The Random-Phase Approximation for Collective Excitations

Abstract

The random-phase approximation (RPA) is a theory of small-amplitude vibrations in the quantum many-body system. The name was coined in the first application of the method by Bohm and Pines [4.1] to the plasma oscillations of an electron gas. The theory is equivalent to a limit of timedependent Hartree—Fock theory in which the amplitude of the motion is small. Consequently, the applicability of the theory is restricted to systems where a Hartree—Fock or some effective mean-field theory provides a good description of the ground state. Thus the theory is best for closed-shell nuclei. To the extent that open-shell nuclei can be described with Hartree—Fock-Bogoliubov theory, a corresponding generalization can be applied, the quasi-particle RPA. The first applications in nuclear physics were to collective quadrupole states in open-shell nuclei by Baranger [4.2] and to the collective octupole state in spherical nuclei by Brown, Evans, and Thouless [4.3]. Early applications to nuclear physics were partly phenomenological, owing to deficiencies in the interaction and numerical limitations in the size of the configuration space. With improved interactions and present computer resources, RPA has proven itself to be a robust theory, capable of predicting and describing in detail many properties of collective excitations.