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.     

Effect of 3He on Third Sound Attenuation in Thick 4He Films

We have performed measurements of third sound attenuation in thick films of superfluid ⁴He in the presence of small amounts of ³He. The attenuation due to ³He appears to depend linearly on the number density of ³He atoms in the film. We discuss the results in context of a recently proposed mechanism where the attenuation is caused by the interaction of the excitations in helium with the trapped vortices.     

Third sound in3He-4He mixture films

We report third-sound studies of³He-⁴He mixture films for 0.3T1.8 K carried out in two different experimental situations. In one experiment detailed measurements of the amplitude of both the temperature and thickness variation of the film were made for pure⁴He and the results for |T/d| are in good agreement with the predictions of Bergman. Mixture studies in this apparatus were made difficult due to the presence of capillary condensation. In spite of this a number of interesting results are reported. Subsequent measurements were made in a new apparatus where capillary condensation effects could be demonstrably avoided. Helium films of 5.7 layers of⁴He were studied as a function of added amounts of³He. BelowT0.7 K the third-sound measurements are consistent with model calculations based on a bilayer film. We conclude that for 0.3T0.6 K films of the type we have studied are isotopically layered in the van der Waals field provided by the substrate.     

A Model for Third Sound Attenuation in Thick 4He Films

Third sound attenuation in thick ⁴He films has been observed to be much greater than predictions based on known mechanisms. We propose a possible mechanism for this observed high attenuation. Pinned vortices, possibly created when the superfluid transition is traversed, undergo driven oscillations in the third sound wave flow field. The dissipation is caused by two related effects. The first is due to the mutual friction between the vortex cores and the normal component. The second, larger contribution, is due to the drag experienced by a vortex-induced surface dimple. Variations in vortex density explain quite naturally the observed lack of reproducibility in attenuation measurements. A vortex density on the order of 10¹⁷m^–2 is required to account for dissipation reported in several experiments. We discuss the temperature, frequency and thickness dependence of the dissipation. The proposed model is also applicable to a vortex contribution to fourth sound attenuation. If third sound attenuation is indeed a signature of a very dense array of pinned vorticity, then our conception of a homogeneous superfluid film needs considerable alteration.     

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.     

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

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

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.     

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.     

Evaporative Cooling of 3He-4He Mixture Films

Heat transport by saturated ³He-⁴He films has been studied at temperatures 50..350 mK and the bulk concentration of ³He ranging from 0.1 ppm to 5%. The cooling of the film, when locally heated above 160 mK, is mainly via 2D flow of surface ³He from colder area followed by evaporation of ³He. At certain heating power the 2D flow becomes a bottleneck, the heated spot runs out of ³He and its temperature abruptly increases. The critical power is nearly proportional to the surface density of ³He. For higher ³He concentrations another distinct step in temperature has been observed at a lower heating power. It is attributed to the existence of an excited ³He surface state whose population starts at ³He surface density of 3.5×10¹⁴ cm^–2. The second state is located about 1.2 K higher in energy than the ground state and provides an additional channel for the 2D flow of ³He.     

Sound attenuation in3He-4He liquid mixtures under pressure

The attenuation of sound was measured in³He-⁴He mixtures with³He concentrations ranging from 2.89 to 8.03% at pressures of 10 and 20 bar. The quasiparticle interaction potentials were then determined at each pressure by analyzing the sound attenuation data. The superfluid transition temperature of³He and other properties in the mixtures were then estimated from the interaction potentials.     

Sound and transport phenomena in spin-polarized3He-4He solutions

Transport phenomena in partially spin-polarized³He-⁴He solutions are investigated. The polarization causes considerable changes in kinetic coefficients and also gives rise to new dissipative processes, such as spin thermodiffusion and second viscosity. The transport coefficients are calculated for degenerate and nondegenerate³He-⁴He solutions. The absorption of first- and second-sound waves is studied. Second-sound propagation is affected by weak dipole interactions and its velocity depends significantly on the frequency.     

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.     

Heat Capacity Measurements of 3He-4He Mixture Films

We report heat capacity measurements from our on-going experiments on two-dimensional liquid ³He on superfluid ⁴He thin films absorbed on Nuclepore. The ³He coverage dependence of the heat capacity for 0.02–0.50 bulk-density layers of ³He with 3.10 bulk-density layers of ⁴He over the temperature range 40≤T≤200 mK is presented. We find the effective mass of ³He on 3.10 layers of ⁴He is greater than that on 4.33 layers of ⁴He, consistent with our previous magnetic susceptibility measurements.     

Sound propagation in 3He-4He mixtures near the superfluid transition

Measurements of the acoustic attenuation and dispersion in liquid ³He-⁴He mixtures near the superfluid transition T (x) are reported. The frequency range is /2gp=1–45 MHz and the ³He mole fraction X of the mixtures is 0.007, 0.05, 0.15, and 0.36. Comparisons are made with the measurements of Buchal and Pobell for similar mixtures obtained in the kHz region, and on the whole, the consistency between the two experiments is very satisfactory. An analysis is then performed using both the kHz and MHz data. In the normal phase, where the energy dissipation is caused by order parameter fluctuations having a lifetime _F , the attenuation data can all be scaled according to the expression = (T )f(_F. Here (T )^1+y, with y being a function of the mole fraction X and _F(T–T )^–x, with x increasing weakly with X. In the superfluid phase, we attempt a similar scaling representation, which is found to be fairly successful, but where x(T\s-T ) is roughly 15% larger than x(T>T ). In the superfluid phase we also analyze the attenuation data, assuming the additivity of relaxation and fluctuation-dissipation mechanism, and discuss the relaxation times so derived. In contrast to the attenuation, the dispersion data cannot be brought satisfactorily into a scaling representation. However, at T , we find U()-U(0)^y as predicted by Kawasaki, where y is in good agreement with the values from attenuation experiments.Supported by a grant from the National Science Foundation.     

Spectrum of Third Sound Cavity Modes on Superfluid 3He Films

We report theoretical calculations of the spectrum of third sound modes for a cylindrically symmetric film of superfluid ³He, and compare these results with experimental data for the mode frequencies and amplitude spectrum of surface waves of superfluid ³He films.     

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.     

Second Sound Measurements Near the Tricritical Point in 3He-4He Mixtures

In this paper we discuss a pulsed second sound experiment, aimed at determining accurately the critical exponent , and the predicted logarithmic correction to scaling, for the superfluid density along a tricritical path in the ³ He- ⁴ He phase diagram. We present an accurate estimate for the limits for closest approach to the tricritical point, as set by gravitationally induced sample inhomogeneities and finite size effects, and discuss some of the complications associated with measurements close to the tricritical point.     

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.     

Search for superfluidity of3He in3He-4He solution

We have tried to cool a³He-⁴He solution down to the microkelvin temperature region to search for a superfluid transition of the³He component in the solution. The contact surface area between the solution and a sintered powder has been increased enormously by the use of a fine platinum powder, to reduce the effect of the residual heat leak directly entering into the solution. Although the heat leak was found to be time dependent, the ultimate ratio of the heat leak to the surface area is about 0.046 pW/m², improved very much from those by the other groups. But the lowest temperature of the solution is still around 0.2 mK, and no evidence of the transition has been observed yet.