We present and discuss numerical predictions for the neutron density distribution of $^{208}$Pb using various non-relativistic and relativistic mean-field models for the nuclear structure. Our results are compared with the very recent pion photoproduction data from Mainz. The parity-violating asymmetry parameter for elastic electron scattering at the kinematics of the PREX experiment at JLab and the neutron skin thickness are compared with the available data. We consider also the dependence between the neutron skin and the parameters of the expansion of the symmetry energy.
Direct hard photon emissions from incoherent proton-neutron bremsstrahlung in collisions of the neutron-rich projectile $^{50}$Ca with $^{12}$C and $^{40}$Ca targets are simulated in the framework of the isospin-dependent quantum molecular dynamics (IQMD) model. By adjusting the diffuseness parameter of neutron density in the droplet model to obtain different neutron skin thicknesses for $^{50}$Ca, the effects of neutron skin thickness on direct hard photon emission are investigated via several probes. The results show that more direct hard photons are produced with increasing neutron skin thi…
We analyze total reaction cross sections, $σ_R$, for exploring their sensitivity to the neutron-skin thickness of nuclei. We cover 91 nuclei of O, Ne, Mg, Si, S, Ca, and Ni isotopes. The cross sections are calculated in the Glauber theory using the density distributions obtained with the Skyrme-Hartree-Fock method in 3-dimensional coordinate space. Defining a reaction radius, $a_R=\sqrt{σ_R/π}$, to characterize the nuclear size and target (proton or $^{12}$C) dependence, we find an empirical formula for expressing $a_R$ with the point matter radius and the skin thickness, and assess two practi…
The interplay between the formation of neutron skin and alpha cluster at the dilute surface of neutron-rich nuclei is one of the interesting subjects in the study of neutron-rich nuclei and nuclear clustering. A theoretical model has predicted that the growth of neutron skin will prevent the alpha clustering at the nuclear surface. Quite recently, this theoretical perspective; the suppression of alpha clustering by the neutron-skin formation was first confirmed experimentally in Sn isotopes as the reduction of the (p, p alpha) reaction cross-section. Motivated by the novel discovery, in this w…
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 208Pb and to constrain the density dependence of the nuclear symmetry energy. The size and shape of the neutron density distribution of 208Pb predicted by mean-field…
The fragment production in collisions of $^{48,50}$Ca+$^{12}$C at 50 MeV/nucleon are simulated via the Isospin-Dependent Quantum Molecular Dynamics (IQMD) model followed by the {GEMINI code}. {By changing the diffuseness parameter of neutron density distribution to obtain different neutron skin size, the effects of neutron skin thickness ($δ_{np}$) on projectile-like fragments (PLF) are investigated. The sensitivity of isoscaling behavior to neutron skin size is studied, from which it is found that the isoscaling parameter $α$ has a linear dependence on $δ_{np}$. A linear dependence between $δ…
The formation of $α$-particle clusters on the surface of heavy nuclei is described in a generalized relativistic mean-field model with explicit cluster degrees of freedom. The effects on the size of the neutron skin of Sn nuclei and ${}^{208}$Pb are investigated as a function of the mass number and the isospin-dependent part of the effective interaction, respectively. The correlation of the neutron skin thickness with the difference of the neutron and proton numbers and with the slope of the nuclear symmetry energy is modified as compared to the mean-field calculation without alpha-cluster cor…
Multi-neutron systems are crucial to understanding the physics of neutron-rich nuclei and neutron stars. Neutron drops, neutrons confined in an external field, are investigated systematically in both non-relativistic and relativistic density functional theories and with ab initio calculations. We demonstrate a strong linear correlation, which is universal in the realm of mean-field models, between the rms radii of neutron drops and the neutron skin thickness of Pb-208 and Ca-48; i.e., the difference between the neutron and proton rms radii of a nucleus. Due to its high quality, this correlatio…
The correlation between the thickness of the neutron skin in Pb-208, and the degree of isospin diffusion in heavy-ion collisions is examined. The same equation of state is used to compute the degree of isospin diffusion in an isospin-depedent transport model and the neutron skin thickness in the Hartree-Fock approximation. We find that skin thicknesses less than 0.15 fm are excluded by the isospin diffusion data.
Probing the neutron-skin thickness through $J/ψ$ photoproduction in ultra-peripheral collisions
Shanghai Institute of Applied Physics, Chinese Academy of Sciences（中国科学院上海应用物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Fudan University（复旦大学）；East China Normal University（华东师范大学）
The neutron density distributions and neutron skin thicknesses in $^{40,48}$Ca are determined from the angular distributions of the cross sections and analyzing powers of polarized proton elastic scattering at $E_p = 295$ MeV. Based on the framework of the relativistic impulse approximation with the density-dependent effective $NN$ interaction, the experimental data is successfully analyzed, providing precise information of neutron and proton density profiles of $^{40,48}$Ca with small uncertainties. The extracted neutron and proton density distributions give neutron skin thicknesses in $^{40,…
We study the relation between neutron removal cross section ($σ_{-N}$) and neutron skin thickness for finite neutron rich nuclei using the statistical abrasion ablation (SAA) model. Different sizes of neutron skin are obtained by adjusting the diffuseness parameter of neutrons in the Fermi distribution. It is demonstrated that there is a good linear correlation between $σ_{-N}$ and the neutron skin thickness for neutron rich nuclei. Further analysis suggests that the relative increase of neutron removal cross section could be used as a quantitative measure for the neutron skin thickness in neu…
We describe a relation between the symmetry energy coefficients c_sym(rho) of nuclear matter and a_sym(A) of finite nuclei that accommodates other correlations of nuclear properties with the low-density behavior of c_sym(rho). Here we take advantage of this relation to explore the prospects for constraining c_sym(rho) 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.
A method is presented to extract the neutron-skin thickness of atomic nuclei from the second and fourth moments of the electric charge distribution. We show that the value of the proton fourth moment must be independently known in order to estimate the neutron skin thickness experimentally. To overcome this problem, we propose the use of a strong linear correlation among the second and fourth moments of the proton distribution as calculated with several energy density functionals of common use. We take special care in estimating the errors associated with the different contributions to the neu…
In these proceedings, we present the measurements of neutron skin thickness and nuclear deformation using isobar $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV by the STAR detector. The significant deviations from unity of the isobar ratios of elliptic flow $v_{2}$, triangular flow $v_{3}$, mean $p_{\rm T}$ fluctuations $\langleδp_{\rm T}^{2}\rangle/\langle p_{\rm T}\rangle^{2}$, and asymmetric cumulant ${\rm ac}_{2}\{3\}$ indicate large differences in their quadrupole and octuple deformations. The significant deviations of the isob…
Nuclear collective motion provides valuable constraint on the size of neutron-skin thickness and the properties of nuclear matter symmetry energy. By employing relativistic nuclear energy density functional (RNEDF) and covariance analysis related to $χ^2$ fitting of the model parameters, relevant observables are identified for dipole excitations, which strongly correlate with the neutron-skin thickness $(r_{np})$, symmetry energy at saturation density $(J)$ and slope of the symmetry energy $(L)$. Using the RNEDF framework and experimental data on pygmy dipole strength ($^{68}$Ni, $^{132}$Sn, $…
Background: Coherent π0 photoproduction on heavy nuclei has been suggested as a reliable tool to infer neutron skin thicknesses. To this aim, various experiments have been performed, especially on 208Pb. Purpose: We analyze the sensitivity of that reaction process to the nucleonic density, and especially to the neutron skin thickness, for 12C, 40Ca and 208Pb, for which reliable data exist, and on 116,124Sn, for which measurements have been performed in Mainz. We study also the role played by the π0-nucleus final-state interaction. Method: A model of the reaction is developed at the impulse app…
The nuclear binding energy is studied using a finite temperature density functional theory. A Skyrme interaction is used in this work. Volume, surface, and symmetry energy contributions to the binding energy are investigated. The case of neutron skin is considered in detail. The neutron skin modifies the mass $A$ dependence of various terms and $I$ dependence of the skin thickness is proportional to $I$ for the case of same central density.
A precise determination of the neutron skin thickness of a heavy nucleus sets a basic constraint on the nuclear symmetry energy (the neutron skin thickness 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 208Pb. We investigate PVES in nuclear mean field approach to allow the accurate extraction of the neutron skin thickness of 208Pb from the parity-violating asymmetry probed in the experiment. We demonstrate a high linear correlation between the parity-violatin…
Available experimental neutron skin thicknesses of even-even stable Ca, Ni, Sn, Pb, and Cd isotopes are evaluated, and separate trends of neutron skin thickness versus relative neutron excess $δ=(N-Z)/A$ are firstly observed for different isotopic chains. This phenomenon is quantitatively reproduced by the deformed Skyrme Hartree-Fock $+$ BCS model with SLy4 force.
Within an isospin- and momentum-dependent transport model IBUU11 using as an input nucleon density profiles from Hartree-Fock calculations based on a modified Skyrme-like (MSL) model, we study the influence of the uncertainty of the neutron skin thickness on the $π^{-}/π^{+}$ ratio in both central and peripheral Pb+Pb collisions at beam energies of 400 MeV/nucleon and 1000 MeV/nucleon. Within the current experimental uncertainty range of neutron skin in $^{208}$Pb, while the neutron skin effect on the \rpi ratio is negligible in central reactions at both energies, it increases gradually with i…
We study whether the neutron skin thickness $Δr_{np}$ of ${}^{208}$Pb originates from the bulk or from the surface of the neutron and proton density distributions in mean field models. We find that the size of the bulk contribution to $Δr_{np}$ of ${}^{208}$Pb strongly depends on the slope of the nuclear symmetry energy, while the surface contribution does not. We note that most mean field models predict a neutron density for ${}^{208}$Pb between the halo and skin type limits. We investigate the dependence of parity- violating electron scattering at the kinematics of the PREX experiment on the…
The relation between the slope of the nuclear symmetry energy at saturation density and the neutron skin thickness is investigated. Constraints on the slope of the symmetry energy are deduced from the neutron skin data obtained in experiments with antiprotonic atoms. Two types of neutron skin are distinguished: the "surface" and the "bulk". A combination of both types forms neutron skin in most of nuclei. A prescription to calculate neutron skin thickness and the slope of symmetry energy parameter $L$ from the parity violating asymmetry measured in the PREX experiment is proposed.
Configurational information entropy (CIE) theory was employed to determine the neutron skin thickness of neutron-rich calcium isotopes. The nuclear density distributions and fragment cross-sections in 350 MeV/u $^{40-60}$Ca + $^{9}$Be projectile fragmentation reactions were calculated using a modified statistical abrasion-ablation model. CIE quantities were determined from the nuclear density, isotopic, mass, and charge distributions. The linear correlations between the CIE determined using the isotopic, mass, and charge distributions and the neutron skin thickness of the projectile nucleus sh…
Motivated by a recent experiment, the distribution of electric dipole strength in the neutron-rich 68Ni isotope was computed using a relativistic random phase approximation with a set of effective interactions that - although well calibrated - predict significantly different values for the neutron-skin thickness in 208Pb. The emergence of low-energy "Pygmy" strength that exhausts about 5-8% of the energy weighted sum rule (EWSR) is clearly identified. In addition to the EWSR, special emphasis is placed on the dipole polarizability. In particular, our results suggest a strong correlation betwee…
The electric dipole (E1) response of 208Pb has been precisely determined by measuring Coulomb excitation induced by proton scattering at very forward angles. The electric dipole polarizability, defined as inverse energy-weighted sum rule of the E1 strength, has been extracted as 20.1+-0.6 fm^3. The data can be used to constrain the neutron skin thickness of 208Pb to 0.168(+-0.009)_expt(+-0.013)_theo(+-0.021)_est fm, where the subscript "expt" refers to the experimental uncertainty, "theor" to the theoretical confidence band and "est" to the uncertainty associated with the estimation of the sym…
The isotopic dependence of the isovector Pygmy dipole response in tin is studied within the framework of the relativistic random phase approximation. Regarded as an oscillation of the neutron skin against the isospin-symmetric core, the pygmy dipole resonance may place important constraints on the neutron skin of heavy nuclei and, as a result, on the equation of state of neutron-rich matter. The present study centers around two questions. First, is there a strong correlation between the development of a neutron skin and the emergence of low-energy isovector dipole strength? Second, could one u…
The neutron skin of $^{208}$Pb has received considerable attention in recent years. A variety of strongly-interacting probes depict a rather consistent picture but pionic probes have not been referred to in this context. We present here neutron-skin values from pionic atoms and from total reaction cross sections of $π^+$ between 0.7 and 2 GeV/c which fit well into the picture. In addition we show that a neutron skin for $^{48}$Ca can be obtained from existing data on pionic atoms and the result agrees with pion scattering experiments and with the scattering of $α$ particles.
In these proceedings, we present the three proposed observables to probe the neutron skin and symmetry energy with relativistic isobar collisions, namely, the isobar ratios of the produced hadron multiplicities ($N_{\rm ch}$), the mean transverse momenta ($\langle p_{\perp} \rangle$), and the net charge multiplicities ($ΔQ$). Our findings suggest potentially significant improvement to neutron skin and symmetry energy determination over traditional low energy methods.
Within an isospin- and momentum-dependent transport model using as an input nucleon density profiles from Hartree-Fock calculations based on a modified Skyrme-like (MSL) model, we study how to eliminate the influence of neutron-skin size difference of initial colliding nuclei in probing the nuclear symmetry energy. Within the current experimental uncertainty range of neutron-skin size of $^{208}$Pb, the Pb+Pb collisions are performed in semicentral and peripheral collisions with impact parameters of 5 and 9fm and at beam energies from 50 MeV/nucleon to 1000 MeV/nucleon, respectively. It is sho…
In this work we propose a new method to measure the evolution of the neutron skin thickness between different isotopes. We consider antiproton-nucleus interactions close to the production threshold of $Λ\overlineΛ$ and $Σ\overlineΛ$ pairs. At low energies, $Λ\overlineΛ$ pairs are produced in p + p collisions, while $Σ\overlineΛ$ pairs can only be produced in p + n interactions. Measuring these cross sections provides information on the neutron skin thickness
We examine whether or not the surface tension acts to increase the nucleon density in the nuclear interior within a compressible liquid-drop model. We find that it depends on the density dependence of the surface tension, which may in turn be deduced from the neutron skin thickness of stable nuclei.
The neutron skin thickness of 48Ca was deduced from the interaction cross section by adopting a microscopic optical potential. The optical potential used was constructed by folding a chiral g matrix and the Skyrme mean-field densities renormalized by considering the information of the interaction cross section. The result was R_skin = 0.139 \pm 0.058 fm.
A new method is proposed to deduce the neutron radii of neutron-rich nuclei. This method requires measuring the reaction cross sections of both the neutron-rich nucleus and its stable isotope at the same energy on a proton target. Using this method and the available experimental data of $^{12,22}$C + $p$ and $^{9,14}$Be + $p$ at 40$A$ MeV, the neutron radii of $^{22}$C and $^{14}$Be have been deduced for the first time.
The correlation between neutron skin-thickness of a neutron-rich nucleus and slope parameter of symmetry energy is assessed as a function of density using relativistic mean field models containing non-linear couplings among different mesons. Models with larger skin were found to probe the slope parameter even at suprasaturation densities, whereas models with smaller skin were observed to be sensitive only at specific subsaturation density, connected to the average density of nuclei. Possible reasons behind this density dependence are explored systematically. These results might be model specif…
The second-order moment of the nuclear charge density($R^2_c$) is dominated by the mean square radius(msr) of the point proton distribution($R_p^2$), while the fourth-order moment($Q^4_c$) depends on the msr of the point neutron one($R_n^2$) also. Moreover, $R^2_n$ is strongly correlated to $R^2_c$ in nuclear models. According to these facts, the linear relationship between various moments in the nuclear mean field models are investigated with use of the least squares method for $^{40}$Ca, $^{48}$Ca and $^{208}$Pb. From the intersection points of the obtained straight lines with those of the e…
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.
The effects of neutron skin on the multiplicity ($N_{\rm ch}$) and eccentricity($ε_2$) in relativistic $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV are investigated with the Trento model. It is found that the Ru+Ru/Zr+Zr ratios of the $N_{\rm ch}$ distributions and $ε_{2}$ in mid-central collisions are exquisitely sensitive to the neutron skin type (skin vs.~halo). The state-of-the-art calculations by energy density functional theory (DFT) favor the halo-type neutron skin and can soon be confronted by experimental data. It is demo…
Photon from neutron-proton bremsstrahlung in p+Pb reactions is examined as a potential probe of the neutron-skin thickness in different centralities and at different proton incident energies. It is shown that the best choice of reaction environment is about 140MeV for the incident proton and the 95\%-100\% centrality for the reaction system since the incident proton mainly interacts with neutrons inside the skin of the target and thus leads to different photon production to maximal extent. Moreover, considering two main uncertainties from both photon production probability and nucleon-nucleon …
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…
Particle production in ultrarelativistic heavy ion collisions depends on the details of the nucleon density distributions in the colliding nuclei. We demonstrate that the charged hadron multiplicity distributions in isobaric collisions at ultrarelativistic energies provide a novel approach to determine the poorly known neutron density distributions and thus the neutron skin thickness in finite nuclei, which can in turn put stringent constraints on the nuclear symmetry energy.
Based on the framework of the Isospin-Dependent Quantum Molecular Dynamics (IQMD) model in which the initial neutron and proton densities are sampled according to the droplet model, the correlation between triton-to-$^{3}$He yield ratio (R(t/$^{3}$He)$=$Yield(t)/Yield($^{3}$He)) and neutron skin thickness ($δ_{np}$) in neutron-rich projectile induced reactions is investigated. By changing the diffuseness parameter of neutron density distribution in the droplet model for the projectile to obtain different $δ_{np}$, the relationship between $δ_{np}$ and the corresponding R(t/$^{3}$He) in semi-pe…
We present a new statistical tool based on random sampling to assess the confidence interval of Pearson's and Spearman's correlation coefficients. These estimators are then used to quantify the statistical correlations among the neutron skin thickness of atomic nuclei and the slope of the symmetry energy in the infinite nuclear medium.
Neutron-skins in coordinate space and proton-skins in momentum space are predicted to coexist in heavy nuclei and their correlation is governed by Liouville's theorem and Heisenberg's uncertainty principle. An analysis of their correlation within a further extended Thomas-Fermi (ETF$^+$) approximation incorporating effects of nucleon short-range correlations reveals generally that protons move faster than neutrons in neutron-skins of heavy nuclei.
We investigate the contributions of various reaction channels to the interaction, reaction, charge-changing and neutron-changing cross sections. The goal is to investigate the relation between microscopic interactions and the symmetry energy component of the equation of state (EoS) of interest for the structure of neutron stars. We have made a comparison of the neutron skins extracted from diverse experimental techniques with those obtained with Hartree-Fock-Bogoliubov calculations with 23 Skyrme and with 8 density-dependent interactions used in the relativistic mean field method. We have show…
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…
Correlations between the thickness of the neutron skin in finite nuclei and the nuclear matter symmetry energy are studied in the Skyrme Hartree-Fock model. From the most recent analysis of the isospin diffusion data in heavy-ion collisions based on an isospin- and momentum-dependent transport model with in-medium nucleon-nucleon cross sections, a value of $L=88\pm 25$ MeV for the slope of the nuclear symmetry energy at saturation density is extracted, and this imposes stringent constraints on both the parameters in the Skyrme effective interactions and the neutron skin thickness of heavy nucl…
The neutron-skin thickness of asymmetric semi-infinite nuclear matter is shown to be a function of Coulomb energy, the asymmetry-energy coefficient($J$), the slope($L$) of the asymmetry energy, and the incompressibility coefficient, in addition to he Fermi momentum and the asymmetry parameter. The relational formula is derived on the basis of the Hugenholtz-Van Hove theorem in the mean-field approximation for nuclear matter. Using the formula as a guide, the neutron-skin thickness($δR$) in $^{208}$Pb is examined. The linear correlation between $L$ and $δR$ appears as a kind of spurious ones th…
In the present work we investigate the main differences in the lead neutron skin thickness, binding energy, surface energy and density profiles obtained with two different density dependent relativistic hadronic models, within the Thomas-Fermi approximation. We show that the asymmetry parameter for low momentum transfer polarized electron scattering is not sensitive to the model parametrization differences.
The dependence between neutron-to-proton yield ratio ($R_{np}$) and neutron skin thickness ($δ_{np}$) in neutron-rich projectile induced reactions is investigated within the framework of the Isospin-Dependent Quantum Molecular Dynamics (IQMD) model. The density distribution of the Droplet model is embedded in the initialization of the neutron and proton densities in the present IQMD model. By adjusting the diffuseness parameter of neutron density in the Droplet model for the projectile, the relationship between the neutron skin thickness and the corresponding $R_{np}$ in the collisions is obta…
The energy of the charge-exchange Anti-analog Giant Dipole Resonance (AGDR) has been calculated for the 208Pb isotope using the state-of-the-art fully self-consistent relativistic proton-neutron quasiparticle random-phase approximation based on the Relativistic Hartree-Bogoliubov model. It is shown that the AGDR centroid energy is very sensitively related to the corresponding neutron-skin thickness. The neutron-skin thickness of 208Pb has been determined very precisely by comparing the theoretical results with the available experimental data on E(AGDR). The result DR(pn)= 0.161(42) agrees nice…
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 thickness of heavy nuclei provides a fundamental link to the equation of state of neutron-rich matter, and hence to the properties of neutron stars. The Lead Radius Experiment ("PREX") at Jefferson Laboratory has recently provided the first model-independence evidence on the existence of a neutron-rich skin in 208Pb. In this contribution we examine how the increased accuracy in the determination of neutron skins expected from the commissioning of intense polarized electron beams may impact the physics of neutron stars.
