RPA-approach to the excitations of the nucleon Part II: Phenomenology

Abstract

The tensor-RPA approach developed previously in part I is applied to the Nambu-Jona-Lasinio (NJL) model. As a first step we investigate the structure of Dirac-Hartree-Fock solutions for a rotationally and isospin invariant ground-state density. Whereas vacuum properties can be reproduced, no solitonic configuration for a system with unit baryon number is found. We then solve the tensor-RPA equation employing simple models of the nucleon ground state. In general the ph interaction effects a decrease of the excited states to lower energies. Due to an enhanced level density at low energies the obtained spectra cannot be matched with the experimental data when a standard MIT-bag configuration is used. However, when the size of the nucleon quark core is reduced to ≈ 0.3f m a fair description of the baryon spectrum in the positive-parity channel is achieved. For this purpose the residual interaction turns out to be crucial and leads to a significant improvement compared with the mean-field spectra.

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

“…On a nonscalar ground state this symmetry is broken. In part II of this paper [34] we will find that for the cases under investigation the spectrum is still approximately symmetric as long as the eigenvalues are real.…”