On the temperature dependence of the velocity of sound in liquid helium

The velocity of the first sound in helium II for the low-temperature region in which the lawT ⁴ ln(const/T) holds is calculated. The constant in the logarithm is shown to be very small, and therefore the known results of the logarithmic approximation are not sufficient.     

On the dispersion of zero sound in liquid4He

A new derivation of Pines' zero-sound model of the phonon in liquid⁴He is presented which shows that the essential assumption in the model is that the mechanism of phonon damping in no way depends upon the mechanism for creating phonon modes. The result of a numerical calculation of the dispersion relation for zero sound in the wave number range 0≤k≤0.2 Å^?1 is given and is shown to be in very good agreement with recent direct measurements of the speed of superthermal phonons in He II by Narayanamurti, Andres, and Dynes.     

Sound velocity in liquid4He under pressure

We have measured the temperature dependence of the sound velocity in liquid ⁴ He at pressures from the vapor pressure to near the solidification pressure. The data were obtained at frequencies from 12 to 105 MHz and covered the temperature range from below 0.1 to nearly 1.0 K. The velocity data at high pressures do not show any anomaly that can be associated with a distinct shoulder found earlier in the sound attenuation. As observed previously at the vapor pressure, the frequency dependence of the velocity data undergoes an inversion at low temperatures; this unexpected behavior is in agreement with recent theoretical treatments.Based on work performed under the auspices of the U.S. Atomic Energy Commission.     

The velocity of second sound in3He-4He mixtures

The formula for the velocity of second sound in dilute³He-⁴He mixtures is derived, taking due account of both the effects of the interactions between the³He quasiparticles and their dispersion. The theory is compared to the recent experimental results of Greywall and Paalanen, and from this comparison it is possible to obtain both the inertial mass and the specific heat effective mass. Both masses are consistent with the mass in infinitely dilute solutions being (2.245±0.01)m ₃. Previous analyses of the velocity of second sound are critically discussed.     

Phonon-phonon interactions and propagation of sound in liquid4He

The quantum-hydrodynamical model for excitations in He II at low temperatures is used to calculate the velocity shift and the attenuation of ultrasound in the collisionless domain. First, starting from a linear spectrum, the self-energy needed for the evaluation of the density-density correlation function is derived in lowest order of perturbation theory. Particular attention is then paid to a self-consistent determination of the real part of the pole of the retarded Green's function. This procedure turns out to be essential for this model. Second, the influence of a nonlinear spectrum and of a finite lifetime of thermal phonons is investigated.     

Temperature dependence of the sound velocities and elastic constants of bcc3He

High-resolution measurements of the sound velocity in 20 crystals of bcc³He at constant molar volume (24.1 cm³/mole) show a monotonic decrease of about 0.1% for longitudinal and 0.3% for transverse velocities for a temperature increase from 0.123 to 0.800 K, the change being approximately proportional toT ⁴. A low-lying transverse mode of 102 m/sec was observed for the first time. The orientation of three samples could be inferred from their absolute velocity, and the temperature dependence of all three elastic constants was calculated. The change in adiabatic bulk modulus is in good agreement with the Mie-Grüneisen equation of state. No effect from the exchange interaction on the velocities could be observed.This work was supported by the National Science Foundation.     

Temperature dependence of the condensate fraction of superfluid4 He

The roton contribution to the temperature dependence of the condensate density is discussed. The analysis is carried out through the inclusion of a gauge symmetry breaking field. Under the hypothesis that the thermal excitation of rotons is the main responsible for the depletion of the condensate, we obtain an explicit result for the temperature dependence of the condensate density which rather well agrees with the available experimental data.     

Thermal expansion,velocity of sound,and compressibility in liquid3He under pressure

We have measured the pressure at constant volumeP _v(T), of liquid³He as a function of temperature from 10 to 600 mK and at starting pressures from 1.6 to 28.1 bar. Simultaneously, we determined the hydrodynamic sound velocityc ₁, at the same pressures and temperatures. From these data we have derived very accurate values of the isobaric expansion coefficient α _p and the adiabatic compressibility κ.     

Pressure dependence of the sound velocity in distilled water

The sound velocity is measured in distilled water in the pressure range 0.1–60 MPa and in the temperature range 0–40°C. The results are given in the form of tables and an equation derived by least-squares processing of the experimental data. Translated from Izmeritel'naya Tekhnika, No. 4, pp. 66–69, April, 1999.     

Elementary excitations and sound speed in liquid 4He at negative pressures

No Heading We present neutron scattering measurements of the phonon-roton excitations of superfluid ⁴He at negative pressures in the porous medium MCM-41. The phonon and maxon energies decrease systematically below bulk values as the density is decreased below the bulk value due to stretching of the liquid. The negative internal pressures are estimated by comparison of the observed maxon energies with extrapolation of positive pressure values and from the sound speed. The maximum negative pressure realized, about –5.5 bar, is consistent with surface tension arguments and the MCM-41 pore diameter of 47 Å. Slight broadening of the intrinsic lineshape is observed, suggesting shorter lifetimes of the excitations.PACS numbers: 61.12.Ex; 61.25.Bi; 62.60.+v; 68.03.Cd; 68.03.Kn; 67.40.Mj     

Zero and first sound velocity and Fermi liquid parameterF 2 s in normal3He

A precise velocity measurement of zero and first sound in normal³He was performed over the pressure range of 0.5 bar and 10 bar at a frequency of 389.1 MHz using a phase detection technique. From these measurements, the Fermi liquid parameter F ₂ ^s was determined as a function of pressure. The new value of F ₂ ^s was positive and less than 0.25 at all pressures below 10 bar. It allows propagation of transverse zero sound mode for all pressures within the current theoretical picture.     

The velocity of second sound in 3He-4He mixtures: A revision

Greywall has recently proposed a new temperature scale for the ³He melting curve thermometer. A reanalysis of the velocity of second sound in ³He-⁴He mixtures using the data of Greywall and Paalanen with this new temperature scale shows that the interaction between ³He quasiparticles is now independent of concentration.     

Fluctuation contribution to the velocity and damping of sound in liquid 3He above the superfluid transition temperature

We have developed a theory, valid for arbitrary frequencies, to calculate the change in the velocity and damping of sound due to fluctuations of the order parameter just above the superfluid transition temperature in liquid ³He. While the theory is approximate, it gives the exact high-frequency limit and is off the exact low-frequency limit by less than 0.5%. We show that careful measurements on the frequency dependence of the fluctuation contribution should allow one to obtain information on the nature of quasiparticle interactions in the normal liquid.     

The velocity of second sound in dilute3He-4He solutions below 0.6°K

The velocity of second soundu ₂ in dilute solutions of³He in⁴He has been measured by a pulse, time-of-flight technique using a new type of mechanical transducer. Tables of measured values ofu ₂ as a function of temperature between 0.03 and 0.6° K are presented for³He concentrations in the range 0.14–6.3% at the saturated vapor pressure and under hydrostatic pressures of 10 and 20 atm. Estimates of the upper limit of the intrinsic attenuation of second sound have also been made and these are consistent with theory provided that the experimental values of the phonon thermal conductivity lifetime are used in place of the values calculated by Baym and Ebner.Work supported by a grant from the National Science Foundation.On leave of absence from University of Nottingham, U.K.     

Energy dependence of the effective mass in liquid3He

The striking behavior of the specific heat of liquid³He as function of temperature at low temperatures requires the effective massm* to change rapidly with temperature; this can be translated into a rapid variation with energy,m*/m dropping from itsE=0 value to 1 over the temperature range 0.5 K. We explore this effect in a model in which the enhancement of the effective mass is due to coupling to spin fluctuations. At very lowT50 mK, the variation in specific heat results fromT ³ lnT terms. The free energy, on the other hand, does not containT ² lnT terms in its dependence on the magnetic field, implying that the susceptibility, which is essentiallym*/(1+F ₀ ^a ), also does not have such logarithmic terms. Consequently, ifm* varies with energy, so mustF ₀ ^a , so as to leave the susceptibility free of this rapid variation. The rough constancy ofm*/(1+F ₀ ^a ) seems empirically to hold to higher energies and temperatures. Ifm*/m drops, with increasing energy, to unity, the spin-fluctuation theory, which is described in terms of Landau parameters at the Fermi surface, goes over into the paramagnon theory. The rapid change with energy of the effective interactions can be understood within the framework of response theory as a shaking off of the relevant collective modes with increasing frequency of the imposed oscillations. The changes in effective interactions have consequences for the interpretation of experiments involving inelastic neutron scattering from liquid³He.Also State University of New York, Stony Brook, New York. Supported in part by U.S. D.O.E. Contract DE-AC02-76ER13001.Also University of Illinois at Urbana—Champaign. Supported in part by U.S. NSF Grant DMR 81-21273.     

Dynamics of the3He A-B interface in the velocity range of second sound

The movingA-B interface emits second sound which extracts the latent heat from the transition region. The amplitude is calculated for all interface velocities . A pronounced maximum is found if is close to the second sound velocity.     

Temperature dependence of the molar volumes of liquid and solid3He at melting pressure nearT N

For temperatures above the solid ordering temperature T_N=0.934 mK, the molar volumes v₁ and v_s of liquid and solid³He at melting pressure, P_m are determined primarily by the melting pressure and the compressibility. However, in the vicinity of T_N and below, v_s(T) is influenced greatly by the expansion coefficient, which becomes large and negative. Using existing thermodynamic data, we find that v_s(T) has a minimum at T_N with a negative slope for T < T_N. A constant-volume, all-solid sample starting at T=0 with the pressure just above P_m would begin to melt as T_N is approached, becoming all-solid again somewhat above T_N.