Sensitivity of elements of the symmetry energy of nuclear matter to the properties of neutron-rich systems

The sensitivity of nuclear symmetry energy elements at the saturation density to the binding energies of ultra-neutron-rich nuclei (neutron-to-proton ratio $\sim 2$) and the maximum mass of a neutron star is explored within a relativistic mean field model. Values of the interaction parameters governing the isovector strengths and the symmetry elements are determined in tighter bounds. Assessments based on the sensitivity matrix reveal that the properties of extreme neutron-rich systems play a predominant role in narrowing down the uncertainties in the various symmetry energy parameters. The calculations are extended over a wide range of nuclear matter density, and the results are discussed.

Figure 1

Optimum values of the objective function (${\chi }_0^2$) are plotted as a function of $\mathrm{\Delta }{r}_{np}$ (neutron skin of ${}^{208}\mathrm{Pb}$) for two families of models, namely, SINPB-Variant and SINPA-Variant (see text for details).

Figure 2

Binding energy differences $\mathrm{\Delta }B [=B(\mathrm{SINPB})-B(\mathrm{SINPA}\left)\right]$ extracted using models SINPB and SINPA for even isotopes of O, Ca, and Ni nuclei plotted as a function of asymmetry $\delta$.

Figure 3

Relative sensitivity of different parameters of the effective Lagrangian density to three groups of fit data used in optimization of SINPA. These groups are nuclear binding energies ($B$), charge radii ($r_{ch}$), and maximum mass of a neutron star ($M_{\max }^{NS}$).

Figure 4

Same as Fig. 3, but with different grouping of the fit data of finite nuclei. One group contains binding energies of highly asymmetric nuclei (${}^{24}\mathrm{O}, {}^{30}\mathrm{Ne}, {}^{36}\mathrm{Mg}$, and ${}^{58}\mathrm{Ca}$) and another contains remaining fit data on the finite nuclei.

Figure 5

Relative sensitivity of the nuclear matter properties at saturation density to the fit data of SINPA with the same grouping as in Fig. 4.

Figure 6

Binding energy per nucleon for symmetric matter $\mathcal{E}$, symmetry energy parameter $C_{\mathrm{sym}}$, and its density derivative $L$ along with their errors as a function of density $\rho /{\rho }_0$ for SINPB and SINPA.

Figure 7

Square of the effective mass of $\mathbf{\rho }$ meson (scaled by ${10}^5$) as a function of density $\rho /{\rho }_0$ plotted for SINPB and SINPA.