with 2D H gas utilized the thermal compression method in homogeneous magnetic field, developed in our laboratory. In this work methods were developed for direct studies of 3D H at high density, and for creating high density samples of H in H2. We measured magnetic resonance line shifts due to collisions in the 2D and 3D H gases. First we observed that the cold collision shift in 2D H gas composed of atoms in a single hyperfine state is much smaller than predicted by the mean-field theory. This motivated us to carry out similar experiments with 3D H. In 3D H the cold collision shift was found to be an order of magnitude smaller for atoms in a single hyperfine state than that for a mixture of atoms in two different hyperfine states. The collisional shifts were found to be in fair agreement with the theory, which takes into account symmetrization of the wave functions of the colliding atoms. The origin of the small shift in the 2D H composed of single hyperfine state atoms is not yet understood. The measurement of the shift in 3D H provides experimental determination for the difference of the scattering lengths of ground state atoms. The experiment with H atoms captured in H2 matrix at temperatures below 1 K originated from our work with H gas. We found out that samples of H in H2 were formed during recombination of gas phase H, enabling sample preparation at temperatures below 0.5 K. Alternatively, we created the samples by electron impact dissociation of H2 molecules in situ in the solid. By the latter method we reached highest densities of H atoms reported so far, 3.5(5)x1019 cm-3. The H atoms were found to be stable for weeks at temperatures below 0.5 K. The observation of dipolar interaction effects provides a verification for the density measurement. Our results point to two different sites for H atoms in H2 lattice. The steady-state nuclear polarizations of the atoms were found to be non-thermal. The possibility for further increase of the impurity H density is considered. At higher densities and lower temperatures it might be possible to observe phenomena related to quantum degeneracy in solid.
In sufficiently large magnetic fields, the weakly bound levels of H2 acquire finite lifetimes owing to hyperfine predissociation and become manifest as scattering resonances in spin-polarized atomic hydrogen (H↓). In this work we investigate in detail the contribution to the reaction kinetics in H↓ due to the resonance, denoted [Formula: see text], arising from the predissociation of the (v,J) = (14,4) level of H2. To characterize the formation and disintegration of [Formula: see text], we calculate the predissociation as a function of both the applied magnetic field and the dissociation energy, D, of the level. Recombination occurs when [Formula: see text] is stabilized in collisions that cause transitions to lower molecular levels. For low H↓, densities, collisions with atoms of the saturated 4He vapour dominate; we calculate the cross section in the distorted wave Born approximation and also use a coupled-channels approach. At higher densities, stabilization occurs in collisions with H↓ as well; the effect of proton exchange between the atom and the molecule is derived. Previous experiments, analyzed neglecting proton exchange, are reanalyzed including this; the dissociation energy D is not as well determined by the data as was previously thought. Prospects for future experiments are discussed.
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 ${{T}_{1}}^{\ensuremath{-}1}$.