Ground-state correlations and restoration of broken symmetry to nuclear mean field theory

Abstract

We reconsider the long-standing problem that the ground-state correlations predicted by the standard quasiboson (random phase) approximation are too large by a factor of two in the limit of weak residual interaction, and are thus inconsistent with the Pauli exclusion principle. We solve this problem by noting that for the derivation of the equations of the random phase approximation (RPA), which determine a set of matrix elements and excitation energies, it is unnecessary to assume that the ground state is the vacuum of a set of boson excitations, whereas in the faculty calculation of the ground-state correlation energy, this assumption is made. For the study of excitation energies and the restoration of symmetries broken by an initial mean-field solution, we apply a symmetry-preserving form of the equations of motion for fermion particle-hole excitation operators rather than for bosons. We illustrate this for the case of translations. We then describe a separate calculation of the ground-state energy that is consistent with the Pauli principle, but can nevertheless be evaluated in terms of the solutions of the RPA equations of motion. In contrast to some earlier work, we treat direct and exchange terms on an equal footing throughout.