Thermal diffusion in3He-4He mixtures near the tricritical point and λ line

It is shown that in the superfluid phase of helium mixtures, near the tricritical point, the thermal diffusion ratiok _T is positive and, both in the tricritical region and along the coexistence curve, behaves as (c/) _T,p [(T _t –T)/T _t ] ^–1 (same exponent as in the normal phase); and near the line,k _T again is positive and behaves as (c/) _T,p . In both cases, quasielastic light scattering is shown to provide a convenient means of measuring the thermal conductivity at the transition.     

Theory of helium under heat flow near the λ point. I. Interface of He I and He II

A He I-He II interface is shown to exist under heat flow and is studied near the point. The temperature in the superfluid region is found to be of the form T –T Q^3/4 if dynamic scaling is assumed, where T is the critical temperature andQ is the heat flow. In the normal region the temperature has a finite gradient. Here we are neglecting a small thermal resistance due to vortices in the superfluid region. In a finite system with size much greater than the correlation length a first-order phase transition occurs as an inverted bifurcation as the temperature at the cooler boundary is lowered slightly below T. Namely, the system will jump from the disordered state to a state in which the two phases are separated by an interface. The theory can be constructed analogously to the theory of superconductors in a magnetic field.     

Critical behavior of the free surface of liquid 4He near the λ point

The noncriticality of the free surface of liquid ⁴He near the point and the finite-size scaling postulate are combined to show that the surface tension can have two singularities, one due to rounding and another due to shifting. The rounding singularity can be reduced, via a further scaling assumption, to that previously suggested by Sobyanin and Hohenberg. Results from calculations based on continuous symmetry models and experiments on topologically 2D ⁴He films are used to argue that the shift singularity is ¦t¦^1–, which is consistent with the leading singularity observed by Magerlein and Sanders.     

Anisotropic second sound in superfluid 4He near T λ in the presence of a heat current

In the presence of a homogeneous heat current the isotropy of superfluid ⁴He is broken and the propagation of second-sound waves becomes anisotropic. We calculate the angular dependence of the velocity and damping of second sound near T within model F of Halperin, Hohenberg and Siggia to leading order in the renormalized couplings. The critical behavior is incorporated using results of the renormalization-group theory. Second-sound waves propagating parallel to the heat current become unstable if the heat current exceeds some critical value. The theory agrees with recent experiments.     

Finite-size and gravity effects on the thermal conductivity of4He near the λ line

This paper reviews the opportunities for microgravity and Earth-based measurements of the thermal conductivityλ(t, L) of⁴He confined in cylindrical geometries of radiusL with axial heat flow at temperatures near the bulk superfluid-transition lineT _λ (P) (t is the reduced temperatureT/T _λ −1). It provides an evaluation of existing data forL=1 μm nearT _λ at saturated vapor pressure (SVP), and uses these to derive a scaling function for the resistivityR(t, L)=1/λ(t, L). The purpose of future measurements over a wide range ofL and of the pressureP will be to test the applicability of this function. In the present paper the scaling function is used to assess quantitatively the effect of gravity on potential Earth-based measurements. It is found that the gravity effect forR is particularly severe belowT _λ . For typical three-mm-high samples at SVP, values ofL significantly larger than 8 μm can only be investigated fully in micro-gravity. At higher pressures the gravity effect is larger. At 30 bar, three-mm samples withL≳4 μm require microgravity for measurements belowT _λ (P). Modern thermometry has sufficient resolution to permit quantitative measurements in micro-gravity of the anticipated finite-size effect for values ofL as large as 50 μm.     

Amplification properties of a HeArCH4 mixture

A multiwire proportional chamber operating in the true proportional region has been used to investigate the amplification properties of a HeArCH₄ gas mixture as a function of the relative concentration of argon in helium-argon. A voltage dependent optimum concentration value of about 0.08 leads to a maximum gaseous amplification. The experimental observations are interpreted in terms of Penning effects.     

Specific heat and superfluid density of bulk and confined4He near the λ-transition

The specific heat and superfluid density of liquid⁴He are calculated using a vortex-ring renormalization group theory, both for the bulk fluid and for confinement in a sphere of diameter L. In the finite geometry the superfluid density remains finite and universal at T, in agreement with Monte Carlo simulations and with finite-size scaling. The specific-heat peak is flattened in the finite geometry, and the onset temperature of the deviation from bulk behavior approaches T more closely as L is increased.     

Cubic spline fits to thermodynamic and transport parameters of liquid 4He above the λ transition

A survey has been made of the more recent experimental measurements of the viscosity, density, thermal expansion coefficient, thermal conductivity, and specific heat of liquid ⁴He from the region up to 4.2 K. Cubic spline fits to these data are provided using a mean squares approach. The fits are used to plot the temperature dependence of the kinematic viscosity, the thermal diffusivity, and the Prandtl number.Research supported by NSF grant CME 80-07478.     

Measurements of the A ⇄ B transition in a magnetic field for superfluid3He near the polycritical point

Measurements of both AB and BA transitions have been made as a function of magnetic field up to 100 G at temperatures and pressures close to the polycritical point (PCP). Forms for the specific heat differenceC _A–C _B=C ₀ (P)–(P)(T _c –T)/T _c and for the magnetization differenceM _A–M _B=H(T _c –T)/T _c fit the data satisfactorily except very nearT _c , where some other mechanism, thought to be a free energy difference due to residual heat flows, tends to stabilize the A phase. The pressure of the PCP, taken to be that at whichC ₀ =0, is found to be 21.22±0.02 bar.Work supported by the U.S. Energy Research and Development Administration under contract number E(04-3)-34, P.A. 143.     

Search for Enhancement of the Isobaric Thermal Expansion Coefficient of Superfluid 4He near T �� by?a?Heat Current

We report an experimental search for the enhancement of the isobaric thermal expansion coefficient (?? _P ) of superfluid ⁴He near the superfluid transition by a heat current (Q). The experiment was carried out using the hot volume technique at constant sample pressure of 1 bar. Liquid helium was contained in a thermal conductivity cell, and a constant heat current, Q=10 or 100 ??W/cm², was supplied from below through the sample column. We performed a sample density calculation based on existing helium properties known in the literature and a proposed enhancement ???? _P (Q). Both calculations, with or without the ?? _P enhancement, agree qualitatively with the measurement. The lack of definitive differentiation indicates that the ?? _P enhancement cannot be definitively resolved by our measurement in spite of applications of high-resolution thermometry and pressure regulation.     

The transport properties of3He-4He mixtures near the lambda line—A short review and outlook

A short review is given on the present status of our knowledge on several transport properties, both in the normal and the superfluid phase in the vicinity of the superfluid transition. The concentration range extends from very dilute mixturesX (³He) 10^–7 to those withX X _t = 0.67, whereX _t is the concentration at the tricritical point. The influence of the earth's gravity field on these properties is discussed. It occurs via the concentration susceptibility and its temperature spread increases withX. The ongoing program at Duke University on the shear viscosity is briefly described.     

High-resolution measurements of the heat capacity of MnBr2·4H2O near its Néel temperature

The heat capacityC _P of the antiferromagnet MnBr₂ ·4H₂O has been measured for polycrystalline and single-crystal samples nearT _N(2.123 K) with temperature resolution of 1×10^–6 K. Similar rounding of the lambda anomaly is found in both cases. For |1 –T/T _N| 10^–1 all data can be well fitted by assuming the samples to consist of many independent subsystems obeying the same power laws but with a Gaussian distribution ofT _N's having a width of 1.1×10^–3 K. ForT>T _N, we findC _P ^–0.12, essentially as predicted for three-dimensional Ising models in the critical region. ForT<T _N and 10^–3 10^–1,C _P ln , which approximates Ising model behavior in this interval but is not expected to be valid for 10^–4. ForT>T _N and 2.5×10^–1, C_P agrees well with predictions for the classical Heisenberg model. This crossover at 10^–1 is consistent with the known anisotropy of the salt and with present theory. The data forT>T _N in the interval 10^–4 10^–3, while not in the range of obvious rounding, appear to be strongly influenced by the mechanism responsible for that rounding.Work supported by the National Science Foundation and the Office of Naval Research. Based on a thesis submitted by L.W.K. to Carnegie-Mellon University in partial fulfillment of the requirements for the Ph.D. degree. A preliminary account of this work was presented at the Atlantic City meeting of the American Physical Society, March 1972 [Bull. Am. Phys. Soc. 17, 299 (1972)].     

Preliminary Measurement of the Critical Casimir Effect near the Tricritical Point in 3He–4He Mixture Films

We report a preliminary measurement of the critical Casimir effect in ³ He- ⁴ He mixture films near the tricritical point. Whereas we had found that the pure ⁴ He film adsorbed on Cu substrates thins due to the critical Casimir force near the lambda transition, in our present experiments we find that the adsorbed mixture film thickens near the tricritical point. This difference in behavior most likely reflects the difference in the universality class of these two phase transitions and the difference in boundary conditions that the order parameter must satisfy at liquid-substrate and liquid-vapor interfaces.     

Laser wavelength tunability of a diode-pumped Nd:LiYF4 laser on the 4F3/2–4I13/2 transition

Abstract

We report a free-running orthogonally polarized dual-wavelength laser at 1313 and 1321 nm with maximum total output power of about 1.73 W using a two-mirror linear cavity. By inserting an etalon into the linear cavity, single-wavelength lasers at 1317 or 1323 nm, two-wavelength lasers at 1317 and 1323 nm, as well as four-wavelength lasers at 1313, 1317, 1323 and 1370 nm can be achieved with maximum output powers of about 0.73, 0.63, 0.78 and 0.25 W, respectively. About 10-nm wavelength tunability from about 1313 to 1323 nm is also realized by inserting the etalon into a three-mirror V-type Nd:YLF laser cavity.     

Specific Heat and Superfluid Density of 4He near T λ of a 33.6 nm Film Formed Between Si Wafers

We report measurements of superfluid density and specific heat of a 33.6 nm film near the superfluid transition. The film is formed between two patterned and directly bonded silicon wafers. These measurements were undertaken with the primary purpose of understanding coupling and proximity effects in a situation when the film was in contact with helium in a larger confinement (Perron et al. in Nat. Phys. 6:499, 2010; Perron and Gasparini in Phys. Rev. Lett. 109:035302, 2012). However, these data are also relevant to issues of correlation-length finite-size scaling. This is the thinnest hard-wall confined film for which such scaling has been tested for the specific heat and superfluid density. One expects that at some small thickness such scaling should fail. We compare our results with previous data of helium in a similar confinement but at larger thickness. We find good agreement with scaling in regions where previous data scaled, and confirm the lack of scaling where previously reported. In our analysis we consider a native oxide growth between the etching and bonding steps of cell fabrication and its effect on our scaling analysis.     

Relaxation of rotating He II following a spin-up of its container: A superfluid Ekman time?

The experiments of Tsakadze and Tsakadze on the relaxation of rotating He II after its container is given a sudden spin-up are discussed. It is shown that the relaxation times observed can be interpreted as Ekman times, analogous to the relaxation times in the corresponding situation with classical fluids if the quantum of vorticity is taken as a characteristic kinematic viscosity. Further experiments to test and explore the analogy are suggested.This work was supported financially by a contract with the Bell Telephone Laboratories program of research in theoretical physics and a studentship from the Scientific and Technical Research Council of Turkey.     

A Novel Design of a Low Temperature Preamplifier for Pulsed NMR Experiments of Dilute 3He in Solid 4He

Recent experimental studies of solid ⁴He indicate a strong correlation between the crystal defects and the onset of a possible supersolid state. We use pulsed NMR techniques to explore the quantum dynamics of the ³He impurities in the solid ⁴He in order to examine certain theoretical models that describe how the disordered states are related to supersolidity. Because of the very small signal-to-noise ratio at low ³He concentration and the long spin-lattice relaxation time (T ₁), it is essential to significantly enhance the NMR sensitivity to be able to carry out the experiments. Here we present the design of a novel low temperature preamplifier which is built with a low noise pseudomorphic HEMT transistor that is embedded into a cross-coil NMR probe. With a low power dissipation of about 0.7 mW, the preamplifier is capable of providing a power gain of 30 dB. By deploying the preamplifier near the NMR coil below 4 K, the noise temperature of the receiver is reduced to approximately 1 K. This preamplifier design also has the potential to be adapted into a low temperature amplifier with both input and output impedance at 50 Ω or a low temperature oscillator.     

The “1958 He4 Scale of Temperatures”: Part 1. Introduction

The generally used practical scale of temperatures between 1° and 5.2° K is the He⁴ vapor pressure scale based on an accepted vapor pressure equation or table. In Sèvres (near Paris), October 1958, the International Committee on Weights and Measures recommended for international use the “1958 He⁴ Scale” based on a vapor pressure table arrived at through international cooperation and agreement. This table resulted from a consideration of all reliable He⁴ vapor pressure data obtained using gas thermometers, and paramagnetic susceptibility and carbon resistor thermometers. The theoretical vapor pressure equation from statistical thermodynamics was used with thermodynamic data on liquid He⁴ and the vapor equation of state to insure satisfactory agreement of the vapor pressure table with reliable thermodynamic data.The International Committee on Weights and Measures at a meeting in Sèvres (near Paris), France, September 29 to October 3, 1958, approved the “1958 He⁴ Vapor Pressure Scale of Temperatures” as an international standard for thermometry from 1° to 5.2° K. This was the culmination of several years of intensive research and cooperation on the helium vapor pressure scale at the Kamerlingh Onnes Laboratory in Leiden, Holland, and the U.S. Naval Research Laboratory in Washington.The vapor pressure of liquid He⁴ has for a long time been used as a standard for thermometry between 1° and 5.2° K. The first measurements of thermodynamic temperatures in the liquid He⁴ range were made with constant volume gas thermometers filled with He⁴. Simultaneous measurements of the vapor pressure of liquid helium in temperature equilibrium with the gas thermometer established a vapor pressure-temperature relation which then was used as the basis for determining thermodynamic temperatures from vapor pressure measurements. With these vapor pressure-gas thermometer measurements there were measurements of He⁴ vapor pressures made simultaneously with measurements of the He⁴ isotherms from which temperatures were obtained by extrapolating the isotherms to zero density (N/V→0) in accordance with the virial equation of state: pV/N = RT[1 + B(N/V) + C(N/V)² + …](1)After the latent and specific heats of liquid He⁴ had been measured, the experimental vapor pressure-temperature relation was improved through the use of the theoretical vapor pressure (P) equation: lnP=i0−L0RT+52lnT−1RT∫0TSldT+1RT∫0PVldP+ϵ(2)where i₀ ≡ ln (2πm)^3/2k^5/2/h³(3)and ? ≡ ln (PV/NRT)?2B (N/V)?(3/2) C (N/V)²(4)L₀ is the heat of vaporization of liquid He⁴ at 0° K, S_l and V_l are the molar entropy and volume of liquid He⁴, m is the mass of a He⁴ atom, B and C are the virial coefficients in eq (1), and the other symbols have their usual meaning. Both theoretically calculated and directly measured vapor pressures were considered in arriving at the 1958 He⁴ Temperature Scale.Equation (2) presupposes that the thermodynamic properties entering the equation have been measured on the thermodynamic scale, otherwise the use of this equation for the calculation of P is not valid. In practice, however, these properties are measured on an empirical scale that only approximates the thermodynamic scale. In general this empirical scale has been a He⁴ vapor pressure scale based on gas thermometer measurements.As T is lowered, the fourth, fifth, and sixth terms in eq (2) become smaller and less important relative to the first three terms. At 1.5° K, the inclusion or exclusion of the sum of the fourth, fifth, and sixth terms in eq (2) affects the temperature calculated from a given value of P by only 0.0005 deg. It may be said then, that below 1.5° K, the vapor pressure of He⁴ is in effect really determined, within the present accuracy of the vapor pressure measurement, by a single empirical constant, the heat of vaporization of liquid He⁴ at 0° K. At present, L_o for He⁴ is normally calculated from vapor pressure data obtained with a gas thermometer. The magnitude of the last three terms in eq (2) increases rather rapidly with rising T, and above the λ-point (2.172° K) the accuracy of the evaluation of these terms is a very important consideration.In Amsterdam in 1948, on the occasion of a General Assembly of the International Union of Physics, a small group of low temperature physicists, meeting informally, agreed to use and recommend for temperature measurements between 1° and 5.2° K, a table of vapor pressures of He⁴, then in use in Leiden, which came to be known as the “1948 Scale” [1].⁵ This scale has sometimes been referred to as the “1949” Scale. From 1° to 1.6°K, the “1948 Scale” was based on vapor pressures calculated by Bleaney and Simon [2] using eq (2). From 1.6° to 5.2° K, the scale was based on measured vapor pressures and temperatures determined with gas thermometers. From 1.6° to 4.2° K, it was based primarily on the vapor pressure measurements of Schmidt and Keesom [3].Even in 1948, when the “1948 Scale” was agreed to, there was evidence in the measurements and calculations of Kistemaker [4] that the “1948 Scale” deviated significantly from the thermodynamic scale. However, it was thought at the time that, on general principles, indicated changes in an existing scale should be made only after these changes had been confirmed. With improvements in the precision and accuracy of physical measurements at low temperatures, irregularities appeared in the temperature variation of physical properties between 1° and 5° K that were in the main reproducible in different substances and properties and were, therefore, attributable to errors in the “1948 Scale” [5]. Stimulated by these results which corroborated Kistemaker’s work, the investigations of the He⁴ vapor pressure scale were undertaken that culminated in the “1958 He⁴ Scale.”Paramagnetic susceptibility and carbon resistor thermometers were later employed in investigations of the He⁴ vapor pressure-temperature relation [6]. These thermometers were used for the interpolation of temperatures between calibration points (temperatures) using an assumed relation connecting temperature and paramagnetic susceptibility or carbon resistance for the calculation of the temperatures. For suitably chosen paramagnetic salts, the Curie-Weiss Law was assumed to hold: χ=CT+Δ(5)where χ is the magnetic susceptibility and C and Δ are empirical constants. Measurements at two temperatures would suffice to determine these two empirical constants if the measurement were really of χ or a quantity directly proportional to χ. However, a calibration of the paramagnetic thermometer at a third calibration temperature is necessary because the arbitrariness in the size and arrangement of the paramagnetic salt samples and the induction coils that surround the salt sample for the susceptibility measurement make the measurement a linear function of χ. Interpolation equations for carbon resistor thermometers are not as simple as eq (5) and do not have a theoretical basis. Hence, vapor pressure data obtained with carbon resistor thermometers are of more limited usefulness for the determination of the He⁴ vapor pressure-temperature relation. Clement used carbon thermometer data to examine the derivative d (ln P)/d (1/T), [7].Important use has been made of He⁴ vapor pressure measurements made with magnetic susceptibility and carbon resistor thermometers in arriving at the “1958 He⁴ Scale.” These vapor pressure measurements were considered along with those made with gas thermometers and vapor pressures calculated using eq (2). Temperature measurements with magnetic and carbon resistor thermometers are much simpler to make than measurements with gas thermometers, and hence vapor pressure data obtained with magnetic and carbon resistor thermometers are more numerous. Also, the measurements made with these secondary thermometers are more precise (to be distinguished from accurate) which makes them especially useful for interpolation between the gas thermometer data.There are, accordingly, three practical methods for determining the He⁴ vapor pressure-temperature relation: (1) By use of the direct vapor pressure measurements made with gas thermometers, (2) through the use of eq (2) with some vapor pressure-gas thermometer data, and (3) through the use of vapor pressure measurements with secondary thermometers which have been calibrated using some gas thermometer data. If all the pertinent experimental data were accurate and all temperatures were on the thermodynamic scale, these three methods would yield results in good agreement with each other, and any one might be relied upon for the construction of the He⁴ vapor pressure-temperature table defining the scale. Because of experimental errors, however, the vapor pressures obtained by the different methods differ when carried to the limit of the sensitivity of the measurements. For He⁴ between 1° and 4.5° K, different choices of the methods and different selections of the experimental data used, weighting factors and corrections to the published data yield scales all within about 4 millidegrees of each other. The primary evidence for this is that 4 millidegrees is the maximum difference between the L55 Scale [8] obtained by method (2) and the 55E Scale [9] obtained by method (3). This then is a measure of the range (total spread) of uncertainty at present in the He⁴ vapor pressure scale of temperatures between 1° and 4.5° K.All published He⁴ vapor pressure measurements, and thermodynamic data needed for eq (2) were independently studied and correlated by H. Van Dijk and M. Durieux at the Kamerlingh Onnes Laboratory in Leiden [8] and by J. R. Clement and J. K. Logan at the U.S. Naval Research Laboratory in Washington [9]. As far as possible, the experimental data of the original investigators were recalculated on the basis of later knowledge of the temperature scale, fundamental constants, and the properties of He⁴. In some cases, limitations were imposed on these recalculations by the incomplete reporting of the experimental data by the original investigator.After working independently, van Dijk and Clement cooperated to compromise their differences. They met first in Leiden, August 1955 and later in Washington, summer of 1957. From January 22 to March 14, 1958, Logan worked at Leiden, and later represented Clement at a conference in Leiden, June 1958, at which agreement was reached on the “1958 He⁴ Scale.” This cooperation was an important factor in the improvement of the scale.Where the differences between the values obtained by handling the experimental data differently are largest (4 millidegrees), the “1958 Scale” falls between the extremes. At other places it is close to the mean of these values and at no place does it deviate by more than 2 millidegrees from the mean. The estimated uncertainty of the “1958 He⁴ Scale” is accordingly ±2 millidegrees between 1° and 4.5° K. At higher temperatures, the estimated uncertainty is larger.Now that the International Committee on Weights and Measures has recommended the “1958 He⁴ Scale” as an international standard it is presumed that henceforth the International Committee on Weights and Measures will take the initiative in improving the scale when changes are needed. Before the International Committee on Weights and Measures assumed responsibility for the He⁴ vapor pressure scale, the Commission on Very Low Temperature Physics in the International Union of Pure and Applied Physics concerned itself with the scale. This began with the informal meeting in Amsterdam in 1948 that resulted in the “1948 Scale.” At the Low Temperature Conferences sponsored by the Commission on Very Low Temperature Physics of the International Union of Physics at Paris in 1955, and at Madison, Wisconsin, in 1957, sessions were held at which the He⁴ vapor pressure scale of temperatures was discussed.The National Bureau of Standards sponsored meetings, for discussion of the helium vapor pressure scale of temperatures, held at the NBS during the spring meetings of the American Physical Society in Washington, 1955 and 1957. Also, the NBS encouraged cooperation in reaching national and international agreement on the scale. It initiated or promoted the meetings for discussion of the differences between the L55 and 55E Scales proposed respectively by Van Dijk and Durieux, and by Clement. These were the meetings held August 26 and 27, 1955 in Leiden (before the Low Temperature Conference in Paris) [10], July 30, 31, and August 1, 1957 in Washington (before the Low Temperature Conference in Madison) [11], and June 13, 14, and 16, 1958 in Leiden (before the meeting of the Advisory Committee on Thermometry of the International Committee on Weights and Measures in Sèvres) [12]. Also, the National Bureau of Standards promoted the arrangement which sent Dr. Logan of the U.S. Naval Research Laboratory to work in the Kamerlingh Onnes Laboratory from January 22, to March 14, 1958.The Scale agreed upon at Leiden, June 13 to 16, 1958 was presented to the Advisory Committee on Thermometry of the International Committee on Weights and Measures at its meeting in Sèvres, June 20 and 21, 1958. The recommendation of the Advisory Committee to the International Committee was as follows [12]:

• “Le Comité Consultatif de Thermométrie,
• “avant reconnu la nécessité d’établir dans le domaine des très basses températures une échelle de température unique,
• “ayant constaté l’accord général des spécialistes dans ce domaine de la physique,
• “recommande pour l’usage général l’ “Echelle ⁴He 1958,” basée sur la tension de vapeur de l’hélium, comme définie par la table annexée.
• “Les valeur des températures dans cette échelle sont désignées par le symbole T₅₈.”

The table of He⁴ vapor pressures that was sent to the International Committee with this recommendation was the table distributed at the Kamerlingh Onnes Conference on Low Temperature Physics at Leiden, June 23 to 28, 1958. It was published in the Proceedings of the Kamerlingh Onnes Conference [13].On the recommendation of its Advisory Committee on Thermometry, the International Committee on Weights and Measures approved the “1958 He⁴ Scale of Temperatures” at its meeting at Sèvres, September 29 to October 3, 1958.The table adopted by the International Committee on Weights and Measures was a table of vapor pressures at hundredth degree intervals. This table was expanded by Clement and Logan making table I of this paper with millidegree entries. Table I was inverted to give tables II and III which express T as a function of vapor pressures. Auxiliary tables were added including a table of the differences between the 1958 Scale and other earlier used scales. Linear interpolation is valid for all tables except at the lower temperature end of table IV.The assistance at Leiden of H. ter Harmsel and C. van Rijn, students of Dr. H. van Dijk at the Kamerlingh Onnes Laboratory, with the computations for the defining and auxiliary tables is gratefully acknowledged.Various members of the Cryogenics Branch of the Naval Research Laboratory at Washington assisted with numerous calculations which contributed toward the development of the present scale. This assistance, especially that of Dr. R. T. Swim, is gratefully acknowledged.     

An evaluation of the average superfluid density of 4He in a cylindrical pore near T λ predicted by the Ginzburg-Pitaevskii-Mamaladze theory

A numerical evaluation of the average superfluid density of ⁴He in a cylindrical pore near T predicted by the Ginzburg-Pitaevskii-Mamaladze theory has been carried out as a function of pore radius and temperature. The results are presented in graphical form and in terms of an accurately fitting closed algebraic form.Supported by U.S. Department of Energy, contract EY-76-S-02-1569.     

Acoustics of a “Dirty” Fermi Liquid: 3He in Aerogel

An acoustic cavity containing ³He in 98% porous silica aerogel was used to investigate the effects of impurity scattering in a Fermi liquid. The pressure and temperature dependence of the sound attenuation in the normal Fermi liquid was extracted from the cavity response. The attenuation of sound displays behavior very different from the bulk owing to strong elastic scattering of quasi-particles by the silica strands. Using a visco-elastic model of the Fermi liquid, we find a mean free path restricted to 340 nm. Information on the sound velocity is inferred from the pressure dependence of the oscillation period of the cavity response. The data can be accounted for by a Biot model of the ³He liquid in the porous aerogel.