Nuclear symmetry energy with mesonic cross-couplings in the effective chiral model

The effective chiral model is extended by introducing the contributions from the cross-couplings between isovector and isoscalar mesons. These cross-couplings are found to be instrumental in improving the density content of the nuclear symmetry energy. The nuclear symmetry energy as well as its slope and curvature parameters at the saturation density are in harmony with those deduced from a diverse set of experimental data. The equation of state for pure neutron matter at subsaturation densities is also in accordance with the ones obtained from different microscopic models. The maximum mass of a neutron star is consistent with the measurement, and the radius at the canonical mass of the neutron star is within the empirical bounds.

Figure 1

Symmetry energy as a function of scaled density $(\rho /{\rho }_0)$ is plotted for three different variants of the effective chiral model as labeled by NCC, SR, and WR obtained in the present work and are compared with those for a few selected RMF models: NL3, IUFSU, BSP, and BKA22. The constraints on the symmetry energy from HIC Sn+Sn [40], IAS [41], and ASY-EOS experimental data [42] are also displayed. The inset shows the blown-up behavior of symmetry energy at low densities.

Figure 2

$K$ and $K_{\tau }$ from different models as labeled in [43, 48] are compared with our models (NCC, SR, and WR). The vertical and horizontal dashed lines represent the empirical ranges for $K$ and $K_{\tau }$ respectively.

Figure 3

Energy per neutron as a function of scaled neutron density $({\rho }_n/{\rho }_0)$ for three different variants of the effective chiral model as labeled by NCC, SR, and WR obtained in the present work and for a few RMF models NL3, IUFSU, BSP, and BKA22 are compared with microscopic calculations [51, 52] as shown by the shaded region.

Figure 4

Pressure as a function of scaled density $(\rho /{\rho }_0)$ for the SNM (left) and the PNM (right). The SNM EOSs for the NCC, SR, and WR models are exactly the same and labeled as “this work.” For comparison, the SNM and PNM EOSs for a few RMF models NL3, IUFSU, BSP and BKA22 are displayed. The SNM and PNM EOSs shown by shaded regions are taken from Ref. [54] (see text for details).

Figure 5

Mass-radius relationships for the NCC, SR, and WR models. The effects of the crustal EOSs are incorporated by using explicitly the BPS and polytropic EOSs (solid lines) at low densities and alternatively using the ZFH method (dashed lines).