Temperature, Pressure, and Concentration Dependence of the Osmotic Pressure of DiluteHe3-He4Mixtures

Abstract

The osmotic pressure of ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures has been measured at temperatures 0.027-0.65 K, for concentrations up to 10-mole% ${\mathrm{He}}^3$, and for hydrostatic pressures of 0.26, 10, and 20 atm. The osmotic pressure was measured directly with a sensitive specially designed diaphragm pressure gauge. The temperature and concentration dependence of the osmotic pressure is in fair agreement with the effective interaction theory proposed by Bardeen, Baym, and Pines (BBP). It also agrees with a simple empirical model which avoids the complicated calculations involved in obtaining the thermodynamic properties at finite temperatures from the BBP theory. The model fits the temperature dependence of other thermodynamic properties of solutions. The osmotic pressure at absolute zero at 10 and 20 atm is used to determine the ${\mathrm{He}}^3$ effective mass and somewhat speculative values of the BBP quasiparticle interaction $V\left(k\right)\mathrm{}$ under pressure. The interaction under pressure is found to have a minimum at a nonzero value of $k$, and it may give rise to a "supermobile" transition at comparatively high temperatures.