RPA approach to the excitations of the nucleon Part I: Theory

Abstract

In this paper we develop a theoretical framework which allows us to study excitations of the nucleon. Assuming an effective two-body interaction as a model for low-energy QCD, we derive a relativistic TDHF equation for a many-body system of quarks. To render the Dirac-sea contribution to the mean field finite, we introduce a symmetry conserving regularization scheme. In the small amplitude limit we derive an RPA equation. The structure of the ph interaction and modifications due to the regularization scheme are discussed. We give a prescription to obtain a nucleon state with good angular momentum (J) and isospin (T ) quantum numbers on mean-field level. To study excitations, we develop a tensor-RPA approach, which is an extension of the conventional RPA techniques to systems with a nonscalar ground state. This allows us to construct excited states with good (J/T ) quantum numbers. We discuss a method to reduce the overcomplete ph-space and compute the tensor-RPA interaction matrix elements. Finally we extend our scheme to include ( 3 2 + , 32 )-states.