Ground-state and low-excited properties of liquid 3He calculated with a two-body potential

Abstract

Although scattering phase shifts reveal that the interaction of two free 3He atoms with the momenta and spins of quasi-particles in liquid 3He is attractive, the experimental spin-averaged effective quasi-particle interaction ( F s) defined in Landau's Fermi-liquid theory is repulsive in liquid 3He. To understand the role of many-body effects in the repulsive interaction, we have calculated the bulk properties of liquid 3He using the Bethe-Goldstone method and using Goldstone perturbation theory. The compressibility yields a value for F 0 s, the angular average of F s. The potential used in our calculations is a hard-core square-well potential adjusted to approximate the phase shifts of the de Boer 6–12 potential. The properties we computed with the Bethe-Goldstone method give good agreement with experiment for effective masses m B ∗ between 1.0 and 1.4 times the true mass. We were unable to determine m B ∗ self-consistently. In liquid 3He three-body correlations are expected to be important. Using techniques developed for nuclear matter by Bethe and his co-workers, we estimated all two and three-body Goldstone diagrams. The properties we computed are in very good agreement with experiment. Since the net three-body energy is obtained in our calculation by adding repulsive and attractive contributions much larger in absolute value than their sum, these numbers should not be taken too seriously. Three-body diagrams contribute most of the binding energy in our calculation. The three-body repulsive energy is about 60% of the two-body repulsive energy. We describe qualitatively how the Pauli principle helps suppress the contributions of higher clusters. As particles are added to a self-bound many-body system or a system under pressure, the binding energy per particle decreases. Those particles originally present are rearranged into an “excited” state. In both the Bethe-Goldstone and Goldstone-perturbation-theory calculations, the rearrangement contributions are large enough to make the calculated effective quasi-particle interaction repulsive.