We describe a relation between the symmetry energy coefficients csym(ρ) of nuclear matter and asym(A) of finite nuclei that accommodates other correlations of nuclear properties with the lowdensity behavior of csym(ρ). Here we take advantage of this relation to explore the prospects for constraining csym(ρ) of systematic measurements of neutron skin sizes across the mass table, using as example present data from antiprotonic atoms. The found constraints from neutron skins are in harmony with the recent determinations from reactions and giant resonances.PACS numbers: 21.10. Gv; 21.65.Ef; A wealth of measured data on densities, masses and collective excitations of nuclei has allowed to resolve basic features of the equation of state (EOS) of nuclear matter, like the density ρ 0 ≈ 0.16 fm −3 , energy per particle a v ≈ −16 MeV, and incompressibility K v ≈ 230 MeV [1] at saturation. However, the symmetry properties of the EOS due to differing neutron and proton numbers remain more elusive to date. The quintessential paradigm is the density dependence of the symmetry energy [1,2,3,4,5,6,7,8,9,10]. The accurate characterization of this property entails profound consequences in studying the neutron distribution in stable and exotic nuclei and neutron-rich matter [2,3,4]. It impacts on heavy ion reactions [5,6,7,8,9], nuclear astrophysics [3,4,10], and on diverse areas such as tests of the Standard Model via atomic parity violation [11].The general expression e(ρ, δ) = e(ρ, 0) + c sym (ρ)δ 2 + O(δ 4 ) for the energy per particle of nuclear matter of density ρ = ρ n + ρ p and asymmetry δ = (ρ n − ρ p )/ρ defines the symmetry energy coefficient c sym (ρ) of a nuclear EOS. It is customary and insightful to characterize the behavior of an EOS around the saturation density ρ 0 in terms of a few bulk parameters, like e(ρ, 0) , 6, 7, 12]. The value of J = c sym (ρ 0 ) is acknowledged to be about 32 MeV. The values of L = 3ρ∂c sym (ρ)/∂ρ| ρ0 and K sym = 9ρ 2 ∂ 2 c sym (ρ)/∂ρ 2 | ρ0 govern the density dependence of c sym around ρ 0 . They are less certain and the predictions vary largely among nuclear theories, see e.g. Ref.[7] for a review.In experiment, recent research in intermediate-energy heavy ion collisions (HIC) is consistent with a dependence c sym (ρ) = c sym (ρ 0 )(ρ/ρ 0 ) γ at ρ < ρ 0 [6,7,8,9]. Isospin diffusion predicts γ = 0.7-1.05 (L = 88 ± 25 MeV) [6,7], isoscaling favors γ = 0.69 (L ∼ 65 MeV) [8], and a value closer to 0.55 (L ∼ 55 MeV) is inferred from nucleon emission ratios [9]. Nuclear resonances are another hopeful tool to calibrate c sym (ρ) below ρ 0 [13,14,15,16]. Indeed, the giant dipole resonance (GDR) of 208 Pb analyzed with Skyrme forces suggests a constraint c sym (0.1 fm −3 ) = 23.3-24.9 MeV [14], implying γ ∼ 0.5-0.65. Note that the Thomas-Fermi model fitted very precisely to binding energies of 1654 nuclei [17] predicts an EOS that yields γ = 0.51. With the caveat that the connection of experiments to the EOS often is not at all trivial [6,7,8,9,13], it is important to seek further clues from th...

A precise determination of the neutron skin Δr(np) of a heavy nucleus sets a basic constraint on the nuclear symmetry energy (Δr(np) is the difference of the neutron and proton rms radii of the nucleus). The parity radius experiment (PREX) may achieve it by electroweak parity-violating electron scattering (PVES) on (208)Pb. We investigate PVES in nuclear mean field approach to allow the accurate extraction of Δr(np) of (208)Pb from the parity-violating asymmetry A(PV) probed in the experiment. We demonstrate a high linear correlation between A(PV) and Δr(np) in successful mean field forces as the best means to constrain the neutron skin of (208)Pb from PREX, without assumptions on the neutron density shape. Continuation of the experiment with higher precision in A(PV) is motivated since the present method can support it to constrain the density slope of the nuclear symmetry energy to new accuracy.

The information on the symmetry energy and its density dependence is deduced by comparing the available data on the electric dipole polarizability αD of 68 Ni, 120 Sn, and 208 Pb with the predictions of Random Phase Approximation, using a representative set of nuclear energy density functionals.The calculated values of αD are used to validate different correlations involving αD, the symmetry energy at the saturation density J, corresponding slope parameter L and the neutron skin thickness ∆rnp, as suggested by the Droplet Model. A subset of models that reproduce simultaneously the measured polarizabilities in 68 Ni, 120 Sn, and 208 Pb are employed to predict the values of symmetry energy parameters at saturation density and ∆rnp. The resulting intervals are: J = 30-35 MeV, L = 20-66 MeV; and the values for ∆rnp in 68 Ni, 120 Sn, and 208 Pb are in the ranges: 0.15-0.19 fm, 0.12-0.16 fm, and 0.13-0.19 fm, respectively. The strong correlation between the electric dipole polarizabilities of two nuclei is instrumental to predict the values of electric dipole polarizabilities in other nuclei.

We study the electric dipole polarizability α D in 208 Pb based on the predictions of a large and representative set of relativistic and nonrelativistic nuclear mean-field models. We adopt the droplet model as a guide to better understand the correlations between α D and other isovector observables. Insights from the droplet model suggest that the product of α D and the nuclear symmetry energy at saturation density J is much better correlated with the neutron skin thickness r np of 208 Pb than the polarizability alone. Correlations of α D J with r np and with the symmetry energy slope parameter L suggest that α D J is a strong isovector indicator. Hence, we explore the possibility of constraining the isovector sector of the nuclear energy density functional by comparing our theoretical predictions against measurements of both α D and the parity-violating asymmetry in 208 Pb. We find that the recent experimental determination of α D in 208 Pb in combination with the range for the symmetry energy at saturation density J = [31 ± (2) est ] MeV suggests r np ( 208 Pb) = 0.165 ± (0.009) expt ± (0.013) theor ± (0.021) est fm and L = 43 ± (6) expt ± (8) theor ± (12) est MeV.

We analyze the neutron skin thickness in finite nuclei with the droplet model and effective nuclear interactions. The ratio of the bulk symmetry energy J to the so-called surface stiffness coefficient Q has in the droplet model a prominent role in driving the size of neutron skins. We present a correlation between the density derivative of the nuclear symmetry energy at saturation and the J /Q ratio. We emphasize the role of the surface widths of the neutron and proton density profiles in the calculation of the neutron skin thickness when one uses realistic mean-field effective interactions. Next, taking as experimental baseline the neutron skin sizes measured in 26 antiprotonic atoms along the mass table, we explore constraints arising from neutron skins on the value of the J /Q ratio. The results favor a relatively soft symmetry energy at subsaturation densities. Our predictions are compared with the recent constraints derived from other experimental observables. Though the various extractions predict different ranges of values, one finds a narrow window L ∼ 45-75 MeV for the coefficient L that characterizes the density derivative of the symmetry energy that is compatible with all the different empirical indications.