Effective3He interactions in dilute3He-4He mixtures

Abstract

The effective interaction between ${}^3$He quasiparticles in dilute liquid ${}^3$He-${}^4$He mixtures affects many of its physical properties. The interaction potential is determined here from the saturation solubility and osmotic pressure data reported recently. The interactions are examined consistently over the entire pressure range of liquid-helium mixtures at very low temperatures, that is, from 0 to 25.6 bar, where the solid phase appears. To reproduce all experimental data, it was necessary to include a concentration dependence in the potential. This dependence, however, turned out to be almost the opposite to what has been proposed earlier. The deduced potential can be used to calculate, among other things, an estimate for the superfluid transition temperature of ${}^3$He-${}^4$He mixtures. In addition, we also find values for some less well-established parameters for helium mixtures, such as the binding energy of a ${}^3$He atom in superfluid ${}^4$He. DOI: http://dx.doi.org/10.1103/PhysRevB.85.134529 ©2012 American Physical Society