Theory of Dilute Mixtures of He^{3} in Liquid He^{4} at Low Temperatures
Abstract
Dilute mixtures of He^{3} in liquid He^{4} are regarded as a set of He^{3} atoms intereacting with elementary excitations of the He^{4}. The coupling between the He^{3} and the He^{4} is chosen phenomenologically and it is not weak but, for low temperatures, its main effects may be eliminated by means of two canonical transformations. The equations which determine the transformations describe the motion of a He^{4} excitation in the presence of one or two He^{3} atoms and, in the latter case, they resemble Faddeev's equations in the threebody problem. At low temperatures, there are few He^{4} excitations and many of the properties of the mixture are determined by the effective He^{3} Hamiltonian produced by the transformation. In this respect, the system behaves like a Fermi liquid. The He^{3}He^{3} potential is essentially momentumindependent and consists of the Van der Waals interaction together with an effectively repulsive potential induced by the He^{4}. It is suggested that a Fermiliquid analysis is the best way of obtaining information about this potential, and the possible existence of a fermion superfluid phase transition is discussed from that point of view.
 Publication:

Physical Review
 Pub Date:
 August 1966
 DOI:
 10.1103/PhysRev.148.138
 Bibcode:
 1966PhRv..148..138E