Fermion Monte Carlo calculations of liquid 3He

No Heading Methods and results for calculations of the ground state energy of the bulk system of ³He atoms are discussed. Results are encouraging: we believe that they demonstrate that our methods offer a solution of the fermion sign problem and the possibility of direct computation of many-fermion systems with no uncontrolled approximations. Although the method is still rather inefficient compared to variational or fixed-node methods, we have been able to obtain useful answers.PACS numbers: 67.55.–s, 02.70.Ss     

Heating effects with spin-polarized3He liquid

Model calculations of the temperature changes expected in rapid meltings of polarized solid³He (Castaing-Nozières decompressions) are presented. After a complete melt, the development of temperature with time shows a strong polarization dependence, contrary to the final temperature reached. The results of partial meltings could, in principle, yield accurate information about the entropy of solid³He.     

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.     

Vapor/liquid equilibrium calculations by constrained free-energy minimization

A method is presented for approximate vapor/liquid equilibrium calculations using an equation of state. The method reduces the number of variables in the free-energy minimization problem by the introduction of suitably chosen additional constraints. It is based on a representation of a multicomponent fluid as a mixture of a small number of weakly polydisperse components. The approximation method can be used to accelerate sequences of vapor/liquid equilibrium calculations, such as are encountered in many engineering applications [plant design, hydrocarbon (oil/gas) reservoir simulation]. In realistic cases computing time has been reduced by up to 65%.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

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.     

Hydrogen isotope and3He impurities in liquid4He

Recently Reynolds, Hayden and Hardy(J. Low Temp. Phys. 84,87 (1991)) analyzed atomic deuterium lifetimes in a cell with walls covered by a saturated⁴He film. They were able to determine the deuterium chemical potential in⁴He and also discussed the possibility of estimating its effective mass. These measurements inspired our attempt to understand the properties of hydrogen isotope impurities in liquid⁴He using the extended Jastrow-Feenberg theory based on the correlated wave function. We present results for hydrogen isotope chemical potentials in the bulk⁴He as a function of density. The accuracy of the method is tested by calculating the chemical potential of the³He impurity. We find a good agreement with existing measurements. We also calculate the effective masses of the hydrogen impurities. For deuterium we predict a value,m _eff=4m _D .     

Nuclear magnetic order in solid 3He

Over the past 20 years our understanding of cooperative magnetic phenomena in solid ³He has expanded greatly. Starting from the concept of atomic exchange, the author explains how early experiments led to the abandonment of the naive Heisenberg nearest neighbor antiferromagnetic Hamiltonian, in favor of a multiple exchange model. He then describes the detailed experimental picture of the spin-ordered phases which has developed over the past decade, and the successes and failures of the multiple exchange model to explain the experimental results. Today solid ³He is a powerful model magnetic system for extending our general understanding of magnetic order, and should continue to play an important role for many years to come.     

Exchange and magnetic order in HCP 3He and adsorbed 3He with triangular lattice

A Schrödinger equation is derived which allows an improvement in the wave function of a quantum crystal inside the tunneling duct for exchange. This equation is used to derive a simple estimate of the exchange rate accurate enough to be used to compare various exchange mechanisms (two-body, three-body cyclic, etc.). We find that the ³ He bulk hcp crystal and ³ He surface triangular crystals have their exchange dominated by three-body cyclic exchange. Therefore the dominant part of the spin Hamiltonian will be Heisenberg nearest neighbor ferromagnetic. This result explains the ferro-magnetic tendency observed in adsorbed ³ He films. A ferromagnetic transition in hcp ³ He at the lowest pressures is predicted at 0.05±0.01 mK, corresponding to a Curie-Weiss constant of 0.075 \+ -0.015 mK.     

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     

Pressure-volume-temperature relations in liquid and solid3He

Liquid and solid³He P-V-T relations were measured over 0.26–1.8 K with concentration on regions near the melting curve. The method used a cell whose volume was varied with diaphragms, the positions of which determined the volume and pressure. The molar volumes of liquidV _lm and solidV _sm along the melting curve were consistent with the directly measured volume change on melting V _m . Below 1 K,V _lm , V_sm, and V _m were greater than previous results. Along the melting curve, the compressibility of the solid became greater than the compressibility of the liquid atT<1.2 K, the difference rising to 12% at 0.32 K. The thermal expansion of the solid became negative below 0.30–0.35 K. The melting curve minimum was measured at 28.932±0.003 atm and 0.319±0.003 K. Starting with the minimum, the melting curve was calculated to 0.02 K, where it should be useful in thermometry. A set of self-consistent data is presented.Work performed under the auspices of the U.S. Atomic Energy Commission.     

Spin-wave phenomena in liquid3He systems

The magnetic effects predicted by Leggett and Rice for Fermi liquids in the collisionless regime have been verified. Spin-echo measurements are reported which demonstrate the existence of spin waves and undamped spin currents in liquid³He and dilute³He-⁴He solutions. The experimental results are compared with the theoretical expressions of Leggett and Rice, and values of the Fermi liquid interaction parameter $$\lambda = \left[ {1/(1 + F_0^a )} \right] - \left\{ {1/[1 + (F_1^a /3)]} \right\}$$ are derived for three samples: liquid³He atP=0 and 27 atm, and a 6.4%³He-⁴He solution. In addition, some techniques for direct observation of individual spin-wave modes are explored and the results reported.     

3He diffusion in liquid isotopic mixtures

Spin echo techniques have been used to study the diffusion of³He in liquid isotopic mixtures with molar concentrations in the range fromX ₃=0.137toX ₃=0.850 over a temperature range from 3.0 to 0.4 K. AboveT the diffusive behavior is very similar to that of pure³He, although there is an increased scattering associated with⁴He. BelowT the diffusion coefficient increases with decreasing temperature and shows a dependence on the³He number density much like that of a classical gas. The excitations of⁴He have little influence on the³He diffusion coefficient, even at temperatures well above 1 K.The Rhodes Trust and the National Research Council of Canada supported one of us (R.B.H.) during the course of this research.     

Spin-dependent correlations in normal liquid 3He

Using a generalized Fermi hypernetted chain method on a Jastrow trial ground-state wave function, which includes a dependence on the z component of the nuclear spin, it is shown that spin correlations make a significant contribution to the ground-state energy of liquid ³He, accounting for much of the energy necessary to stabilize unpolarized liquid ³He relative to completely polarized ³He.Work supported in part by NSF grant DMR 7926447 and by the Deutsche Forschungsgemeinschaft.     

Neutron interactions in liquid 2 3 He

The exothermic neutron capture reaction n+ ₂ ³ He→p+ ₁ ³ H has recently been used to deposit a well known energy in liquid ₂ ³ He. In this paper we describe calculations of the distribution of the energy deposited in the interaction region resulting from such capture reactions in liquid ₂ ³ He. This calculation is of interest in the interpretation of the low temperature experiments to simulate cosmic string formation in the early Universe. In addition we calculate the fraction of the energy which is absorbed by interactions with atomic electrons compared to the total, including non ionising mechanisms (the so-called Lindhard factors).     

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.     

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.     

Nuclear refrigeration of liquid He3

A nuclear demagnetization cryostat in which liquid He³ has been successfully cooled below 0.7 mK is described. After a general discussion on nuclear refrigeration the essential parts of the apparatus and its operation and performance are explained. The important detail of how to measure the temperature of He³ is also described. The paper is concluded with suggestions for future improvements.