Correlations in strongly interaction Fermi liquids

This thesis is to study correlation effects in strongly interacting Fermi liquids like electron gas or liquid 3He. In the first part, a systematic way of constructing effective interactions for self-energy calculation in Fermi liquid systems is developed in which effects of density- and spin-fluctuation and of multiple scattering between particles are included by means of the local field factors. The self-energy expression is then used to study effective masses in electron and electron-hole liquids where significant derivation from the RPA results are found in both cases. In the second part, a detailed study of a model Fermi-liquid system built to simulate liquid 3He is presented. Within the STLS theory and the above theory for self-energy, it was found that this model system does possess a number of properties qualitatively very similar to what is observed in the realistic system. The theory also provides some physical insights in the microscopic foundation of the Aldrich-Pines polarization-potential theory, and also on the properties of liquid 3He under pressure. The model and theory are then extended to study the case when the system is spin-polarized