The Effective Mass and Binding Energy of 4He in 3He in the Fermi Liquid Region

We have measured the solubility of ⁴ He in liquid ³ He down to about 40 mK and at pressures from zero up to 24 atm. The solubility was obtained from the thickness of the superfluid film in contact with unsaturated solutions of ⁴ He in ³ He as a function of temperature. By fitting the solubility data to Fermi liquid theory, we obtained the parameters m ₄ ^* and as a function of pressure. Here, m ₄ ^* is the effective mass of ⁴ He in liquid ³ He and the difference in binding energy between ⁴ He in pure ⁴ He and ⁴ He in liquid ³He. This difference has a minimum near 10 atm. The average of the results for m ₄ ^* , at different pressures, is (1.3 ± 0.2)m ₄. This agrees with the many body calculations of de Saavedra et al., and with the Stokes hydrodynamic mass using the partial volume of ⁴ He in ³ He, v ₄ ^* . The partial volume was obtained by taking the derivative of with respect to pressure.     

Specific Heat of the Surface Layers on the Amorphous Substrate in Solid and Liquid 3He

We have observed an excess heat capacity in liquid and bcc solid ³He at low temperatures. The heat capacity in the normal fluid is found to be the sum of the heat capacity of bulk normal fluid and a temperature-independent heat capacity C due to amorphous solid layers on the silver sinter surface, where C=7.3±6.8 JK^–1m^–2 corresponds to 1.6±0.6 amorphous solid layers. The heat capacity for bcc solid ³He is the sum of the heat capacity originating from the multiple-exchange interaction and a temperature independent heat capacity. The excess heat capacity C=12.1±3.1 JK^–1m^–2 for bcc solid corresponds to 1.9±0.3 amorphous solid layers. Our result indicates that the amorphous solid layers on an amorphous substrate yield a universal C in unit area throughout liquid, solid and adsorbed ³He.     

Temperature Dependence of Spin-Density Fluctuations in Liquid 3He

The dynamic structure factor S(Q,E) in normal liquid ³ He, which contains information on both density and spin-density fluctuations, has been measured by inelastic neutron scattering both well below and close to the Fermi temperature. The data extend to smaller wave vectors and energies than covered in earlier experiments, and give a much better determination of the line shape of the spin-density response. Together with the temperature dependence, this allows to discriminate between different theoretical models for the nuclear spin fluctuations, and provides information on the quasiparticle dispersion and effective mass.     

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

Additional data from our on-going experiments 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 1.4 bulk-density atomic lagers, on a ⁴ He film of thickness 4.33 bulk-density atomic lagers. This is a two-dimensional Fermi liquid system, in which we can change the ³ He coverage and thus tune the Fermi temperature.     

Specific Heat Anomaly in bcc Solid 3He

We have studied the origin of the excess specific heat (anomaly) above 10 mK in bcc solid ³ He near melting pressure. We applied strong magnetic fields to the sample to see whether the anomaly arises from spin polarons due to vacancies. The specific heat is the same before and after applying magnetic fields of 10-12 T. This result possibly indicates that the anomaly arises from the origin different from vacancies. Next, in order to check whether the anomaly comes from the surface magnetism, we measured the specific heat by coating the surface of sintered silver with three layers and two layers of ⁴ He. The results showed that unexpected large heat capacity due to phase separation of solid ³ He-⁴ He surpassed and smeared the original specific heat anomaly. We are investigating the origin of the anomaly further.     

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.     

Effective Interaction and Superfluidity in Two-dimensional Liquid 3He

Effective interaction of two-dimensional liquid ³He is studied with the (selfconsistent) reaction matrix theory. The theory is found to be valid in the dilute region, _2D 0.02 Å^–2, where _2D is the areal density. In the region, the attractive interaction in the p-wave channel is the most dominant, and the system is expected to undergo a transition to a p-wave superfluid state, except for the dilue limit. The transition temperature is estimated to be of the order of mK in the clean limit. In the dilute limit, _2D 0.002 Å^–2, an s-wave superfluid state becomes more stable than a p-wave one, but the transition temperature is found to be of the order of 0.1 mK at most. Furthermore, in the reaction matrix theory, it is found that a d-wave superfluid state becomes more stable than a p-wave one at _2D 0.035 Å^–2.     

Physical Mechanisms for Effective Mass Enhancement in 3He

We use structural information from simulations and from variational ground state calculations for calculating the effective mass of ³He at zero temperature. It is found that the relatively large effective mass is due to a combination of several physical effects: Density fluctuations cause an effective mass enhancement due to predominantly hydrodynamic backflow. This effect is, around the Fermi momentum, a smooth function of the single particle wave number; its magnitude is consistent with the effective mass of ⁴He impurities in ³He. Spin-fluctuations, on the other hand, cause a pronounced peak of the effective mass around the Fermi wave number. We also find, consistent with earlier work, an instability of the single particle spectrum at about 2.5 k _F, this is due to the coupling to density fluctuations in the maxon region.     

Specific Heat Anomaly in Solid 3He due to Vacancy Waves

We observed the excess specific heat (anomaly) other than nuclear origins above 10 mK in bcc solid ³ He of 24.21 cm ³/mole. We checked whether it arises from spin polarons due to vacancies out of equilibrium by applying a strong magnetic field, in which vacancies should diffuse and vanish due to high polarization. The specific heat is the same before and after applying a magnetic field of 10 T. This fact indicates that vacancies did not vanish even in a strong field or the anomaly arises from the origin different from vacancies.     

Pressure Dependence of Excitations of Liquid 4He

No Heading Confinement of liquid ⁴He in porous glasses increases its solidification pressure and suppresses the superfluid transition temperature T. It has been reported that a sufficiently high degree of confinement suppresses T to zero at high pressure, signifying a quantum phase transition. We evaluate the behaviour of the excitation spectrum at wave vectors Q < 2.3 Å^–1 at pressures well above 25 bar by calculating the dynamic structure factor, S(Q, E), using the theory of hybridization of one- and two-particle excitations. The aim is to explore whether well-defined excitations exist at high pressures, and whether there is some critical pressure at which they disappear. We find that as the pressure increases, the one-particle excitation energy is well-defined if its energy lies below the two-roton energy, and ceases to exist as a well-defined excitation if its energy lies above the two-roton energy. We relate these findings to potential inelastic neutron scattering measurements.     

Effective Heat Conductivity and Relaxation Processes in Superfluid Mixtures of 3He-4He

The effective thermal conductivity coefficient'ceff in superfluid ³He-⁴He mixtures with concentration of 9.8% ³He has been studied experimentally between 100 and 500 mK, where the main contribution to the kinetic processes is made only by phonons and ³He impurity excitations. In this case the effective thermal conductivity is a combination of diffusivity, thermal conductivity and thermal diffusion. The κ _eff value was found from stationary measurements of the temperature gradients caused by the thermal flow and from the temperature relaxation kinetics. Both the methods provide consistent resugts which also agree with those on effective thermal conductivity calculated in terms of the kinetic theory of phonon-impuriton system.     

Specific heat of amorphous3He films and confined liquid3He

We have measured the heat capacities of³He films and liquid³He in porous Vycor glass at 10 to 600 mK. With increasing the film thickness from 1 to 3 atomic layers, the specific heat evolves gradually from that typical to solid to that of liquid³He. At about 2 atomic layers, however, its low-temperature part is nearly temperature-independent; we interpret this as a result of gradual freezing of spins in an amorphous solid³He film with decreasing the temperature. The contribution of liquid³He in the center of the Vycor pores can be described as the specific heat of bulk liquid³He at corresponding pressures in the range 0 to 28 bar. The thickness of amorphous solid on the pore walls increases with external pressure roughly linearly. Preplating the walls with⁴He allows to determine the positions of³He atoms contributing to the surface specific heat at 10 to 50 mK. In addition, the contribution from the specific heat of³ He -⁴He mixing at 100 to 600 mK is discussed as a function of pressure and amount of⁴He.0n leave from ISSP Acad. Sci. of Russia, Chernogolovka, Russia     

Polarization potentials and elementary excitations in liquid 3He

The results of a generalized polarization potential calculation of the particle and spin density fluctuation excitation spectra of ³He in the low-temperature limit are described and compared with the recent neutron scattering experiments of Sköld and Pelizzari. The extent to which the range and shape of the effective repulsive interaction between particles of parallel and antiparallel spin may differ is explored, and it is shown that changes of only a few percent have experimentally observable consequences. Good agreement with experiment is found for the dispersion of zero sound; the wave vector dependence of the enhancement of the low-frequency part of the spin density fluctuation excitations, and the coherent and incoherent static structure factors, are examined and compared with experiment for identical and slightly different repulsive parallel and antiparallel spin interactions. Simple qualitative arguments are presented which suggest that for wave vectors 0.4q 1.2»^-1, the zero-sound mode will be little affected as the temperature is raised to 1.2K, while the low-frequency spin fluctuation excitation spectrum undergoes considerable broadening, again in accord with experiment. Changes in the zero-sound dispersion relation with pressure are shown to be sensitive to the range of the repulsive part of the effective quasiparticle interaction, and it is suggested that experiments at 20 atm will help determine the physical origin of the comparatively large range (3 ») required to explain the experimental results for ³He at SVP.Sherman Fairchild Distinguished Scholar at Caltech during the academic year 1977–78.Work supported at the University of Illinois by NSF Grants DMR 75-22241 and DMR 76-24011.     

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.     

‘Heat from Above’ Heat Capacity Measurements in Liquid 4He

We have made heat capacity measurements of superfluid ⁴He at temperatures very close to the lambda point, T _λ, in a constant heat flux, Q, when the helium sample is heated from above. In this configuration the helium enters a self-organized (SOC) heat transport state at a temperature T _soc(Q), which for Q≥100 nW/cm² lies below T _λ. At low Q we observe little or no deviation from the Q=0 heat capacity up to T _SOC(Q); beyond this temperature the heat capacity appears to be sharply depressed, deviating dramatically from its bulk behaviour. This marks the formation and propagation of a SOC/superfluid two phase state, which we confirm with a simple model. The excellent agreement between data and model serves as an independent confirmation, of the existence of the SOC state. As Q is increased (up to 6 µW/cm²) we observe a Q dependent depression in the heat capacity that occurs just below T _SOC(Q), when the entire sample is still superfluid, This is due to the emergence of a large thermal resistance in the sample, which we have measured and used to model the observed heat capacity depression. Our measurements of the superfluid thermal resistivity are a factor of ten larger than previous measurements by Baddar et al.     

Heat flow in superfluid 3He

The thermal resistance in both superfluid phases of ³He has been measured at 20.0 and 29.6 bar in zero magnetic field. Heat conduction in ³He-B is shown to be primarily hydrodynamic, and a regime of reproducible heat flow behavior in the A phase is reported. The viscosity of each phase as a function of temperature is calculated using an equation of the two-fluid model, and critical velocity effects are discussed.Work supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34 P.A. 143.     

Recent High Resolution Measurements of the Specific Heat and Isothermal Compressibility Near the 3He Liquid-Gas Critical Point

Measurements of the specific heat at constant volume and isothermal compressibility have been made along a near critical isochore in the liquid-gas critical region of ³ He. The critical density was determined to within 0.1% from pressure-density measurements along a near critical isotherm in the single phase region. The specific heat was measured in the gravity affected region in the reduced temperature range |T/T _c – 1| 3 × 10^–4 using a slow cooling drift technique. A new electrostriction technique was developed to measure the isothermal compressibility along isochores and isotherms near the critical point. Initial measurements that validate this new technique will also be presented.