An intepretation of time-dependent Hartree-Fock theory

Abstract

The eigenvalue equation of the random phase approximation (RPA) has been applied successfully to nuclear vibrations, but it is difficult to justify the approximation in physical terms. Some authors derive the equations from time-dependent Hartree-Fock (TDHF) theory, on the grounds that it is more physical. In this paper we point out that this claim is dubious. The meaning of TDHF theory, especially of the wave function, is not nearly as apparent as might appear at first sight. We study the TDHF and RPA methods, and show that the approximations involved in the two approaches are in fact equivalent. In particular it is demonstrated that the TDHF method is not an adiabatic approximation and neither is it a classical or semi-classical treatment. A new interpretation of TDHF theory is developed; this gives insight into the mechanism of nuclear vibrational motion, and exhibits its relationship with other methods.