RESPONSE FUNCTIONS FOR INFINITE FERMION SYSTEMS WITH VELOCITY DEPENDENT INTERACTIONS

Response functions of infinite Fermi systems are studied in the framework of the self-consistent random phase approximation (RPA). Starting from an effective interaction with velocity and density dependence, or equivalently from a local energy density functional, algebraic expressions for the RPA response function are derived. Simple formulae for the energy-weighted and polarizability sum rules are obtained. The method is illustrated by applications to nuclear matter and liquid 3He. In nuclear matter, it is shown that existing Skyrme interactions give spin-isospin response functions close to those calculated with finite range interactions. The different renormalization of longitudinal and transverse Coulomb sum rules in nuclear matter is discussed. In 3He, the low-lying collective spin oscillation can be well described in a wide range of momenta with a Skyrme-type interaction if the relevant Landau parameters are fitted. For the high-lying density oscillation, the introduction of a finite range term in the energy functional improves considerably the agreement with the data. © 1992 Academic Press, Inc. All rights reserved.