The solubility of spin-polarized3He in4He and the superfluidity of3He in3He-4He mixtures

We investigate the possibility of a large enhancement of the T = 0 finite solubility of³He in⁴He due to spin-polarization. The size of the effect depends on the fraction of³He atoms in the system. We present two different approaches for the limits of a small and a large number of³He atoms compared to the number of⁴He atoms. Since the possible³He superfluid phase transition depends on³He density, we calculate the consequences of this change in the solubility for its superfluid transition temperature. It is shown that for small fractions of³He, the transition temperature is enhanced mostly due to the enlargement of the up-spin Fermi sphere. In the opposite limit the transition temperature is enhanced as a result of the increased³He solubility.     

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T ₁, T ₂, and T ₁have been measured for ³He-⁴He solid mixtures at the exchange plateau region (~0.5K). The ³He concentrations X ₃of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm³/mole in hcp phase. The spectral density function J() for dipolar field fluctuations was determined in the low-frequency branch from T ₁measurements and in the high-frequency branch from conventional T ₁measurements. It was found that J() is given by J() = cJ()|_3–4 + (1–c)J()|_3–3, where J()|_3–4 is the spectral density function due to the ³He-⁴He tunneling motions, and J()|_3–3 is that due to the ³He-³He tunneling motions. Using the Torrey theory, the correlation frequency of the ³He-⁴He tunneling motions was evaluated from T ₁data, and was found to be in good agreement with Landesman 's theory.Supported in part by the Japan Society for the Promotion of Science through a grant to Y.H.     

3He-3He quasiparticle interaction in3He-4He mixtures under pressure

Based on our recent phase separation curve of³He-⁴He solution at elevated pressures, we propose new³He-³He quasiparticle interaction potentials, which reproduce the existing experimental results pretty well except for³He effective mass under pressure.     

3He-3He and 4He-4He Cross Sections in Matter at Low Temperature

The Galitskii-Migdal-Feynman (GMF) formalism is applied to liquid ³He and (for the first time) to liquid ⁴He. The effective total, diffusion and viscosity cross sections, as well as the effective scattering length and the effective range, are calculated. For liquid ³He, it is found that S-wave scattering dominates for wave number k<0.5 Å^?1. At the Fermi momentum k _F, the effective partial cross section σ _? (and thus the total cross section σ _T) has a singularity (virtual state). This singularity may be interpreted as a signature of superfluidity or a quasi-bound state. For k>2 Å^?1, the effective total cross section is nearly constant. On the other hand, it is found in liquid ⁴He that S-wave scattering dominates for k<0.3 Å^?1, and a peak exists in σ _T arising from a peak in the effective D-wave cross section. This resonance corresponds to a quasi-bound state trapped by the ?=2 centrifugal barrier. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the matter cross section at low temperatures. This effect is absent in the ³He gas. It is, therefore, a purely many-body effect in liquid ³He. With increasing energies, the matter results approach the vacuum results. This indicates that the high-energy behavior is dominated by the self-energy contribution; the many-body effects can be neglected.     

3He-4He mixtures in aerogel

Superfluid density and heat capacity experiments on³He-⁴He mixtures in 98% porous aerogel show that in this system the coexistence boundary is detached from the superfluid transition line. The tricritical point is removed, and there is a superfluid phase on the³He rich side of the phase diagram. The presence of heat capacity peaks along the transition line down to a⁴He concentration of only 8% indicates the 3-dimensional nature of this transition.This work is supported by NSF under grants DMR-9008461 and DMR-9311918.     

Adiabatic Fountain Resonance for 4He and 3He-4He Mixtures

We report an analysis of a superfluid Helmholtz resonance in the case of helium confined in a superleak. The resonance of the superfluid is achieved under nearly adiabatic conditions. Equations are derived for the resonance frequency, the temperature oscillations of the superleak and the phase relation of this signal relative to an ac heat input. The resonance frequency yields the superfluid fraction of the confined helium. Data are analyzed as function of frequency and temperature and yield parameters such as the dissipation and thermal conductivity which determine the resonance line shape. Estimates are made of the thermodynamic parameters in the resonance equation by using derivatives along the pressure-temperature-concentration lambda surface. These parameters are compared with results from the analysis of the resonance.     

Bound states of3He in3He-4He mixture films

³He atoms dissolved in super fluid⁴He may form aimers (³He)₂ in twodimensional (2D) geometries. We study dimer formation in films of dilute³He-⁴He mixture. After designing a schematic³He-⁴He interaction potential we calculate the dimer binding energy for various substrates. It is shown that³He impurity states localized near the substrate give rise to the largest magnitudes of the binding energies.Unité de Recherche des Universités Paris XI et Paris VI associée au CNRS.     

The dielectric formalism for3He-4He mixtures

The microscopic theory of³He-⁴He mixtures with a Bose condensate is formulated in terms of the dielectric formalism. By expressing all correlation functions in terms of proper, irreducible contributions, one sets the stage for approximate calculations that will be consistent with various exact sum rules and Ward identities, just as in the case of pure⁴He. The present analysis includes a symmetry-breaking term that allows us to deal with the continuity equations properly, and is valid at finite temperature. As a specific application, we express the normal fluid density _N in terms of the static⁴He current-current correlation function. We also give the first formal proof that in the presence of a moving condensate, the³He atoms make no direct contribution to the superfluid flow.     

Compression of3He by refluxing4He: HEVAC effects in3He-4He mixtures

The effect of a refluxing ⁴ He gas facing a Rollin film on the concentration distribution of ³ He atoms is described. In some situations, a large concentration enhancement of the colder part can result. Possible applications are briefly discussed.Unité de recherche de l'Ecole Normale Supérieure et de l'Université Pierre et Marie Curie, associé au CNRS (URA 18).     

Sound attenuation and3He-3He interaction in3He-4He liquid mixtures at saturated vapor pressure

The interaction potential between³He quasiparticles in³He-⁴He liquid mixtures is determined from the sound attenuation at saturated vapor pressure. Sound attenuation was measured in mixtures with³He mole fraction ranging from 0.0289 to 0.0573. The superfluid transition temperature of³He in mixtures and other properties were then estimated from the deduced interaction potential.     

Specific Heat Measurements of 3He in 3He-4He Mixture Films

Preliminary data for the heat capacity of ³ He in ³ He- ⁴ He mixture films on a Nuclepore substrate are reported over the temperature range 90T165 mK, for ³ He coverages between 0.05 and 1.7 bulk-density atomic layers, and a ⁴ He film thickness of 4.33 bulk-density atomic layers. In this two-dimensional Fermi liquid system, a step structure appears in the specific heat as a function of ³ He coverage, similar to the step previously observed in the magnetization.     

The Two-Dimensional World of 3He in 3He-4He Mixture Films

For thin films of ⁴ He at low temperatures the addition of sub-monolayer numbers of ³ He atoms results in the ³ He residing in a ground state at the free surface of the ⁴ He film. For low ³ He coverage the ³ He are a nearly ideal two-dimensional Fermi system. With increasing numbers of ³ He atoms the interactions among the ³ He increase. The results from a number of experiments that reveal the remarkable properties of this rich, interacting, two-dimensional ³ He system are described. These results include the magnetization, the energetics of the ³ He atoms in quantum states, the diffusion of the ³ He along the ⁴ He film, and the ³ He effective mass. The techniques employed include NMR, specific heat, quartz crystal microbalance and third sound. A clearer picture of the properties of the ³ He is now emerging, and preliminary numbers for the ³ He coverage dependence of the Fermi Liquid parameters are presented. Prospects for the observation of superfluidity of the ³ He in this system are discussed.     

The spin diffusion coefficient of3He in3He-4He solutions

The transport properties of³He in³He-⁴He solutions with molar concentrations of 5, 9, 14, and 24% have been studied for 0.9 KT2.5 K. The spin diffusion coefficientD _s and the longitudinal relaxation timeT ₁ were measured by the spin-echo method for temperatures both above and below the solution lambda temperatureT . The spin-echo method measures the diffusion coefficient for magnetizationD _s, which differs from the usual diffusion coefficient for particlesD belowT .D _s depends on the³He-³He scattering cross section _FF and the³He-roton/phonon cross section _FB, whileD depends only on _FB. The distinction betweenD _s andD is elaborated in terms of a simple mutual-friction model for diffusion. The two scattering mechanisms are clearly evident in the behavior ofD _s as a function of concentrationx and temperature. The contribution due to the³He-³He scattering is inversely proportional tox, indicating that the³He can be treated in first approximation as a classical gas (the Pomeranchuk model). The predictions of various theoretical models are compared with the results, where possible, but most of the previous theoretical work is not applicable to the concentration range and temperatures of these measurements.Supported in part by the National Science Foundation and the U.S. Office of Naval Research.     

Pulsed Nonlinear Sound in Superfluid 4He and 4He-3He Mixtures

Sound modes in ⁴ He and ⁴ He- ³ He mixtures which arise out of the two-fluid equations are made up up a vector convective flow and scalar temperature changes. A method for modeling nonlinear pulses of sound with geometric approximations to the vector and scalar components has recently been applied towards understanding nonlinear second sound near the lambda point. ⁶ The same method may be used, in general, for modeling linear and nonlinear sounds in Helium II. We demonstrate with a model for nonlinear second sound pulses in ³ He- ⁴ He mixtures and compare the results to experimental observations.     

Structure Factors of 3He-4He Mixtures

We briefly summarize the present understanding of the dynamic structure factors of liquid ³He-⁴He mixtures in the phonon-maxon-roton region and then present a new calculation using the memory function formalism. Results agree well with experimental data.     

Density of dilute 3He-4He solutions

The number density of dilute ³He-⁴He solutions under saturated vapor pressure is calculated within the framework of quantum hydrodynamics. For temperatures T small compared to the ³He Fermi temperature T _F, results are given for ³He concentrations large enough to manifest ³He quasiparticle interactions. The nondegenerate regime (TT _F) is also considered in the limit of small ³He concentration. Relevance to experimental determination of quasiparticle energies and interactions is emphasized.Supported by the National Science Foundation under Grant No. GP-40831.     

3He Transverse Excited State Occupation in Thin 3He-4He Films

The discovery that ³ He was occupying transverse excited states at submonolayer coverages in ³ He-⁴ He mixture films on a Nuclepore substrate, was a surprise. In this note we discuss the relationship between theory and experiment in attempting to understand the physics of this behavior. We first discuss various single-atom-limit calculations of the level spacing between the ground-state and first excited state. We then introduce a free, quasi-particle picture for analyzing experimental magnetization step data and compare those results with the single-atom-limit calculations. The experiments clearly show excited state occupation at submonolayer coverages in contradistinction with the calculations. We then briefly discuss a microscopic, semi-phenomenological theory which, in agreement with experiment, yields ³ He occupation of the first excited state at submonolayer coverages. The mechanism is a model ³ He-³ He effective interaction due to one ripplon exchange. This effective interaction is density dependent and very long ranged. It strongly modifies the small-k properties of the ³ He self-energy and, in particular, causes the ground-state to first excited state level spacing to decrease with increasing ³ He areal density.     

A combined 3He-4He dilution refrigerator

A refrigerator capable of operating both in evaporation and dilution modes is described. The refrigerator provides preliminary cooling of investigated samples down to a starting temperature of about 0.3 K and permits the location of samples directly in the mixing chamber as well as their replacement at any stage of operation.The replacement of samples lasts about 20 min. The cooling time for a sample from room temperature down to 15 mK is about 3 h. The minimal temperature is 10 mK, and the ³He circulation rate is about 5 × 10^?4mols^?1.     

Liquid-Vapor Coexistence in Two-Dimensional 3He-4He Mixtures

We present results from an ongoing study of the Liquid (L)-Vapor (V) coexistence boundary for single layer mixtures of ³ He and 4He adsorbed on two layers of H ₂ plating graphite. We are studying mixtures with ³ He molar fractions, x, of approximately 0.05, 0.1, 0.35, and 0.5, which we compare with previously published data for the pure isotopes. For the concentrations under study, we have approximate determinations of the L- V critical temperatures and of the low temperature density of the condensed phase.