4He Impurities in 3He: Energetics and Dynamics

We have developed the optimized Fermi Hypernetted Chain Theory of a single impurity atom in a Fermi liquid, and have applied the theory to a ⁴He atom in bulk ³He. Previous applications of the theory for one component have produced excellent agreement with the experimental equation of state of ⁴He; the resulting equation of state of bulk ³He is about 0.4 K above the experimental one. Within the same theory, we obtain the pressure dependence of the chemical potential of ⁴He in bulk ⁴He, ³He in ³He, as well as the chemical potential of a ⁴He impurity in ³He. The pressure dependence of the impurity chemical potential agrees well with the experimental data, but we have a constant energy offset of about 1.2 K that disallows conclusive statements. This offset is partly explained by the relative inaccuracy of the ³He equation of state. We then calculate the self-energy of a single ⁴He impurity in ³He. Our results for the effective mass m^* ₄ fall within the experimental error of the best available data; they increase from about m^* ₄/m₄1.4 at zero pressure, to m^* ₄/m₄1.6 at p=20 atm. We show that this effective mass enhancement is, to about equal parts, due to hydrodynamic backflow and to the coupling to particle-hole excitations. When the latter are turned off in the collective approximation of the impurity-background correlations one obtains a significantly lower effective mass, m^* ₄/m₄1.2–1.35.     

3He Impurities in 4He Systems Adsorbed on Curved Substrates

It is shown that ³He impurities in sufficiently large ⁴He systems adsorbed onto substrates with curved geometries form surface bound states, analogous to the Andreev state on a planar liquid--vapor interface. We report the analysis performed for superfluid ⁴He adsorbed on the external surface of the nano-fullerene C₆₀ and on cylindrical nano-wires of Au. It is found that a single ³He impurity diluted into such adsorbed structures behaves as on films on planar substrates and as on pure ⁴He clusters.     

Hydrogen isotope and3He impurities in liquid4He

Recently Reynolds, Hayden and Hardy(J. Low Temp. Phys. 84,87 (1991)) analyzed atomic deuterium lifetimes in a cell with walls covered by a saturated⁴He film. They were able to determine the deuterium chemical potential in⁴He and also discussed the possibility of estimating its effective mass. These measurements inspired our attempt to understand the properties of hydrogen isotope impurities in liquid⁴He using the extended Jastrow-Feenberg theory based on the correlated wave function. We present results for hydrogen isotope chemical potentials in the bulk⁴He as a function of density. The accuracy of the method is tested by calculating the chemical potential of the³He impurity. We find a good agreement with existing measurements. We also calculate the effective masses of the hydrogen impurities. For deuterium we predict a value,m _eff=4m _D .     

NMR Studies of 3He Impurities in 4He in the Proposed Supersolid Phase

Preliminary results are reported for measurements of the NMR relaxation times of very dilute ³He in samples of solid ⁴He at low temperature, 0.25 K <T< 1.3 K. The results were obtained for carefully prepared samples with different ³He concentrations. The measurements of the spin-spin relaxation time, T ₂, show several interesting features. A temperature independent plateau attributed to the exchange motional narrowing is observed down to the lowest temperature studied, and the observed variation of T ₂ with ³He concentration favors the nonlinear theory suggested by Landesman. The best fit to the data is given by T ₂ ∝ x ₃ ^?1.89±0.1 rather than x ₃ ^?1 . No evidence of an exchange-phonon bottleneck for the spin-lattice relaxation is seen down to 25 mK. The vacancy activation energy is determined to be 13.5±0.3 K for a sample with x ₃=5×10^?4 and molar volume 20.9 cm³.     

Condensate Fraction in Liquid 4He

The condensate fraction n ₀ in the ground state of liquid ⁴He is computed by means of an unbiased Quantum Monte Carlo technique. Unlike previous calculations of the same type, the method adopted here is in principle exact, errors being only statistical. At the equilibrium density, our estimate for n ₀ is 0.069 ± 0.005; this is consistent with the most recent experimental measurements, but significantly lower than most existing theoretical estimates. Results are provided in the density range from the spinodal (where n ₀ is maximum, ≈30%) up to the melting density. The condensate fraction remains finite in the high pressure metastable liquid, decaying exponentially with density.     

Recombination of Spin Polarized Atomic Hydrogen Adsorbed on a Dilute 3He-4He Mixture

We have been searching for two-dimensional (2-D) superfluidity of spin-polarized atomic hydrogen (H) adsorbed on liquid helium surface. We have investigated H adsorbed on ³ He- ⁴ He mixtures instead of pure ⁴ He because the thermal coupling of H to the mixtures is stronger than ⁴ He. ESR at 129 GHz was carried out to detect H at 4.5 T by using the Fabri-Perot confocal cavity with the cold spot located at the confocal point and thus the 2-D H signal was effectively detected. We investigated the two-body bulk and surface recombination processes of H on a 3% ³ He ³ He- ⁴ He mixture film. From the analysis of the surface recombination process, we found the adsorption energy of H was a 0.6 K for the mixture film in the temperature range between 120 mK and 250 mK, greater than the 0.3–0.4 K found previously for pure ³ He and a 67% ³ He ³ He- ⁴ He mixture.     

Lattice Relaxation in Solid 4He: Effect on Dynamics of 3He Impurities

We present a new simplified derivation of the effect of lattice relaxation that accompanies the quantum tunneling of ³He impurities in solid ⁴He on the nuclear spin-lattice relaxation of the ³He impurities for very low impurity concentrations. As a result of the larger zero point motion of the ³He impurity compared to the ⁴He atoms, a significant lattice distortion accompanies the impurity as it moves through the lattice and the dynamics of the impurity depends on both the interaction energy between two ³He atoms and on the relaxation of the lattice for the tunneling impurity. Using a phenomenological model for the lattice relaxation we compare the nuclear spin-lattice relaxation rates observed at low temperatures with the dependence on temperature expected for a ⁴He lattice relaxation comparable to that observed by Beamish et al. (Phys. Rev. Lett. 96:195304, 2006).     

The Fermi Liquid theory of4He in3He

The Zharkov-Silin Fermi Liquid theory of solutions of⁴He in normal (non-superfluid) liquid³He is reviewed and slightly extended. The theory is expected to be valid only below 0.1 K, and it predicts that there should be a hundred-fold increase in the diffusion coefficient as the temperature is lowered into this region. The limited range of validity explains the apparent disagreement between the recent very low temperature measurements of the phase separation line by Nakamura et al. and extrapolations from higher temperatures. In the low temperature experiments the⁴He concentration X₄ is so small that there is no macroscopic phase separation, only a gradual thickening of the⁴He-rich film on the walls. We confirm that the phase separation temperature T_ps(X₄) estimated from the thickening is close to the values which would be observed in an ideal experiment with a macroscopic phase. Fits to T_ps(X₄) including the new data show that the⁴He effective mass m ₄ ^* is close to, and may be equal to, the bare mass m₄. The difference in binding at zero pressure between⁴He in liquid⁴He and in liquid³He is (E₄₄–EE₄₃)/k_B=(0.21+0.03/–0.01)) K. Using the volume measurements of Laheurte to calculate the pressure dependence of E₄₃ indicates that the difference in binding has a minimum of (0.0±0.2) K near 11 atm. This implies that the solubility of⁴He in³He is enhanced in this region of pressure. The behavior of the spinodal line at low temperature, and the possibility of observing Bose condensation in a metastable solution of⁴He in liquid³He are also discussed.     

Cooling Mechanism of Spin Polarized Atomic Hydrogen Adsorbed on Dilute 3He-4He Mixture Film

We cooled down the two-dimensional (2-D) spin-polarized atomic hydrogen (H) adsorbed on a small surface called cold spot, whose temperature was kept much colder than the rest of the sample cell. The 2-D density of H was controlled by an input flux of H into the sample cell. We investigated the surface recombination of H adsorbed on 3% ³ He ³ He- ⁴ He mixture. ESR at 129GHz was carried out to detect H by mirror cavity with the cold spot located at the confocal point. We calculated the thermal boundary resistance between the absorbed H and the mixture. From the temperature dependence of the surface recombination together with calculated boundary resistance, we obtained the temperature dependence of _a. The result agrees with the previous measurement. Two-D H on the mixture film was cooled well down to 40mK.     

Excitations of Liquid 4He in Disorder

We discuss the effect of disorder and confinement on the excitations in superfluid and normal liquid ⁴ He. Neutron scattering measurements of the excitations to date are limited to helium in aerogel. There the phonon-roton energy and width are slightly modified by disorder but there is no evidence for additional excitations at low energy nor of a gap in the phonon energy at long wavelengths. Experimental difficulties are discussed. In a recent path-integral Monte-Carlo study, in which a high density of point impurities are introduced at random positions, a significant broadening and energy shift are found together with additional low-energy excitations.     

Kinetics of Liquid 3He Droplets in Solid 4He Matrix

Precise measurements of pressure in the crystal at constant volume were used to obtain the data on growth and dissolution kinetics of liquid ³ He droplets formed as a result of isotopic phase separation of solid ³ He- ⁴ He Mixtures. We studied several crystals with an initial ³ He concentration of 2.05% in the pressure range of 26–27 bar. It is shown that the growth of the liquid droplets during the stepwise cooling of the two-phase crystal is correctly described by the superposition of two exponential processes: diffusion decomposition with a small time constant and strain relaxation with a big time constant. The strain layer near the droplet boundaries is due to a great difference in molar volume between the droplets and the matrix, and leads to a plastic deformation of the matrix and to a non-equilibrium ³ He concentration in the matrix. Under such conditions quantum diffusion is significantly suppressed and ³ He atom transport occurs only as the strain is relaxed.     

Vibronic Transitions of Atomic Bubbles in Condensed 4He

Laser spectroscopy of atomic dopants can be used as a tool for the investigation of elementary excitations in quantum fluids and solids. Here we present results of a laser-spectroscopic study of transition-metal (Au, Cu) atoms in liquid and solid ⁴He. In particular we observe transitions of inner shell electrons that have not been studied before. Such transitions are weakly perturbed by the interaction with the helium matrix and display a characteristic structure composed of a sharp zero-phonon line and a relatively broad phonon wing.     

The Effect of 3He Impurities on Anomalous Oscillations in the Expansion of Solid 4He

The regular periodic intensity bursts recently observed in the expansion of solid ⁴He into vacuum have anomalies that have been attributed to a transition to some new solid phase induced by excess vacancies. Here it is shown that a small concentration of ³He, from 1% down to 0.1%, added to the ⁴He solid is sufficient to remove all the anomalies. The origin of the observed anomalies is discussed in the light of these new experiments.      

Bose-Einstein Condensation in Liquid 4He in Vycor

We present neutron scattering measurements of Bose-Einstein condensation (BEC) in liquid ⁴He confined in Vycor. The data show clear evidence of a condensate in Vycor with a condensate fraction comparable to that of bulk superfluid ⁴He, approximately 7.5% at low temperature and SVP. The temperature dependence of n₀(T) is also similar to that in the bulk with critical temperature for BEC, T_BEC, in the range 1.80BEC<2.05 K. The data are not accurate enough to show whether T_BEC for Vycor is the same or greater than the depressed critical temperature for superfluidity, T_c=1.95 K.     

Tortuosity and Dissipation of Liquid 4He in Aerogel

No Heading Flow of liquid ⁴He through silica aerogel has been studied by means of a torsional oscillator. Preliminary results on the tortuosity and dissipation of the ⁴He flow in 88%-porous aerogel are compared with earlier measurements on a 92%-porous sample where a transverse sound resonant technique was used. A hydrodynamic model for saturated superfluid helium in porous media is presented and its predictions are compared with the experimental results.PACS numbers: 67.40.HF, 67.40 Pm, 61.43.Gt     

Transverse Resonances in Aerogel with Liquid 4He

We present preliminary studies of transverse resonances in a thin disk of aerogel filled with normal and superfluid ⁴ He in the temperature range 1.4 to 3 K. We observed a broad temperature independent mode in the normal phase and three narrow critical modes in the superfluid phase. The system was modeled by combining the equations of superfluid hydrodynamics of helium with those of elasticity of aerogel. Analytical solutions were obtained for a resonator of square profile and two types of boundary conditions at the transducers/aerogel interface. Comparison of the model solutions with the experimental data showed that the dynamics of the oscillation was dominated by compression rather than shear as in pure transverse sound. Recommendations for future improvements are made.     

Compressibility of 4He Liquid Confined in Nuclepore

Adding and removing ⁴ He from an experimental cell which contains the porous material Nuclepore results in capillary condensation, hysteresis and avalanches. The volume of liquid in the nearly cylindrical pores is monitored with a capacitance technique. For the situation when all of the pores are full, the initial removal of ⁴ He from the cell results in a slight non-hysteretic decrease in the capacitance, which we attribute to the isothermal compressibility of ⁴ He. As ⁴ He atoms are removed, the surface tension at the meniscus applies a negative pressure to the liquid in the filled pores, which results in a reduction of the density and a decrease in the capacitance. We present results for ⁴ He capillary condensed in 2000 Å pore diameter Nuclepore.     

Measurement of the 4He Chemical Potential in Phase-Separated 3He-4He Liquid Mixtures

As a first step towards thermodynamic measurements in highly polarised dense ³ He fluids, an accurate determination of the ⁴ He chemical potential ₄ was performed in unpolarised phase-separated ³ He- ⁴ He liquid mixtures at low pressures (0-1 bar) over a temperature range 0.12 - 0.65 K. A method introduced by H. London and relying on heat flush effects was used. Two volumes containing : a) a cold, phase-separated helium mixture and b) a warmed, pure ⁴ He liquid are connected by a narrow tube, and their temperatures are recorded under various conditions. The results agree with existing data obtained by the same technique for T >0.2K, but cannot be analysed with the simple regular solution model fitting vapour pressure data at T >0.6K. The sensitivity of the technique is shown to be sufficient to observe expected effects of nuclear polarisation on ₄.     

Hybrid Density Functional for Liquid 4He

No Heading An alternative density functional for studying adsorption of ⁴He onto solid surfaces is suggested, where the helium-helium interaction is screened at small distances by the two-body distribution function g(r) and the gradient-gradient term of the Orsay-Trento proposal is replaced by a contribution written in terms of the gradient of g(r). Results for helium adsorption onto planar Na substrates are reported.PACS numbers: 67.40.Db, 67.70.+n, 68.10.–m, 68.15.+e