Extended Skyrme interactions for nuclear matter, finite nuclei, and neutron stars

Recent progress in theory, experiment, and observation challenges the mean-field models by using the conventional Skyrme interaction, suggesting that the extension of the conventional Skyrme interaction is necessary. In this work, by fitting the experimental data of a number of finite nuclei together with a few additional constraints on nuclear matter using the simulated annealing method, we construct three Skyrme interaction parameter sets; namely, eMSL07, eMSL08, and eMSL09, based on an extended Skyrme interaction which includes additional momentum and density-dependent two-body forces to effectively simulate the momentum dependence of the three-body force. The three new interactions (i) can reasonably describe the ground-state properties and the isoscalar giant monopole resonance energies of various spherical nuclei used in the fit as well as the ground-state properties of many other spherical nuclei, (ii) nicely conform to the current knowledge on the equation of state of asymmetric nuclear matter, (iii) eliminate the notorious unphysical instabilities of symmetric nuclear matter and pure neutron matter up to a very high density of $1.2{\mathrm{fm}}^{-3}$, and (iv) simultaneously support heavier neutron stars with mass larger than two times the solar mass. One important difference of the three new interactions involves the prediction of the symmetry energy at supra-saturation densities, and these new interactions are thus potentially useful for the future determination of the largely uncertain high-density symmetry energy. In addition, the predictions of nuclear matter, finite nuclei, and neutron stars made using the three new interactions are compared with those made using the three typical interactions BSk22, BSk24, and BSk26 from the Brussels group.

Figure 1

Deviations of the binding energies (plus symbols) and charge rms radii (cross symbols) of a number of nuclei with atomic number $Z$ obtained from SHF calculations with eMSL07, eMSL08, and eMSL09 from those measured in experiments [80, 81, 82]. The bands indicate a deviation within $\pm 1\%$.

Figure 2

(a) Pressure of symmetric nuclear matter $P_{\mathrm{SNM}}\left(\rho \right)$, (b) the binding energy per nucleon of pure neutron matter $E_{\mathrm{PNM}}\left(\rho \right)$, and (c) the symmetry energy $E_{\mathrm{sym}}\left(\rho \right)$ as functions of densities obtained from HF calculations using eMSL07, eMSL08, eMSL09, BSk22, BSk24, and BSk26. Several constraints from analyzing experimental data and the predictions of theoretical calculations are also included for comparison (see text for the details).

Figure 3

(a) Density dependence of the symmetry energy $E_{\mathrm{sym}}\left(\rho \right)$ and (b) EOSs of pure neutron matter $E_{\mathrm{PNM}}\left(\rho \right)$ for the extended Skyrme interactions eMSL07, eMSL08, eMSL09, BSk22, BSk24, and BSk26. The shaded band in panel (a) is taken from Ref. [107]. The $E_{\mathrm{PNM}}\left(\rho \right)$ of APR is taken from Ref. [9] while that of BHF is from Ref. [87].

Figure 4

Density dependence of the Landau parameters of symmetric nuclear matter for the extended Skyrme interactions eMSL07, eMSL08, eMSL09, BSk22, BSk24, and BSk26. The short-dash-dotted lines indicate the critical stability conditions.

Figure 5

Similar to Fig. 4 but for pure neutron matter.

Figure 6

Mass-radius relation of neutron stars obtained with eMSL07, eMSL08, eMSL09, BSk22, BSk24, and BSk26. Some recent observational constraints [31, 32, 115, 116, 117] are also included for comparison (see text for details).