Effective interactions, transport properties, and elementary excitations in helium three-helium four mixtures

A unified theory of effective interaction, elementary excitations, transport properties, and possible superfluidity of 3He-4He mixtures has been developed. The basic approach is patterned after that of Aldrich and Pines (AP) for pure 4He and 3He , 1n which the consequence of the strong interactions in 3He and 4He is described in terms of self- consistent fields. The strength of these fields are determined by physical arguments, static measurement, and sum rule considerations. A set of pseudopotentials has been developed to describe the 3He-3He and 3He-4He interactions. In the long wavelength and zero concentration limit, these potentials are obtained by the thermodynamic argument of Bardeen, Baym, and Pines. At finite concentration and finite momentum-transfer, we obtain these potentials with the aids of a scaling law and the AP pseudopotential theory. From these pseudopotentials we calculate the scattering amplitudes, transport cofficients, and normal-superfluid transition temperature as functions of 3He concentration. We obtain good agreement between theory and experiment for low temperature transport coefficients, and predict the 3He superfluid transition temperature to be ~ 10-8oK. The change in the density fluctuation excitation spectrum of 4He atoms in 3He-4He mixtures is calculated by including three physical effects: (i) the change in the particle density, (ii) mode-mode coupling iv between 4He and 3He density fluctuation, (iii) direct scattering of 4He rotons against 3He quasiparticles. By using the theory developed by Aldrich and Pines, the pseudopotentials developed in this thesis and the 3He quasiparticle spectrum proposed by Greywall, we calculate the first two effects without any free parameter, and obtain excellent agreement with experiment at low temperatures (T < O.7°K). A schematic model is introduced to describe the effect of roton-3He quasiparticle collisions; it explains the energy shift near the roton minimum and the increase in line width of the phonon-maxon-roton spectrum at high temperatures (T > 1K)U of I OnlyThesi