Velocity of Sound, Density, and Grüneisen Constant in LiquidHe4

Abstract

By measuring the pressure dependence of the velocity of sound, we have determined both the pressure dependence of the density and the Gruneisen constant u of liquid He. Measurements were made below 0.1 K and in the vicinity of 0.5 K. Our determinations of the pressure dependence of the density agree quite well with that determined by Boghosian and Meyer, who used a capacitance bridge. Since the latter results rely on the validity of the Clausius-Mossotti relation and a pressure-independent electric polarizability, the present work can be interpreted as supporting both of these assumptions.We found that u(pp) -= (p/c)dc/dp = 2.84 under the vapor pressure at 0.1 K. Using this value of u to calculate the attenuation of sound according to a three-phonon mechanism, we obtain an attenuation of less than half the measured value. Thus, the present theory of sound attenuation must be incomplete.

Roton-Phonon Interactions in SuperfluidHe4

“…We assume that the energy of quasiparticles with momentum p close to the roton minimum p R can be parameterized by the Landau spectrum p = ∆ + (p − p R ) 2 /(2m ) with m being the roton mass, while quasiparticles in the phonon region with momentum q are assumed to have a linear dispersion ω q = cq. We use numerical values of ∆/k B = 8.622 K [1], p R / = Q R = 1.931Å −1 [1], µ = m /m He = 0.144 [1], c = 238.3 m/s [13], and ρ = 0.14513 g/cm 3 [14], and express linewidths and energy shifts in units of Kelvin.…”

Quantum Monte Carlo Simulation of Overpressurized LiquidHe4

“…The DMC energies are accurately parameterized, from the spinodal point up to the highest 1. The dashed line is the extrapolation from experimental data [6,22]; the symbols correspond to experimental data for the liquid [18] and solid phases [19].…”

Three-phonon relaxation in isotropic and anisotropic phonon systems of liquid helium at different pressures

“…From (21) it is clear, that the probability density does not depend on the angles between the momenta of the interacting phonons as long as such processes are allowed by the conservation laws (9) and (10). It follows from (21), that the most probable process is when e e e ¢ = ¢¢ = /2.…”

“…Expression (5) is obtained from an analysis of experimental data [10] and (6) from [7][8][9]11,12]. Here and below values of the variables are given in CGS units except thatp c is in Kelvin and pressure in bar.…”

“…max p = 8 9 K. We note that p min and p max can be expressed in terms of the function y and its first derivative. From the conservation laws (9) and (10) …”