Effects of the symmetry energy on the isovector properties of neutron-rich nuclei within a Thomas-Fermi approach

Abstract

We employ a variational method, in the framework of the Thomas-Fermi approximation, to study the effect of the symmetry energy on the neutron skin thickness and the symmetry energy coefficients of various neutron rich nuclei. We concentrate our interest on 208 Pb, 124 Sn, 90 Zr, and 48 Ca, although the method can be applied in the totality of medium and heavy neutron rich nuclei. Our approach has the advantage that the isospin asymmetry function α(r), which is the key quantity to calculate isovector properties of various nuclei, is directly related with the symmetry energy as a consequence of the variational principle. Moreover, the Coulomb interaction is included in a self-consistent way and its effects can be separated easily from the nucleon-nucleon interaction. We confirm, both qualitatively and quantitatively, the strong dependence of the symmetry energy on the various isovector properties for the relevant nuclei, using possible constraints between the slope and the value of the symmetry energy at the saturation density. PACS number(s): 21.65. Ef, 21.65.Mn, 21.65.Cd, 21.10.Gv

Constraints on the nuclear equation of state from nuclear masses and radii in a Thomas-Fermi meta-modeling approach

“…8, along with the results from the full ETF calculation with the optimized empirical data set of Table I. It is clear from the figure that within the uncertainties of the empirical parameters, our model predicts neutron skins compatible with experimental results, with a comparable level of precision as complete ETF calculations [47].…”

“…However, other correlations shown in the literature with E sym or K sym [11,47] are not observed here, which might again indicate the model dependence of these correlations.…”

Evolution of newborn rapidly rotating magnetars: Effects ofR-mode and fall-back accretion

“…A polytropic EOS of N = 0 or 1 is usually used, while the resulting timescales for these two polytropic EOSs differ only by roughly a factor of two (we refer to a review by Andersson et al (2001) and references therein). The effects of more realistic EOSs have been tested by Papazoglou & Moustakidis (2016), whose results show only small differences from those of the N = 1 polytropic EOS. Following Alford et al (2012a,b), we consider the Akmal-Pandharipande-Ravenhall (APR) EOS (Akmal et al 1998), since this EOS gives a better approximation of the equilibrium configuration than the polytropic EOSs for r-mode oscillations.…”

Nuclear Symmetry Energy Effects on the Bulk Properties of Neutron-rich Finite Nuclei

“…The energy density functional is an extension to the above formula, where the total energy of finite nuclei is a functional of the total density ρ(r) and the isospin asymmetry function α(r) [1],…”

“…Instead of solving this differential equation, we are using a trial function given by the Fermi-type formula [1]…”