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.     

Phonon dispersion in He II at long wavelengths and low temperatures

Phonon dispersion in liquid He II at long wavelengths and low temperatures is calculated using a generalized polarization potential approach and shown to yield results in good agreement with both superthermal phonon propagation and neutron scattering experiments at pressures up to 24 bar. It is shown that the long-wavelength dispersion relation is of the form _q =s ₀ q(1+₂ q ²+₃ q ³+...) suggested by Feenberg and by Kemoklidze and Pitaevskii, but that the validity of such an expansion is restricted to wave vectorsq0.1Å ^–1. For larger values ofq, one can force a polynomial fit, containing only odd powers ofq, to the dispersion curve and other parameters of interest, but the number of terms which must be kept is so large as to render such an approach unwieldy.Work supported in part by the National Science Foundation Grant NSF DMR72-03026.     

Pressure dependence of elementary excitations in3He

The elementary excitation spectrum and static structure function are calculated at several pressures, using the polarization potential theory of Aldrich and Pines. The elementary excitation spectrum is found to be in excellent agreement with the recent measurements of Schermet al. The relative contribution of single-pair, multipair, and collective excitations to the static structure function is also calculated; the latter is found to be in good agreement with neutron and X-ray scattering measurements.     

NMR in superfluid3He at very low temperatures

Just a few years ago it was generally believed that the NMR properties of superfluid³He far below T_c would not be qualitatively different from those found at higher temperatures. Surprisingly, the strange enhancement of relaxation processes at around 0.4 T_c named catastrophic relaxation, was then found. Recently an extremely long lived induction signal with new dynamical properties was discovered in the region of 100 K. Some of the newly discovered properties can be partly explained, although there are still many unsolved problems. The main aim of this article is to raise new questions for future investigations at the lowest temperatures presently possible.     

Adiabatic expansion of3He in4He at very low temperatures

In this paper the results of the investigation of a one-shot cooling technique, called adiabatic expansion of³He in superfluid⁴He, are reported. The expansion cooler basically consists of an expansion cell and a⁴He reservoir connected by a superleak. In the expansion cell nearly pure³He is gradually diluted to a saturated mixture by the injection of superfluid⁴He from the⁴He reservoir. The expansion of the³He produces cooling, which, in the ideal (isentropic) case can lower the temperature by a factor 4.56. In practice, the performance of this cooling method is limited by irreversibilities and heat leaks. In this paper several irreversible processes such as heat conduction, viscous effects, and supercritical⁴He flow, have been analyzed. Furthermore the effect of³He in a sinter layer in the expansion cell is discussed. The experiments have shown that the fountain pressure in the⁴ He reservoir is very suitable for driving the⁴He in and out of the expansion cell. During an expansion/extraction the⁴He chemical potential difference across the superleak is zero. The realised cooling factor, defined as the ratio of the initial temperature and the final temperature, is about 3.5 for initial temperatures between 20 mK to 190 mK. This value is lower than the ideal factor of 4.56 that can be obtained for isentropic expansions. The discrepancy is mainly due to the relatively large heat leak. The lowest temperature obtained in this investigation was 5.7 mK. The analyses have revealed no fundamental limitations for obtaining lower temperatures.     

Heat flow through superfluid4He at low temperatures

The heat conductivity of superfluid⁴He has been measured as a function of temperature between 0.1 and 0.7 K at different pressures between zero and 24 atm. The experiment gives direct evidence that the heat conductivity varies asT ³ at very low temperatures.     

The nuclear magnetic susceptibility of dilute solutions of3He in4He at low temperatures

A theory of the nuclear magnetic susceptibility of dilute solutions of ³ He in ⁴ He at low temperatures is presented. It is shown that ^–1 is a linear function of the corresponding inverse free fermion magnetic susceptibility. It is also shown that the experimental Curie constant differs from the theoretical one by an amount which is of the order of the ³ He concentration. It follows that the existing experimental results are not adequate for the calculation of the Fermi liquid magnetic susceptibility enhancement factor.     

Turbulence generated by vibrating wire resonators in superfluid 4He at low temperatures

No Heading We have measured responses of vibrating wire resonators in superfluid ⁴He at millikelvin temperatures. We find evidence for turbulence generation above a critical velocity on the order of a few cm/s. At the critical velocity for the onset of turbulence, the resonator velocity abruptly decreases and shows hysteretic behavior. Surprisingly we find that the resonant frequencies of the resonators increase in the turbulent regime. We also find that the critical velocity may be reduced by the presence of turbulence generated by a neighboring vibrating wire resonator, allowing the detection of existing turbulence in the low temperature regime.PACS numbers: 67.40 Vs, 67.40 Pm     

The molar polarizability of3He at low temperatures and its density dependence

Simultaneous capacitance and PVT measurements on liquid and gaseous³He under a variety of temperature and pressure conditions indicate that the molar polarizability of the classical Clausius-Mossotti equation can best be expressed as:(mole/cm³)=0.123413–0.002376 (g/cm³). Some significant, but often neglected, experimental corrections are discussed.Work performed under the auspices of the U.S. Atomic Energy Commission.     

Theory of the osmotic pressure of dilute mixtures of3He in liquid4He at low temperatures

The osmotic pressure of dilute mixtures of³He in liquid⁴He is calculated and compared with experiment. One parameter, which is a measure of the difference between the mean potential energy of³He atoms and⁴He atoms in the mixture is determined from the experiments, and good agreement is obtained with the measured values of as a function of concentration and temperature. It is shown that the osmotic pressure does not provide any accurate information about the effective interaction between³He atoms. A comparison with earlier calculations of the osmotic pressure and of the³He chemical potential is made.Work performed under the auspices of U.S. Atomic Energy Commission.     

An equilibrium theory of the dilute solutions of3He in superfluid4He at very low temperatures

An equilibrium theory of the dilute solutions of ³ He in superfluid ⁴ He is derived systematically. The theory is based on a model which (a) goes beyond the parabolic Landau-Pomeranchuk approximation for the ³ He quasiparticle energy by taking into account the fourth-order term in the momentum expansion of this quantity, (b) disregards contributions to the ³ He quasiparticle effective interaction whose order in the momentum is higher than two, and (c) allows the effective interaction to be nonlocal. The simplicity of the model enables the development of a unified parametrization of the various equilibrium properties of the solutions. The expressions obtained for these properties are both easy to apply and highly accurate over a wide temperature range spanning from T=0 to temperatures of the order of the ³ He quasiparticle degeneracy temperature. It is shown that the parameters appearing in the expression for the ³ He quasiparticle effective interaction at fixed ⁴ He number density are replaced in the fixed-pressure, low-temperature expansions of the equilibrium properties by other parameters whose appearance in the theory seems to be due to the renormalization of this interaction by the interactions between the ³ He quasiparticles and the virtual fluctuations of the ⁴ He number density Finally, a comparison is made between theory and experiment. Three quantities are considered in detail : the ³ He osmotic pressure and the ³ He quasiparticle inertial and specific heat effective masses. The analysis of the experimental data makes it possible to determine the parameters associated with the effective interaction at several pressures. It is found that the theory is, in general, in a very good accord with the experimental situation and that, within its framework, the experimental values of the osmotic pressure and the two effective masses are indeed consistent with one another.     

Nuclear spin-lattice relaxation in bulk and divided samples of solid 3He at low temperatures

At temperatures in the region of 0.1 K, the nuclear spin-lattice relaxation in solid ³ He exhibits some unusual features which suggest that the mechanism might be diffusion in the spin system to surfaces within the crystal at which relaxation takes place rapidly. The results of a number of measurements of the diffusion of magnetization in solid ³ He specimens, including the influence of magnetic field, are presented. Relaxation time measurements on specimens formed in sintered glass give results consistent with the diffusion hypothesis, and for such specimens we can calculate the relaxation time and its magnetic field dependence with surprising accuracy. Similar calculations applied to bulk specimens, however, fail to account for the observations. The evidence suggests that the relaxation process in bulk specimens is not controlled by diffusion. An empirical formula is proposed which fits the relaxation data in bulk specimens over a range of parameters, although no physical process with the required properties can be identified.Work supported by research grants from the Science Research Council, who also provided financial support for RPG and JPS, and by Queen's College, Oxford, through a Junior Research Fellowship held by WST.     

Spin relaxation of 3He to paramagnetic centers in surfaces at very low temperatures

The memory function formalism is used to derive a generalized golden rule expression for the spin-lattice relaxation rate 1/T ₁ for ³He to paramagnetic centers embedded in or residing on surfaces in contact with the ³He. This expression is applied to several simple models of relaxation to paramagnetic spins which do not interact among themselves, both for ³He in the Fermi-liquid phase and for a solid surface layer of ³He on the substrate. The magnitude of 1/T ₁ is calculated for each case as well as the temperature and magnetic field dependence. Finally, the relationship between the spin-lattice relaxation rate and the Kapitza conductance across surfaces via magnetic interactions is determined.Supported by National Science Foundation grant number DMR77-18329.Research performed under the auspices of ERDA.     

Thermal contact between cerium magnesium nitrate and liquid3He at very low temperatures

A new experimental arrangement has been used to measure the times for equilibrium between cerium magnesium nitrate (CMN) and liquid³He. Measurements have been made on a single crystal of CMN from temperatures of 5.5–15 mK and on a powdered specimen from temperatures of 2.5–35 mK. The thermal resistance deduced from the single-crystal data is proportional toT ^–2. The thermal resistance obtained from the powder data may be separated into three contributions: a resistance which is proportional toT ^–2in series with a parallel combination of a phonon resistance (with resistivity _P =3×10 ^–4 T ^–3sec·cm²·K ⁴ ·erg ^–1 ) and a magnetic resistance (with resistivity _M =9×10 ² T sec·cm ² ·erg ^–1 in zero applied magnetic field). A reduction in the magnetic resistance was observed when the powdered CMN was placed in a magnetic field, the magnitude of this reduction being comparable to that expected from a Redfield-like theory. TheT ^–2resistance is discussed in terms of two-dimensional energy transport within the CMN. The 17-Hz susceptibility of the powdered CMN was measured in magnetic fields of 0, 18.9, 30.2, and 37.8 G. The magnetic temperatureT* (H=37.8 G) was found to differ by +0.5 mK from the magnetic temperature in zero field whenT* (H=0)=3 mK.Work supported by the U.S. Atomic Energy Commission under Contract No. AT(04-3)-34, P.A.143.Supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under AFOSR Contract No. AFOSR/F-44620-72-C-0017.     

3He低温热力学性质实验数据综述

全面收集整理了3He在相变曲线、液体区、气体区和临界区低温热力学性质的实验数据和关联式,为建立3He覆盖不同区间的状态方程以及开发3He低温物性数据程序奠定了基础,同时也可供3He低温物性的研究人员参考.     

The velocities of first and second sound in dilute solutions of3He in superfluid4He at very low temperatures

A unified theory of first and second sound in dilute solutions of ³ He in superfluid ⁴ He at very low temperatures is presented. The theory is based on the detailed semimicroscopic model for the ³ He quasiparticle excitations described by Disatnik and Brucker a few years ago. In contrast with Khalatnikov's macroscopic theory, the application of this model enables the derivation of relatively simple expressions for the sound velocities in which no omissions of terms representing contributions due to the thermal expansion are made. The sound velocities are given in the final expressions in terms of various parameters of the ³ He quasiparticle spectrum and effective interaction. These expressions are both highly accurate and easy to use over a wide temperature regime spanning from the quantum limit to temperatures of the order of the ³ He quasiparticle degeneracy temperature. The actual application of the theory to measurements of the sound velocities is described in detail. Numerical values or estimates for various characteristic parameters of the ³ He quasiparticle system, including in particular the ³ He quasiparticle effective mass, are obtained from the comparison between the theory and the experiment. The example of the second sound velocity is used to illustrate a procedure for analyzing data from very low-temperature measurements of the equilibrium properties of the solutions, which is expected to produce meaningful information regarding the parameters of the basic model. In practice, the theory is found to be in a very good accord with the measurements of the sound velocities. The result obtained for the zero concentration limit of the ³ He quasiparticle effective mass (m ₀ =2.19m ₃ ) is somewhat lower than the empirical estimates reported in the past. On the other hand, this result is in very good agreement with variational calculations based on the detailed microscopic theory of the solutions. A discussion of this and other results obtained from the comparison between theory and experiment is included.Work supported in part by the United States-Israel Binational Science Foundation.Killed in action, 16 October 1973.     

Heat release,refrigeration and thermometry in3He-4He solutions at very low temperatures

We report on our measurements performed in liquid³He-⁴He solutions in the microkelvin temperature range at the Bayreuth nuclear demagnetization cryostat. One aspect of our work is the application of the vibrating wire technique for thermometry in the ballistic regime of phase-separated solutions. The establishment of reliable thermometry along with the particular design of our experimental cells enables us to study two main limitations on the minimum temperature of about 100K achieved in³He-⁴He solutions so far: the thermal resistance between the liquid and the cell, and the origins of the heat leaks.     

3He impurity excitations in solid4He

The problem of³He mobility in dilute³He-⁴He solid mixtures has been treated both theoretically and experimentally. The Hamiltonian of the system can be reduced to the Hamiltonian of strongly interacting impurity quasiparticles corresponding to some time-averaged states. The experiments carried out on solid mixtures with³He concentration 2.17%, 0.75%, 0.25%, or 0.092% by the NMR method show that at sufficiently low (T<1.2 K) temperatures the diffusion coefficient becomes temperature independent and inversely proportional to³He concentration. These results substantiate qualitative conclusions of the theory. Analysis of the experimental data makes it possible to take into account the phonon part of the³He diffusion coefficient and to obtain, up to a constant, the³He-⁴He exchange energyJ10^–7 K. All the facts mentioned above testify to the substantially quantum nature of the³He diffusion process in dilute³He-⁴He mixtures.     

Measurements of the viscosity and the slip length on liquid3He at low temperatures

Measurements of the viscosity and the slip length are reported for both the normal liquid and superfluid³He within the slip approximation. We used the hollow torsional oscillator. For the normal liquid³He the slip length is shorter than the theoretical expectation and there is no anomaly near the superfluid transition, but the viscosity shows the anomalous deviation from the Fermi liquid behavior which is thought to be attributed to the superfluid fluctuation. For the superfluid³He, the temperature dependence of the slip length agrees with the theory qualitatively and the viscosity agrees well with the theory quantitatively as far as the slip approximation is valid.     

Measurement of the magnetic susceptibility of normal fluid3He at very low temperatures

We present pulsed NMR measurements of the low temperature (0.003 K) magnetic susceptibility of normal liquid ³ He as a function of pressure. Our results agree well with the extrapolation from 0.035 K of the data of Ramm et al. We calculate new values for the Fermi liquid parameter F ₀ ^a using the heat capacity data of Greywall.