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.

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.

The fission barriers of the nuclei 254 Fm, 256 Fm, 258 Fm, 258 No, and 260 Rf are investigated in a fully microscopic way up to the scission point. The analysis is based on the constrained Hartree-Fock-Bogoliubov theory and Gogny's D1S force. The quadrupole, octupole, and hexadecapole moments as well as the number of nucleons in the neck region are used as constraints. Two fission paths, corresponding to the bimodal fission, are found. The decrease with isotope mass of the half-life times of heavy Fm isotopes is also explained.

A systematic study of 160 heavy and superheavy nuclei is performed in the Hartree-Fock-Bogoliubov (HFB) approach with the finite-range and density-dependent Gogny force with the D1S parameter set. We show calculations in several approximations: with axially symmetric and reflection-symmetric wave functions, with axially symmetric and non-reflection-symmetric wave functions, and finally with some representative triaxial wave functions. Relevant properties of the ground state and along the fission path are thoroughly analyzed. Fission barriers, Q α factors, and lifetimes with respect to fission and α decay as well as other observables are discussed. Larger configuration spaces and more general HFB wave functions as compared to previous studies provide a very good agreement with the experimental data.

We study whether the neutron skin thickness r np of 208 Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to r np arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical of relativistic models, predict a bulk contribution in r np of 208 Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that r np of 208 Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of r np of 208 Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of r np . We also note that most models predict a mixed-type (between halo and skin) neutron distribution for 208 Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the 208 Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the 208 Pb nucleon densities.

The neutron skin thickness of nuclei is a sensitive probe of the nuclear symmetry energy and has multiple implications for nuclear and astrophysical studies. However, precision measurements of this observable are difficult to obtain. The analysis of the experimental data may imply some assumptions about the bulk or surface nature of the formation of the neutron skin. Here we study the bulk or surface character of neutron skins of nuclei following from calculations with Gogny, Skyrme, and covariant nuclear mean-field interactions. These interactions are successful in describing nuclear charge radii and binding energies but predict different values for neutron skins. We perform the study by fitting two-parameter Fermi distributions to the calculated self-consistent neutron and proton densities. We note that the equivalent sharp radius is a more suitable reference quantity than the half-density radius parameter of the Fermi distributions to discern between the bulk and surface contributions in neutron skins. We present calculations for nuclei in the stability valley and for the isotopic chains of Sn and Pb.

Abstract. The density dependence of the symmetry energy around saturation density, characterized by the slope parameter L, is studied using information provided by the neutron skin thickness in finite nuclei. An estimate for L is obtained from experimental data on neutron skins extracted from antiprotonic atoms. We also discuss the ability of parity-violating elastic electron scattering to obtain information on the neutron skin thickness in 208 Pb and to constrain the density dependence of the nuclear symmetry energy. The size and shape of the neutron density distribution of 208 Pb predicted by mean-field models is briefly addressed. We conclude with a comparative overview of the L values predicted by several existing determinations.