Small-amplitude limit of the nuclear Born-Oppenheimer method.

Abstract

We examine here how the nuclear Born-Oppenheimer (NBO) method describes the collective dynamics of nuclei undergoing small-amplitude oscillations around the equilibrium state. After specifying the NBO trial wave function, and assuming that the intrinsic state is not very different from the Hartree-Fock (HF) ground state, we show that the NBO method yields the random phase approximation (RPA) equations. We then derive an expression for the ground state energy. This expression, which contains zero-point energy correction terms, is smaller than the static HF energy. Next, we derive the correlated ground state energy and then show that it is identical with the corresponding expressions obtained from the generator-coordinate method, from the properly quantized adiabatic time-dependent Hartree-Fock approach, and from the RPA.