ALBERT

Notes: Abstract We describe a simulation of the scattering in beams of helium atoms. The number of atoms N in the beams is reduced by a large scaling factor λ while the collision cross-section is increased by λ. This leaves the rate of scattering for each particle unchanged. As an example, we predict the outcome of a low temperature atomic beam experiment to measure the 4 He- 4 He atomic scattering cross-section σ at low energies. Because of the existence of a very weakly bound dimer, the low energy cross-section is expected to be unusually large, ∼1.83 × 10 5 Å 2 . In the simulation N/λ is small enough for the trajectories of all the scaled atoms to be calculated numerically. The simulation shows that the experiment is quite practicable. The proposed apparatus is just over 20 cm long, and a few centimeters wide, small enough to fit in a dilution refrigerator. The heaters and bolometers are assumed to be similar to those used in previous low temperature scattering experiments. We show that, using low intensity beams, the cross-section can be measured as a function of the relative velocity v r between ∼2 and ∼8 m/sec, corresponding to relative energies between ∼1 and ∼16 mK. By fitting σ(v r) one can determine the scattering length and effective range of the interaction. We predict that, at high intensity where multiple scattering is very important, the two beams coalesce into one.

Notes: We give a concise review of the empirical properties of liquid and solid 3He-4He mixtures and their phenomenological interpretation. The bulk of the paper is about dilute solutions of 3He in liquid 4He at temperatures well below the tricritical point, where the roton and phonon excitations are comparatively unimportant. We describe the thermodynamic properties in terms of the Landau-Pomeranchuk 3He quasiparticles and the effective interaction between them, introduced by Emery and Bardeen, Baym and Pines. The scattering amplitude, needed to fit the low temperature transport properties, and the effective interaction are related, provided the multiple virtual scattering calculated by Fu and Pethick is included. The multiple scattering should always be included, even for very small concentrations. We present the evidence for the velocity dependence of the effective interaction, and urge that this also be taken into account in the interpretation of experiments. We give a short description of spin-polarized liquid mixtures and of the possibility of pairing superfluidity in solutions of 3He in liquid 4He. The existence of supersaturated solutions may be a way to attain p-wave pairing at accessible temperatures. Beacause of phase separation, the concentration of 4He in dilute mixtures of 4He in liquid 3He becomes very small as the temperature is lowered, making it unlikely that a degenerate Bose gas of 4He quasiparticles can be produced. In addition, the superfluid 4He film on the walls of the vessel makes the achievement of a supersaturated solution very difficult. We briefly review the measurements of the phase separation, the density and specific heat, and show that the spectrum of the 4He quasiparticles and the role of their effective interactions are still in doubt. In solid 3He-4He mixtures the thermodynamic properties and the phase diagram, including the crystallographic transformation, fit the regular solution model very well. On the other hand, dilute solid solutions of either 3He or 4He in the other isotope have NMR relaxation times and spin diffusion which agree with the theory of impuritons (mass fluctuation waves) which tunnel more or less freely through the crystal. The reconciliation of these two theories and an explanation of the accuracy of the regular solution model remain mysteries. A deviation from the regular solution model, the fluctuation specific heat above the phase separation temperature, is discussed in detail. The review includes two tables which list most of the experiments on liquid and solid 3He-4He mixtures published between 1975 and 1990.

Notes: Abstract The Zharkov-Silin Fermi Liquid theory of solutions of4He in non-superfluid liquid3He has been applied to the recent phase separation data of Nakamura et al. At zero pressure, the difference in binding between a4He atom in liquid4He and in liquid3He is smaller than previous estimates, and the4He effective mass is close to the bare mass. The volume measurements of Laheurte show that the difference in binding has a minimum near ∼11 atm. This implies an enhanced solubility of4He in3He below 0.1 K at this pressure, although there is experimental evidence that the solubility at 0 K remains zero.

Notes: Abstract The Zharkov-Silin Fermi Liquid theory of solutions of4He in normal (non-superfluid) liquid3He is reviewed and slightly extended. The theory is expected to be valid only below ∼0.1 K, and it predicts that there should be a hundred-fold increase in the diffusion coefficient as the temperature is lowered into this region. The limited range of validity explains the apparent disagreement between the recent very low temperature measurements of the phase separation line by Nakamura et al. and extrapolations from higher temperatures. In the low temperature experiments the4He concentration X4 is so small that there is no macroscopic phase separation, only a gradual thickening of the4He-rich film on the walls. We confirm that the phase separation temperature Tps(X4) estimated from the thickening is close to the values which would be observed in an ideal experiment with a macroscopic phase. Fits to Tps(X4) including the new data show that the4He effective mass m 4 * is close to, and may be equal to, the bare mass m4. The difference in binding at zero pressure between4He in liquid4He and in liquid3He is (E44−EE43)/kB=(0.21+0.03/−0.01)) K. Using the volume measurements of Laheurte to calculate the pressure dependence of E43 indicates that the difference in binding has a minimum of (0.0±0.2) K near ∼11 atm. This implies that the solubility of4He in3He is enhanced in this region of pressure. The behavior of the spinodal line at low temperature, and the possibility of observing Bose condensation in a metastable solution of4He in liquid3He are also discussed.

Notes: Abstract The effect of a heat current across the atomically rough crystal-superfluid interface in4He has been studied below 1 K. The chemical potential difference Δμ and temperature difference ΔT were measured simultaneously, the ΔT by means of a “superfluid melting-curve thermometer.” The results give the mean phonon transmission coefficient across the interface $$\bar \tau $$ and a dimensionless quantity β that determines the Onsager coefficient linking Δμ with the heat current. The transmission probability $$\bar \tau $$ is proportional toT 2 below 0.2 K, in agreement with other experiments and with various theories, and it depends slightly on the crystal orientation, increasing near thec axis. The coefficient β, which is roughly independent of temperature and orientation, agrees with a recent theory of Bowley and Edwards.

Notes: Abstract The properties of3He films on a Nuclepore substrate have been measured by pulsed NMR at a Larmor frequency of 10 MHz between 1.3 and 4.2 K. The3He film thickness was varied from 0.14 to 2 layers. The spin-spin relaxation timeT 2 agrees well with previous measurements of3He films on Mylar and Vycor glass at low temperatures. The spin-lattice relaxation timeT 1 for submonolayer films shows a strong temperature dependence consistent with a thermally activated process. This behavior has not previously been observed on amorphous substrates. The spin diffusion coefficient was measured for the thickest films at 4.2 and 2.6 K and found to be consistent with free atom motion of the3He in the vapor. In thin films or at low temperatures, the diffusion was too small to be observed. The magnetic coupling between the3He nuclei in a film and the protons in the Nuclepore substrate was determined from the effect of the3He on the proton-lattice relaxation time. It is about 100 times weaker than the interaction between3He and the fluorine nuclei in a Teflon substrate.

Notes: Abstract Experiments to measure the kinetic coefficients of the helium crystal surface, which have been criticized by Grabinski and Liu,1 are analyzed to determine the effect of heat flow through the surface and the effect of nonhydrostatic crystal strain. The experiments studied are the low-temperature measurements of the damping of melting-freezing waves in4He, the high-temperature relaxation of the4He crystal surface after an electrostatic disturbance, the relaxation in shape of a3He crystal, and the measurement of the Onsager cross-coefficient using a heat current in4He. After a review of the theory, in which the dependence of the growth coefficient on the thermal conditions of the experiment is discussed, the corrections to published results due to heat flow are shown to be small and within the experimental errors. The effect of nonhydrostatic strain is shown to be second order and consequently negligible in most existing measurements of kinetic or static properties. However, if sufficiently large, nonhydrostatic strain produces an instability of the surface that was predicted by Grinfeld.7 This effect may explain a corrugation of the surface observed by Bodensohn et al.9 during rapid cooling. The threshold for the Grinfeld instability and the frequency and damping of melting-freezing waves below the threshold is discussed. We propose a new experiment to study the instability and to measure the elastic and plastic properties of the crystal.

Notes: Abstract Standing spin-wave modes in liquid3He have been studied by cw NMR at Larmor frequencies of 1, 2, and 4 MHz and pressures of 0, 6.3, and 12.3 bar. The spin waves, which produce peaks in the NMR line, are visible at temperatures below 5 mK at zero pressure. With the assumption of a slightly simplified sample shape and no transverse spin relaxation at the walls, the theory of Leggett fits the spin-wave frequencies in the normal liquid very well, giving a value of the Fermi liquid parameterF 1 a =−0.6±0.2 at zero pressure. The width of some of the peaks is larger than expected from other determinations of the quasiparticle diffusion time τ D . This could be due to wall relaxation or to deviations from the assumed sample geometry. In the superfluid A1 and A phases, where the data cannot be fitted to existing theories, the spin-wave modes are shifted in frequency and suffer additional damping as the temperature is decreased. At still lower temperatures in the B phase an inversion of the spin-wave spectrum from one side of the NMR line to the other is observed, agreeing quantitatively with the predictions of the 1975 theory of Combescot.