A SEMICLASSICAL APPROXIMATION TO TIME-DEPENDENT HARTREE-FOCK THEORY

摘要

Working within a Time-Dependent Hartree-Fock framework, we develop a semiclassical approximation appropriate for large systems. We demonstrate that the standard semiclassical approach, the Thomas-Fermi approximation, is inconsistent with Hartree-Fock theory when the basic two-body interaction is short-ranged (as in nuclear systems, for example). However, by introducing a simple extension of the Thomas-Fermi approximation, we overcome this problem. We also discuss the infinite nuclear matter problem and point out that Time-Dependent Hartree-Fock theory yields collective modes of the zero sound variety instead of ordinary hydrodynamic (first) sound. We thus emphasize that one should be extremely circumspect when attempting to cast the equations of motion of Time-Dependent Hartree-Fock theory into a hydrodynamic-like form.