Dynamics of3He impurities in4He films

Using a microscopic theory we calculate the binding energy of³ He impurities in films of⁴ He absorbed to a graphite substrate. Without adjustable parameters, we obtain excellent agreement with the experimental binding energies for the ground state of the He impurity. By introducing a timedependent variational wave function, the impurity atom acquires a hydrodynamic effective mass for its motion parallel to the surface due to hydrodynamic backflow, and the excited states have a finite lifetime. When these effects are included, both the energy of the first excited state of the impurity, and the effective mass of the ground state, agree well with experimental data.A comparison with recent density functional results is carried out. It is shown that the substrate bound states on strong potentials are spurious and due to the inappropriate treatment of the effective mass within that theory.     

3He impurities on the bulk surface of liquid4He: Possible existence of excited states

We study, using a density-functional approach, the properties of the two-dimensional system formed by³He atoms on the surface of liquid⁴He, as a function of³He coverageN _s , at zero temperature. We find several types of surface states accessible to the³He atoms. For small values ofN _s , the surface tension is, as expected, linear inN _s ² . For a coverage of about half a monolayer, a new type of surface state starts being occupied, and this produces a change in the slope of as a function ofN _s ² and, more clearly, a step in the surface specific heat, which increases by a factor of almost two. Another step is predicted to occur for a coverage of 1.3 monolayer. Existing data are compatible with this structure of surface states but are not numerous enough to prove or disprove the existence of steps.Unité de Recherche des Universités Paris 11 et Paris 6 Associée au CNRS.     

Effects of 4He impurities on 3He nuclear spin-lattice relaxation in hcp solid 3He

Nuclear spin-lattice relaxation properties of hcp solid ³He with ⁴He impurities have been studied. At temperatures below the exchange plateau region, three kinds of relaxation time were observed. To analyze the data, a phenomenological four-bath model was developed, the four baths being the Zeeman bath, the phonon bath, an X-bath, and a Y-bath. The X-bath consists of the exchange bath and a part of the ⁴He-⁴He elastic interaction bath. The Y-bath is the main part of the elastic interaction bath. We measured the concentration dependence of the energy constants of all the baths, as well as the temperature and concentration dependences of the three kinds of relaxation time. The relaxation behavior corresponding to the process between the X-bath and the Y-bath could not be expressed by a single exponential function of time and the relaxation rate was strongly dependent on the concentration. This process may be related to the internal thermal equilibrium process within the elastic interaction bath. The impurity-dependent relaxation time between the X-bath and the phonon bath had a temperature dependence of T ^–n with n = 7.4±0.3.     

Nuclear magnetic susceptibility of solid3He with4He impurities

The nuclear magnetic susceptibility of bcc solid³He with a small concentration of⁴He is calculated in the high-temperature approximation. The exchange Hamiltonian used for the system is that obtained from a Hubbard-like cell model developed in earlier work. A brief discussion is also given of our general approach to the study of the magnetic properties of impure solid³He as compared to other approaches to the problem.     

Finite-amplitude acoustic waves in liquid3He and4He

Finite-amplitude acoustic waves have been propagated in liquid³He and⁴He. The acoustic cell has been operated at 83, 250, and 420 MHz and down to 17 mK. Our measurements of the anharmonic effects are in agreement with theoretical predictions and with previous experimental work that investigated a restricted temperature range.     

Effects of3He impurities on the4He solid-liquid interface

Using crystallization waves we have measured the interfacial stiffness, , and the temperature dependence of the growth resistance, (Km)^–1, of the⁴He solid-liquid interface in the presence of³He impurities. For the purest⁴He sample, (Km)^–1 is consistent at the lowest temperatures with the assumption that the growth velocity is limited by the scattering of ballistic phonons from the moving interface. At higher concentrations of³He, we observe that (Km)^–1 increases exponentially with temperature below 0.25 K. We observe that decreases with increasing³He concentration.     

Vibrating-wire measurements in vacuum,liquid3He and liquid3He-4He mixtures

In order to overcome the 200µK - barrier in the refrigeration of liquid ³ He- ⁴ He mixtures we have constructed an experimental cell using only pure materials to minimize possible origins for heat leaks into the liquid. With this arrangement we were able to cool a saturated6.8%- mixture to a temperature of 150µK. A vibrating wire which was immersed in pure ³ He floating on top of the phase-separated mixture was used as a thermometer. This wire was calibrated in a second experiment with pure ³ He only in the cell. In superfluid ³ He-B at T0.15 mK the damping of the wire due to the quasiparticles becomes very small, and we observe typical characteristics of the vacuum damping of the wire which was extensively examined before filling any liquid into the cell.     

Influence of4He impurities on nuclear spin relaxation in solid3He

The NMR properties of solid³He, mainly the ratio of the heat capacities of exchange and Zeeman energies and the exchange-lattice relaxation times are very sensitive to the presence of⁴He impurities, while the transverse relaxation timeT ₂ does not depend on the impurity concentration when the latter remains small. These properties can be explained in two different ways. (1) We assume an enhancement of exchange interactions around⁴He impurities. We derive the consequences of such an assumption and compare them with experimental results. For two molar volumes in the bcc phase, the locally enhanced exchange is equal to approximately7J, withJ being the exchange in pure³He. (2) Guyer and Zane introduce a mass fluctuation wave to explain the excess of heat capacity and the dependence of the longitudinal relaxation time with concentration. Both these models give rise to a four-energy bath system. As in the bcc phase, the exchange-lattice relaxation time in the hcp phase decreases when × increases at low enough⁴He concentrations. ForV=18.48 cm³ we deduce the coefficient for translational diffusion from high-temperature experiments with the help of Torrey's theory for spin-lattice relaxation.This paper is based on a thesis to be submitted in partial fulfillment of the requirements for the degree ofDocteur ès Sciences in Physics at theFaculté des Sciences d'Orsay in 1970. This thesis will be registered at the CNRS under the number AO 3704.     

Calculation of third-sound velocities for superfluid4He films with3He impurities

The velocities of third sound in superfluid⁴He films containing submonolayer densities of³He are calculated from the variation of film height with the concentration of³He. The present model assumes that the population of the first-excited, transverse, surface state of the³He impurities directly increases the height of the film because these atoms are preferentially found within the film rather than on the surface. The relative populations of the ground-state and the first excited-state are calculated from a many-body, mean-field theory which takes account of the first two transverse branches of the spectra of the states. Intermolecular and one-ripplon exchange interactions are included. Graphs of the variation of third-sound velocity with³He density are given.     

Polarized liquid3He in a4He circulating dilution refrigerator

We have used a⁴He circulating dilution refrigerator to produce cold liquid³He with a steady state out-of-equilibrium nuclear spin polarization. Polarizations on the order of 15% (more than 7 times higher than the equilibrium polarization in the external field of 6.6 T) have been obtained in the mixing chamber of the refrigerator at temperatures between 10 and 15 mK. The polarization is enhanced at high pressure because the molar susceptibility of concentrated³He is larger than that of the dilute phase. The polarization exchange between the dilute and concentrated phases (in direct contact in the heat exchanger of the refrigerator) amplifies the enhancement. The polarization diminishes below a pressure of 2.6 bar. This allows us to scale and reinterpret susceptibility data of the dilute phase¹ in combination with the effective mass deduced from osmotic pressure measurements². We find 1+F ₀ ^a = 0.89±1% on the phase separation line in the pressure range 0–20 bar.We would like to thank Profs. D.M. Lee and M.S. Tagirov for the many discussions during their visits.     

Binding energy of one4He impurity in liquid3He

A variational microscopic calculation of the binding energy of a⁴He impurity (_i) in homogeneous liquid³He at zero temperature is presented. Starting on an extended Jastrow-Slater wave function including three-body correlations, the expression for _I is derived and the appropriated FHNC formalism for this problem is reviewed. In the framework of the Average Correlation Approximation (ACA), it is proved that it is possible to obtain the chemical potential of the impurity only from liquid³He magnitudes with a good accuracy. Our results are consistent with both a recent experimental determination of _I at zero pressure and the non-solubility of⁴He in³He. However, numerical uncertainties preclude a firm conclusion about the latter property.     

Ground-state properties of a3He impurity in liquid4He monolayers

We present the results of ground-state energies, radial distribution functions, liquid structure functions and effective interactions for a³He impurity in a⁴He background in two dimensions. The hypernetted-chain scheme for the system described by a Jastrow-type wavefunction is used, taking into account the triplet correlations and elementary diagrams up to fifth order. Solving the Euler-Lagrange equations for the two-body distribution functions, which contain triplet correlation and elementary diagrams, improves the results considerably. Furthermore, as a³He impurity is inserted into the⁴He background, the ground-state energy increases, but the equilibrium density decreases from 0.0350 Å^–2 to 0.0336 Å^–2. The radial distribution function is broadened, while its maximum is lowered and shifted to the right (the direction of increasing radial distance) due to its larger zero-point energy, with therefore less localization of the³He particle. The results are compared with Monte Carlo results and other studies.     

Magnetic susceptibility and collisionless spin waves in liquid3He and3He-4He mixtures

The transverse spin susceptibility for a Fermi liquid in a uniform magnetic field is calculated in the collisionless regime using the Landau theory of Fermi liquids. The singularities corresponding to the l=0 and l=1 spin waves are investigated in pure and dilute³He as a function of the wave vector q up to the threshold of the Landau damping.     

Dielectric constant and molar volume of saturated liquid 3He and 4He

Measurements are reported of the dielectric constant of ³He in the temperature range from 0.5 to 2.4 K and of ⁴He from 0.7 to 4.2 K. From these measurements the molar volumes of the two isotopes have been calculated for the same temperature ranges, using the polarizabilities reported by Kerr and Sherman.Work performed under the auspices of the U.S. Energy Research and Development Administration.     

Osmotic pressure of very dilute liquid mixtures of3He in4He

The osmotic pressure of very dilute liquid mixtures of³He in⁴He has been measured for the concentration range 0.08–0.6 mole%³He, and the temperature range 20–400 mK. The results are used to check the validity of different proposals for the³He–³He effective interaction.Work supported in part by the Gerald I. Swope Fund and the Batsheva de Rothschild Foundation.     

Multiple positive ionic mobilities in normal liquid 3He contaminated with 4He

The positive ion in liquid ³He contaminated with 5 × 10^\s-4 parts of ⁴He is found at low temperatures to be able to exist in a number of discrete states with different mobilities. At a temperature of around 30 mK transitions from one species to another are observed. These transitions take place at a rate proportional to the ⁴He solubility. The different states may represent discrete values of ³He/⁴He ratio in the solid ion and immediately surrounding liquid.     

Simultaneous measurements of heat capacity and pressure coefficient of liquid He4 and He3 - He4 mixtures

An apparatus for simultaneous measurements of heat capacities and pressure coefficients was designed and constructed for experimental studies of critical phenomena near the lambda points of liquid He⁴ and He³ - He⁴ mixtures.The pressure was measured with a capacitance pressure sensor involving a copper-beryllium thin plate (0.4 mm thickness). An oscillator circuit, including the capacitance pressure sensor, and driven by a tunnel diode was attached to the bottom of the calorimeter. The resolutions of temperature and pressure in this apparatus are ～ 2 × 10^?7 K and ～2 × 10^?6 bar (～2 × 10^?1 N m^?2) respectively.     

The magnetic susceptibility of dilute mixtures of3He in liquid4He

The relative changes in the low-temperature susceptibility of a number of dilute mixtures of³He in liquid⁴He at various pressures are reported and analyzed. Under elevated pressures, the solubility of³He in⁴He increases and the effects of the interaction between³He quasiparticles clearly become larger. However, no evidence of a BCS pairing transition was found in direct measurements of susceptibility and nuclear resonance frequency down to the temperature 1.5 mK in saturated solutions with a pressure of 21 bar.Guggenheim Fellow on leave from Cornell University, Ithaca, New York.     

Phase separation under pressure in dilute liquid mixtures of4He in3He

We present the results of phase separation under pressure in some dilute⁴He mixtures. The effect of pressure is to reduce the phase separation temperature for a given concentration. However, the general shape of all phase-separation curves seem to show that atT=0 K, no dilute ⁴ He solutions will exist. The analysis of our results using the isotopic impurity model shows also that ⁴ He- ⁴ He quasiparticle interaction is not detectable and so is certainly very small. The difference of behavior between dilute ⁴ He and dilute ³ He solutions has a statistical origin.     

Propagation of solitary waves in a mixture of liquid3He and superfluid4He

The effect of an admixture of liquid³He on the propagation of solitary waves in superfluid⁴He is investigated. In the local density approximation, the mean field equations are reduced to the two-fluid equations describing the dynamics of the mixture of two liquids. The nonlinear perturbation approach is used to obtain a set of equations describing the density and velocity fluctuations of the homogeneous mixture at rest. The self-consistent solution of these equations is shown to be the solitary waves. Using a pseudopotential method, we perform numerical calculations to study the changes in the general properties of the waves caused by the³He impurity.