Solubility ofHe3in LiquidHe4at 0°K

Abstract

In an earlier publication 1 the problem of the equilibrium between the two phases in a phaseseparated liquid He 3 -He 4 mixture near 0°K has been discussed on the basis of the theory of impurities in liquid helium put forward by Landau and Pomeranchuk. 2 ' 3 The theory gives the way in which the excitation spectrum of the liquid is modified by the presence of the impurity; e.g., a small concentration X of He 3 modifies the Landau (phonon + roton) excitation spectrum of liquid-helium II by adding a branch of Fermi particles, equal in number to the number of He 3 atoms, and with energy-momentum relation e = -E 3 (X) +p 2 /2m 3 *. The effective mass ra 3 * has been determined from second sound measurements 4 to be 2.5 times the real mass of He 3 at the saturated vapor pressure. The binding energy E s is found 5 from vapor-pressure data to be rather close to L 3°, the latent heat of vaporization per atom of pure liquid He 3 at 0°K, although it actually depends slightly on X. In a similar way the Fermi quasiparticle spectrum of pure liquid He 3 is modified by the addition of a Bose branch when He 4 is dissolved in it. 8 The thermodynamic properties of dilute He s -He 4 mixtures can thus be calculated in a straightforward way using standard formulas of statistical mechanics. In particular, in a mixture in which phase separation has occurred, one can equate the chemical potentials of each isotope in the two phases to obtain the concentration in each phase as a function of T. It was found earlier 1 that the upper He 3 -rich phase is almost pure He 3 for T^ 0.2°K and this has been confirmed by experiment. 7 The theory also shows that it is possible, in principle, for He 3 to remain dissolved in He 4 up to a certain concentration, even at C^K. 1 This is true for any solution in which He 3 is more strongly bound than it is in pure liquid He 3 . The maximum solubility at 0°K, X 0 , is then determined by equating the latent heat of vaporization of He 3 from the solution to that from the pure liquid:-W + *W = -L 3-where kTj? is the Fermi energy of He 3 in solution (calculated for a gas of the same number density and with mass m 3 *). Determinations of E 3 (X) from vapor-pressure data are not at present sufficiently precise to demonstrate that this possibility is realized in nature.A more sensitive method of determining E 3 (X) than from vapor pressures is from measurements of the phase-separation temperatures T$ of dilute solutions of known X. This has been done in the present work by measuring the heat capacity of the solutions under their saturated vapor pressure down to temperatures of about 0.1 °K or less. The solutions were contained in a nylon calorimeter packed with small crystals of cerium magnesium nitrate used as a refrigerant and as a thermometer. The phase separation appears as a discontinuity AC in the specific heat (Fig. 1), as was previously observed at higher temperatures by Ouboter, Beenakker, and Taconis. 5 We found such discontinuities in solutions withX = 0.08, 0.10, 0.12, and 0.15 but not with X = 0.04, 0....

Boson-induceds-wave pairing in dilute boson-fermion mixtures

“…Already in the 1960's Pines [1] suggested that the effective interaction between 3 He atoms in solution in superfluid 4 He could be attractive due to the exchange of density fluctuations of bosonic background. This attraction was then observed experimentally by Edwards et al [2] and Anderson et al [3]. From the experimental data Bardeen, Baym and…”

“…for the interaction of two particles with reduced mass m red , and given the solutions with wavenumber k to the corresponding radial Schrödinger equations: u (1) l (r; k) and u (2) l (r; k), the associated phase shifts δ …”

Thermodynamic Properties of Liquid 3He-4He Mixtures Between 0.15 K and 1.8 K

“…Also shown are specific heats predicted by the ideal specific heat model used by Radebaugh [1], and by the non-ideal model proposed by Greywall [39] [10] and those from Radebaugh's model [1] at three different 3 He concentrations: 4.66%, 15% and 29.1%. On the other hand, the measurements of Edwards et al [35] [10] and Alvesalo et al [14], and the values of Radebaugh [1]. 3 He concentrations over which properties of 3 He- 4 3 He- 4 He mixtures.…”

“…[33], Alvesalo et al [14], Goellner et al [13], Ahlers and Greywall [31],and Qin et al [27]. [2], Edwards et al [35], de Bruyn Ouboter et al [10], and Alvesalo et al [14]. 3 He mixture measured by de Bruyn Ouboter et al [10].…”

Expansion of a quantum degenerate boson-fermion mixture

“…The most appealing one is certainly the Bardeen-Cooper-Schrieffer (BCS) type superfluidity, since the presence of bosonfermion interaction in the mixture is expected to induce an effective attraction between fermions by exchanging density fluctuations of the bosonic background [5,6], analogously to that of superfluid 3 He and 4 He in lowtemperature physics [7,8]. With this respect, the recently reported quantum degenerate mixtures of 40 K (fermion) and 87 Rb (boson) by the LENS group would be particularly interesting due to the large boson-fermion attraction, which has been directly manifested by the collapse of the degenerate fermions above a critical number of particles [4], or alternatively, by the observation that the Bose-Einstein condensate (BEC) coexisting with the Fermi gas inverts its aspect ratio more rapidly than a pure condensate during the ballistic expansion [3].…”