The remaining uncertainties of isovector nuclear interactions call for reliable experimental measurements of isovector probes in finite nuclei. Based on the Bayesian analysis, although the neutron-skin thickness data or the isovector giant dipole resonance data in $^{208}$Pb can constrain only one isovector interaction parameter, correlations between other parameters are built. Using combined data of both the neutron-skin thickness and the isovector giant dipole resonance helps to constrain significantly all isovector interaction parameters, thus serves as a useful way in the future analysis.
We put a stringent constraint on the isovector nuclear interactions in the Skyrme-Hartree-Fock model from the centroid energy $E_{-1}$ of the isovector giant dipole resonance in $^{208}$Pb as well as its electric polarizability $α_D$. Using the Bayesian analysis method, $E_{-1}$ and $α_D$ are found to be mostly determined by the nuclear symmetry energy $E_{sym}$ at about $ρ^\star=0.05$ fm$^{-3}$ and the isovector nucleon effective mass $m_v^\star$ at the saturation density. At $90\%$ confidence level, we obtain $E_{sym}(ρ^\star) = 16.4 ^{+1.0}_{-0.9}$ MeV and $m_v^\star/m = 0.79 ^{+0.06}_{-0.0…
Isoscalar density is a sum of neutron and proton densities and isovector is a normalized difference. Here, we report on the experimental evidence for the displacement of the isovector and isoscalar surfaces in nuclei, by $\sim$$0.9 \, \text{fm}$ from each other. We analyze data on quasielastic (QE) charge exchange (p,n) reactions, concurrently with proton and neutron elastic scattering data for the same target nuclei, following the concepts of the isoscalar and isovector potentials combined into Lane optical potential. The elastic data largely probe the geometry of the isoscalar potential and …
Recent improvements in the experimental determination of properties of the Isovector Giant Quadrupole Resonance (IVGQR), as demonstrated in the A=208 mass region, may be instrumental for characterizing the isovector channel of the effective nuclear interaction. We analyze properties of the IVGQR in 208Pb, using both macroscopic and microscopic approaches. The microscopic method is based on families of non-relativistic and covariant Energy Density Functionals (EDF), characterized by a systematic variation of isoscalar and isovector properties of the corresponding nuclear matter equations of sta…
We search for potential isovector signatures in the neutron-rich oxygen and calcium isotopes within the framework of a relativistic mean-field theory with an exact treatment of pairing correlations. To probe the isovector sector we calibrate a few relativistic density functionals using the same isoscalar constraints but with one differing isovector assumption. It is found that under certain conditions, the isotopic chain in oxygen can be made to terminate at the experimentally observed ${}^{24}$O isotope and in the case of the calcium isotopes at ${}^{60}$Ca. To produce such behavior, the resu…
The vibrational structure of the Pygmy Dipole Resonance (PDR) is investigated within a quantum many-body treatment with extended separable interactions able to encode the dependence of nuclear symmetry energy on density. A new picture of PDR is unveiled in terms of a combined dynamics of the neutron skin and of the core isovector polarization, which determines the isoscalar features of PDR while reproducing the isovector properties of Giant Dipole Resonance. The key role played by the variation with density of the symmetry energy on shaping the low-lying dipole response and its isoscalar-isove…
Within a Bayesian statistical framework using the standard Skyrme-Hartree-Fock model, the maximum {\it a posteriori} (MAP) values and uncertainties of nuclear matter incompressibility and isovector interaction parameters are inferred from the experimental data of giant resonances and neutron-skin thicknesses of typical heavy nuclei. With the uncertainties of the isovector interaction parameters constrained by the data of the isovector giant dipole resonance and the neutron-skin thickness, we have obtained $K_0 = 223_{-8}^{+7}$ MeV at 68% confidence level using the data of the isoscalar giant m…
The isoscalar and isovector particle densities and the surface tension coefficients at the average binding energy are used to derive analytical expressions of the neutron skin thickness and the isovector stiffness of sharp edged proton-neutron asymmetric nuclei. For most Skyrme forces these quantities are significantly larger than the well known ones. Using the analytical isovector surface energy constants in the framework of the hydrodynamical and the Fermi-liquid droplet models the mean energies and the sum rules of the isovector giant dipole resonances are in fair agreement with the experim…
Recent precise parity-violating electron scattering experiments on $^{48}$Ca (CREX) and $^{208}$Pb (PREX-II) provide a new insight on the formation of neutron skin in nuclei. Within the energy density functional (EDF) framework, we investigate the implications of CREX and PREX-II data on nuclear matter symmetry energy and isovector properties of finite nuclei: neutron skin thickness and dipole polarizability. The weak-charge form factors from the CREX and PREX-II experiments are employed directly in constraining the relativistic density-dependent point coupling EDFs. The EDF established with t…
We show in the Skyrme-Hartree-Fock approach that unambiguous correlations exist between observables of finite nuclei and nuclear matter properties. Using this correlation analysis to existing data on the neutron skin thickness of Sn isotopes, we find important constraints on the value E_{sym}(rho_0) and density slope L of the nuclear symmetry energy at saturation density. Combining these constraints with those from recent analyses of isospin diffusion and double neutron/proton ratio in heavy ion collisions leads to a value of L=58\pm 18 MeV approximately independent of E_{sym}(ρ_0).
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…
Efficiency corrected single ratios of neutron and proton spectra in central $^{112}$Sn+$^{112}$Sn and $^{124}$Sn+$^{124}$Sn collisions at 120 MeV/u are combined with double ratios to provide constraints on the density and momentum dependencies of the isovector mean-field potential. Bayesian analyses of these data reveal that the isoscalar and isovector nucleon effective masses, $m_s^* - m_v^*$ are strongly correlated. The linear correlation observed in $m_s^* - m_v^*$ yields a nearly independent constraint on the effective mass splitting $Δm_{np}^*= (m_n^*-m_p^*)/m_N = -0.05_{-0.09}^{+0.09}δ$.…
In the present work, we use a finite range effective interaction to calculate the neutron skin thickness in $^{48}$Ca and correlate these quantities with the parameters of nuclear symmetry energy. Available experimental data on the neutron skin thickness in $^{48}$Ca are used to deduce information on the density slope parameter and the curvature symmetry parameter of the nuclear symmetry energy at saturation and at subsaturation densities. We obtained the constraints such as $54.5\leq L(ρ_0) \leq 97.5$ MeV and $47.3\leq L(ρ_c) \leq 57.1$ MeV for the density slope parameter. The constraints on …
The neutron skin and halo distributions in medium and heavy nuclei are calculated within the extended Thomas-Fermi approximation. Calculations are carried out for the effective Skyrme-like forces using the direct variational method. The analytical expression for the isovector shift of the rms radii $Δr_{np}$ as a sum of skin- and halo-like terms is obtained. The contribution of halo and skin terms to $Δr_{np}$ are found to be approximately equal.
We study the correlation between the neutron skin development and the low-energy dipole response associated with the pygmy dipole resonance (PDR) in connection with the properties of symmetry energy. We perform our investigation within a microscopic transport model based on the Landau-Vlasov kinetic equation by employing three different equations of state in the isovector sector. Together with the giant dipole resonance (GDR) for all studied systems, we identify a PDR collective mode whose energy centroid is very well described by the parametrization E_{PDR}=41 A^{-1/3}. A linear correlation b…
Background: Measurements of neutron radii provide important constraints on the isovector sector of nuclear density functionals and offer vital guidance in areas as diverse as atomic parity violation, heavy-ion collisions, and neutron-star structure. Purpose: To assess the impact of spin-orbit currents on the electromagnetic- and weak-charge radii of a variety of nuclei. Special emphasis is placed on the experimentally accessible electroweak skin, defined as the difference between weak-charge and electromagnetic-charge radii. Methods: Two accurately calibrated relativistic mean field models are…
Background: Neutron-skin thickness is an excellent indicator of isovector properties of atomic nuclei. As such, it correlates strongly with observables in finite nuclei that depend on neutron-to-proton imbalance and the nuclear symmetry energy that characterizes the equation of state of neutron-rich matter. A rich worldwide experimental program involving studies with rare isotopes, parity violating electron scattering, and astronomical observations is devoted to pinning down the isovector sector of nuclear models. Purpose: We assess the theoretical systematic and statistical uncertainties of n…
Constraining the nuclear symmetry energy with electric dipole polarizability and neutron skin characteristics in \texorpdfstring{$^{208}\mathrm{Pb}$}{208Pb} within antisymmetrized molecular dynamics
China Institute of Atomic Energy（中国原子能科学研究院）；Department of Physics, Graduate School of Science, Tohoku University（东北大学理学研究科物理学系）；Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University（广西师范大学核物理与技术重点实验室）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
We perform Time Dependent Hartree-Fock (TDHF) calculations to investigate the small amplitude dipole response of selected neutron-rich nuclei and Sn isotopes. A detailed comparison with the dipole strength predicted by Random-Phase Approximation (RPA) calculations is presented for the first time. TDHF results are also confronted to Vlasov calculations, to explore up to which extent a semi-classical picture can explain the properties of the nuclear response. The focus is on the low-energy response, below the Giant Dipole Resonance region, where different modes of non negligible strength are ide…
Constraining neutron-proton effective mass splitting through nuclear giant dipole resonance within transport approach
College of Science, University of Shanghai for Science and Technology（上海理工大学理学院）；Istituto Nazionale di Fisica Nucleare (INFN), Laboratori Nazionali del Sud（意大利国家核物理研究所南部分离实验室）；INFN, Sezione di Catania（意大利国家核物理研究所卡塔尼亚分部）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（复旦大学-国家自然科学基金委理论核物理上海研究中心）；Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University（中山大学中法核工程与技术学院）；Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), and Institute of Modern Physics, Fudan University（复旦大学现代物理研究所、核物理与离子束应用教育部重点实验室）
We show that the neutron skin thickness $Δr_{np}$ of heavy nuclei is uniquely fixed by the symmetry energy density slope $L(ρ)$ at a subsaturation cross density $ρ_c \approx 0.11$ fm$^{-3}$ rather than at saturation density $ρ_0$, while the binding energy difference $ΔE$ between a heavy isotope pair is essentially determined by the magnitude of the symmetry energy $E_{\text{sym}}(ρ)$ at the same $ρ_c$. Furthermore, we find a value of $L({ρ_c})$ leads to a negative $E_{\text{sym}}({ρ_{0}})$-$L({ρ_{0}})$ correlation while a value of $E_{\text{sym}}({ρ_{c})}$ leads to a positive one. Using data o…
The effect of correlations between the slope and the curvature of the symmetry energy on ground state nuclear observables is studied within the extended Thomas-Fermi approximation. We consider different isovector probes of the symmetry energy, with a special focus on the skin of $^{208}{\rm Pb}$. We use a recently proposed meta-modelling technique to generate a large number of equation of state models, where the empirical parameters are independently varied. The results are compared to a set of calculations using 17 different Skyrme interactions. We show that the curvature parameter plays a no…
The charge-exchange (3He,t) scattering to the isobaric analog state (IAS) of the target can be considered as "elastic" scattering of 3He by the isovector term of the optical potential (OP) that flips the projectile isospin. Therefore, the accurately measured charge-exchange scattering cross- section for the IAS can be a good probe of the isospin dependence of the OP, which is determined exclusively within the folding model by the difference between the neutron and proton densities and isospin dependence of the nucleon-nucleon interaction. Given the neutron skin of the target is related directl…
Bayesian analyses on both isoscalar and isovector nuclear interaction parameters are carried out based on the Korea-IBS-Daegu-SKKU (KIDS) model under the constraints of nuclear structure data of $^{208}$Pb and $^{120}$Sn. Under the constraint of the neutron-skin thickness, it is found that incorporating the curvature parameter $K_{sym}$ of nuclear symmetry energy as an independent variable significantly broadens the posterior probability distribution function (PDF) of the slope parameter $L$, and affects the related correlations. Typically, the anticorrelation between $L$ and the symmetry ener…
We investigate the isoscalar and isovector E1 response of neutron-rich nuclei, within a semi-classical transport model employing effective interactions for the nuclear mean-field. In particular, we adopt the recently introduced SAMi-J Skyrme interactions, whose parameters are specifically tuned to improve the description of spin-isospin properties of nuclei. Our analysis evidences a relevant degree of isoscalar/isovector mixing of the collective excitations developing in neutron-rich systems. Focusing on the low-lying strength emerging in the isovector response, we show that this energy region…
According to the Hugenholtz-Van Hove theorem, the nuclear symmetry energy $S(ρ)$ and its slope $L(ρ)$ at arbitrary densities can be decomposed in terms of the density and momentum dependence of the single-nucleon potentials in isospin-asymmetric nuclear matter which are potentially accessible to experiment. We quantify the correlations between several well-known isovector observables and $L(ρ)$ to locate the density range in which each isovector observable is most sensitive to the density dependence of the $S(ρ)$. We then study the correlation coefficients between those isovector observables a…
The recent high-resolution measurement of the electric dipole (E1) polarizability (alphad) in 208Pb [Phys. Rev. Lett. 107, 062502 (2011)] provides a unique constraint on the neutron-skin thickness of this nucleus. The neutron-skin thickness (rskin) of 208Pb is a quantity of critical importance for our understanding of a variety of nuclear and astrophysical phenomena. To assess the model dependence of the correlation between alphad and rskin, we carry out systematic calculations for 208Pb, 132Sn, and 48Ca based on the nuclear density functional theory (DFT) using both non-relativistic and relat…
Based on the accurately calibrated interaction FSUGold, we show that including isovector scalar $δ$ meson and its coupling to isoscalar scalar $σ$ meson in the relativistic mean field (RMF) model can soften the symmetry energy $E_{\rm{sym}}(n)$ at intermediate densities while stiffen the $E_{\rm{sym}}(n)$ at high densities. We find this new RMF model can be simultaneously compatible with (1) the constraints on the equation of state of symmetric nuclear matter at suprasaturation densities from flow data in heavy-ion collisions, (2) the neutron skin thickness of $^{208}$Pb from the PREX-II exper…
We present an equation of state (EoS) for neutron stars using the relativistic mean-field model with isoscalar- and isovector-meson mixing. Taking into account the results of the neutron skin thickness, $R_{\rm skin}$, of $^{208}$Pb reported by the PREX collaboration, the dimensionless tidal deformability of a canonical neutron star observed from GW170817, and a $2.6$ $M_{\odot}$ compact star implied by the secondary component of GW190814, a new effective interaction is constructed so as to reproduce the saturation condition of nuclear matter and the ground-state properties of finite, closed-s…
The strong dependence of Coulomb energies on nuclear radii makes it possible to extract the latter from calculations of the former. The resulting estimates of neutron skins indicate that two mechanisms are involved. The first one---isovector monopole polarizability---amounts to noting that when a particle is added to a system it drives the radii of neutrons and protons in different directions, tending to equalize the radii of both fluids independently of the neutron excess. This mechanism is well understood and the Duflo-Zuker (small) neutron skin values derived 14 years ago are consistent wit…
The effective-surface approximation is extended taking into account derivatives of the symmetry-energy density per particle with respect to the mean particle density. The isoscalar and isovector particle densities in this extended effective-surface approximation are derived. The improved expressions of the surface symmetry energy, in particular, its surface tension coefficients in the sharp-edged proton-neutron asymmetric nuclei take into account important gradient terms of the energy density functional. For most Skyrme forces the surface symmetry-energy constants and the corresponding neutron…
The experimental and theoretical studies of Giant Resonances, or more generally of the nuclear collective vibrations, are a well established domain in which sophisticated techniques have been introduced and firm conclusions reached after an effort of several decades. From it, information on the nuclear equation of state can be extracted, albeit not far from usual nuclear densities. In this contribution, which complements other contributions appearing in the current volume, we survey some of the constraints that have been extracted recently concerning the parameters of the nuclear symmetry ener…
A benchmark experiment on 208Pb shows that polarized proton inelastic scattering at very forward angles including 0° is a powerful tool for high-resolution studies of electric dipole (E1) and spin magnetic dipole (M1) modes in nuclei over a broad excitation energy range to test up-to-date nuclear models. The extracted E1 polarizability leads to a neutron skin thickness r_skin = 0.156+0.025-0.021 fm in 208Pb derived within a mean-field model [Phys. Rev. C 81, 051303 (2010)], thereby constraining the symmetry energy and its density dependence, relevant to the description of neutron stars.
The density dependence of the symmetry energy, instrumental in understanding the behaviour of the asymmetric nuclear matter, is investigated within the extended relativistic mean field (ERMF) model which includes the contributions from the self and mixed interaction terms for the scalar-isoscalar ($σ$), vector-isoscalar ($ω$) and vector-isovector ($ρ$) mesons upto the quartic order. Each of the 26 different parameterizations of the ERMF model employed are compatible with the bulk properties of the finite nuclei. The behaviour of the symmetry energy for several parameter sets are found to be co…
Revisiting neutron-skin thickness and dipole polarizability constraints on the symmetry energy in Antisymmetrized Molecular Dynamics
China Institute of Atomic Energy（中国原子能科学研究院）；Tohoku University（东北大学）；Guangxi Normal University（广西师范大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）
With a newly improved isospin- and momentum-dependent interaction and an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, we have investigated the effects of the slope parameter $L$ of the nuclear symmetry energy and the isospin splitting of the nucleon effective mass $m_{n-p}^*=(m_n^*-m_p^*)/m$ on the centroid energy of the isovector giant dipole resonance and the electric dipole polarizability in $^{208}$Pb. With the isoscalar nucleon effective mass $m_s^*=0.7m$ constrained by the empirical optical potential, we obtain a constraint of $L=64.29\pm11.84 (\rm MeV)$ and $m_{n-p}^*=…
The radii of nucleon distribution, bulk density, and neutron skin in nuclei beyond the β-stability line are studied within the direct variational method. We evaluate the partial equation of state of finite nuclei and demonstrate that the bulk density decreases beyond the beta stability line. We show that the growth of the neutron skin in unstable nuclei does not obey the saturation condition because of the polarization effect. The value of the neutron-skin thickness Δr_{np}=\sqrt{<r_n^2>}-\sqrt{<r_p^2>} is caused by the different radii (skin effect) and only slightly by the different shapes (h…
The isospin dependence of in-medium nuclear effective interactions is a fundamental issue in nuclear physics and has broad ramifications in astrophysics. Its uncertainties, especially the difference of neutron-proton interactions in the isosinglet and isotriplet channels, affect significantly the density and momentum dependence of the isovector single-nucleon potential and nucleon-nucleon short-range correlation in neutron-rich matter. Consequently, the neutron-proton effective mass splitting and the density dependence of nuclear symmetry energy are still rather uncertain. Heavy-ion reactions …
The determination of nuclear symmetry energy, and in particular, its density dependence, is a long-standing problem for nuclear physics community. Previous studies have found that the product of electric dipole polarizability $α_D$ and symmetry energy at saturation density $J$ has a strong linear correlation with $L$, the slope parameter of symmetry energy. However, current uncertainty of $J$ hinders the precise constraint on $L$. We investigate the correlations between electric dipole polarizability $α_D$ (or times symmetry energy at saturation density $J$) in Sn isotopes and the slope parame…
Four quantities deducible from nuclear structure experiments have been claimed to correlate to the slope parameter $L$ of the symmetry energy; the neutron skin thickness, the cross section of low-energy dipole (LED) mode, dipole polarizability $α_D$, and $α_D S_0$ (i.e. product of $α_D$ and the symmetry energy $S_0$). By the calculations in the Hartree-Fock plus random-phase approximation with various effective interactions, we compare the correlations between $L$ and these four quantities. The correlation derived from different interactions and the correlation from a class of interactions tha…
