Dirac Shell Quark-core Model for the Study of Non-strange Baryonic Spectroscopy

Abstract

A Dirac shell model is developed for the study of baryon spectroscopy, taking into account the most relevant results of the quark-diquark models. The lack of translational invariance of the shell model is avoided, in the present work, by introducing a scalar-isoscalar fictitious particle that represents the origin of quark shell interaction; in this way the states of the system are eigenstates of the total momentum of the baryon. Only one-particle excitations are considered. A two-quark core takes the place of the diquark, while the third quark is excited to reproduce the baryonic resonances. For the N (939) and ∆(1232), that represent the ground states of the spectra, the three quarks are considered identical particles and the wave functions are completely antisymmetric. The model is used to calculate the spectra of the N and ∆ resonances and the nucleon magnetic moments. The results are compared to the present experimental data. Due to the presence of the core and to the one-particle excitations, the structure of the obtained spectra is analogous to that given by the quark-diquark models.

A local reduction of the Dirac equation applied to the study of quark interactions

“…In particular, the aim is to find a reduction of the DLE equation by establishing a relationship, or correlation, between the lower and upper components of the Dirac spinors of each interacting fermion. This correlation has the same structure of the solutions of the one-body Dirac equation in the "spin-symmetry" case [35,36]. We recall that a simplified Dirac-Coulomb equation was proposed for atomic systems [37].…”

“…This case, traditionally denoted as spin-symmetry case [35,36], allows for simple solutions of the Dirac equation, in which the spin-orbit interaction is absent and the orbital angular momentum and the spin are decoupled.…”

“…Also, the same definitions of Eqs. ( 33)- (36) for the two-body equal mass problem are used here. The correlated Dirac state is given by Eq.…”

“…In the CM frame, one has to specify the relative variables of the bound system; for equal mass particles, using Eqs. ( 33) - (36), one defines…”