Quark mean field model with pion and gluon corrections

The properties of nuclear matter and finite nuclei are studied within the quark mean field (QMF) model by taking the effects of pions and gluons into account at the quark level. The nucleon is described as the combination of three constituent quarks confined by a harmonic oscillator potential. To satisfy the spirit of QCD theory, the contributions of pions and gluons on the nucleon structure are treated in second-order perturbation theory. In a nuclear many-body system, nucleons interact with each other by exchanging mesons between quarks. With different constituent quark mass, $m_q$, we determine three parameter sets for the coupling constants between mesons and quarks, named QMF-NK1, QMF-NK2, and QMF-NK3, by fitting the ground-state properties of several closed-shell nuclei. It is found that all of the three parameter sets can give a satisfactory description of properties of nuclear matter and finite nuclei, moreover they also predict a larger neutron star mass around $2.3M_{\odot }$ without hyperon degrees of freedom.

Figure 1

The effective nucleon masses $M_N^{*}$ as a function of the quark mass correction $\delta m_q$ for quark masses $m_q=250$ MeV (dotted curve), $m_q=300$ MeV (dashed curve), and $m_q=350$ MeV (solid curve).

Figure 2

The contributions of confinement potential, pion correction, and gluon correction to the effective nucleon mass $M_N^{*}$ as a function of the quark mass correction $\delta m_q$ at quark mass $m_q=350$ MeV. $M_Q, M_{\pi }$, and $M_G$ represent the confinement contribution, pion correction, and gluon correction, respectively.

Figure 3

The charge density distributions of ${}^{40}\mathrm{Ca}$ (a) and ${}^{208}\mathrm{Pb}$ (b) for QMF-NK1, QMF-NK2, and QMF-NK3 compared with the experimental data.

Figure 4

The difference between the ${}^{48}\mathrm{Ca}$ and ${}^{40}\mathrm{Ca}$ charge densities for QMF-NK1, QMF-NK2, and QMF-NK3, compared with the experimental data.

Figure 5

EOSs of symmetric nuclear matter and pure neutron matter in QMF-NK1, QMF-NK2, and QMF-NK3 for (a) $y_p=0.5$ and (b) $y_p=0.0$.

Figure 6

The mass-radius relations for neutron stars with QMF-NK1, QMF-NK2, and QMF-NK3.