Weak 3He Pairing in 3He-He(II) Mixtures

In this paper a theoretical study of a possible phase transition in dilute He-3-He(II) mixtures is presented using the Galitskii-Migdal-Feynman formalism. The effective scattering length is calculated from the Galitskii-Migdal-Feynman T-matrix, which is essentially the effective scattering amplitude dependent on the medium. It is found that at very low He-3 concentrations the s-wave effective scattering length for He-3-He(II) varies discontinuously from positive to negative values at some critical concentration. This indicates a crossover from a regime with dimers to another with the Cooper pairs. The binding energy of the weakly-bound dimers He-3(2) is computed. The effective p-wave scattering lengths are calculated and compared to the effective s-wave scattering lengths at low and high concentrations. It is found that p-scattering has an important effect on the instability of these mixtures at concentrations x > 1%. Finally, the transport coefficients are computed and compared to the theoretical predictions of Fu and Pethick and the experimental results of Konig and Pobell.