Nuclear Symmetry Energy Probed by Neutron Skin Thickness of Nuclei

Abstract

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...

Incompressibility of neutron-rich matter

“…A similar value of K τ ∼ −500 MeV has been reported from independent experimental evidence available from isospin diffusion observables in nuclear reactions [19,22] and from neutron skins of nuclei [25]. Tables II and III confirm that the hybrid model is consistent with both of the indicated K 0 and K τ values.…”

Accurate calibration of relativistic mean-field models: Correlating observables and providing meaningful theoretical uncertainties

“…Second, for the neutron-skin thickness of 208 Pb we find a theoretical error comparable to the one assumed for L and a correlation coefficient between the two observables of almost one (0.995). Such a strong correlation is consistent with two recent studies that employ a large number of accurately-calibrated relativistic and non-relativistic interactions to uncover the correlation [47,48]. Also consistent with recent studies [6,48], is the fact that the proposed 1% measurement of the neutron radius of 208 Pb by the PREx collaboration [42,43] may not be able to place a significant constrain on L. For example, our covariance analysis suggests that the 20% uncertainty assumed for L translates into a theoretical error in the neutron skin of 0.037 fm-or about a 0.7% uncertainty in the neutron radius of 208 Pb.…”

Neutron skin thickness from the measured electric dipole polarizability inNi68,Sn120, andRoca-Maza1, Viñas2, Centelles3 et al. 2015Phys. Rev. CSelf Cite225322543View full textAdd to dashboardCite

“…Future electroweak measurements will help narrow these intervals even further. Given the strong correlation between the neutron skin thickness of a neutron-rich nucleus and the slope of the symmetry energy L [33,36,60], it is reasonable to expect that the α D J-∆r np correlation will extend to the α D J-L case, as it has been explicitly shown for 208 Pb; see …”

“…In keeping with the fact that the ratio J/Q and the slope parameter L display a strong correlation [33], this semi-classical result clearly indicates that the electric dipole polarizability is related to properties of the nuclear symmetry energy [34]. Given its isovector character, it is also natural to expect that a semi-classical expression exists relating the neutron skin thickness ∆r DM np to bulk nuclear properties, such as the ratio J/Q, the density of nuclear matter at saturation ρ 0 ≡ 3/(4πr 3 0 ), and the relative neutron excess I = (N −Z)/A [33,35,36]. As elaborated in great detail in Ref.…”