Equation of state of nuclear matter from empirical constraints

From empirically determined values of some of the characteristic constants associated with homogeneous nuclear matter at saturation and subsaturation densities, within the framework of a Skyrme-inspired energy density functional, we construct an equation of state (EoS) of nuclear matter. This EoS is then used to predict values of density slope parameters of symmetry energy $L\left(\rho \right)$, isoscalar incompressibility $K\left(\rho \right)$, and a few related quantities. The close consonance of our predicted values with the currently available ones for the density dependence of symmetry energy and incompressibility gleaned from diverse approaches offers the possibility that our method may help in settling their values in tighter bounds. Extrapolation of our EoS at supranormal densities shows that it is in good harmony with the one extracted from experimental data.

Figure 1

Plots for the variation of $e_{\mathrm{sym}}$ as a function of density $\rho$. The values of $e_{\mathrm{sym}}$ represented by the full and the dashed lines are obtained using two different definitions as given by Eqs. (5) and (6). The blue, magenta, and black lines correspond to $L_0=50$, 65.4, and 75 MeV at $\rho ={\rho }_0$. With $L_0=65.4$ MeV, one magenta line falls over the other; they can-not be distinguished from each other.

Figure 2

The normalized squared errors, ${\left(\frac{\partial X}{\partial Y_i}\frac{\Delta Y_i}{\Delta X}\right)}^2 \left(=x_i^2\right)$, are color coded. The quantities $X$ and $Y_i$ are given along the ordinate and abscissa respectively.

Figure 3

Our results for the equivalent density shown as a shaded region as a function of mass number. The blue triangles are from Ref. [10], the magenta line is from Ref. [6].

Figure 4

The EoS for symmetric nuclear matter (upper panel) and for pure neutron matter (lower panel). The red, yellow, and green shaded regions represent the experimental data taken from Refs. [53, 54, 55, 56]. The blue shaded regions are the EoS obtained in this work. See text for details.