Correlations between low-lying electric dipole (E1) strength and neutron skin thickness are systematically investigated with the fully self-consistent random-phase approximation using the Skyrme energy functionals. The presence of strong correlation among these quantities is currently under dispute. We find that the strong correlation is present in properly selected nuclei, namely in spherical neutron-rich nuclei in the region where the neutron Fermi levels are located at orbits with low orbital angular momenta. The significant correlation between the fraction of the energy-weighted sum value and the slope of the symmetry energy is also observed. The deformation in the ground state seems to weaken the correlation.
We present predictions for proton skins based on isospin-asymmetric equations of state derived microscopically from high-precision chiral few-nucleon interactions. Moreover, we investigate the relation between the neutron skin of a nucleus and the difference between the proton radii of the corresponding mirror nuclei.
The symmetry energy for nuclear matter and its relation to the neutron skin in finite nuclei is discussed. The symmetry energy as a function of density obtained in a self-consistent Green function approach is presented and compared to the results of other recent theoretical approaches. A partial explanation of the linear relation between the symmetry energy and the neutron skin is proposed. The potential of several experimental methods to extract the neutron skin is examined.
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 have extensively investigated characters of the low-energy $E1$ strengths in $N>Z$ nuclei, by analyzing the transition densities obtained by the HF+RPA calculations with several effective interactions. Crossover behavior has been confirmed, from the skin mode at low energy to the $pn$ mode at higher energy. Decomposing the $E1$ strengths into the skin-mode, $pn$-mode and interference fractions, we show that the ratio of the skin-mode strength to the full strength may be regarded as a generic function of the excitation energy, insensitive to nuclides and effective interactions, particularly …
Covariant density functional theory is used to analyze the evolution of low-lying M1 strength in superfluid deformed nuclei in the framework of the self-consistent Relativistic Quasiparticle Random Phase Approximation (RQRPA). In nuclei with a pronounced neutron excess two scissor modes are found. Besides the conventional scissor mode, where the deformed proton and neutron distributions oscillate against each other, a new soft M1 mode is found, where the deformed neutron skin oscillates in a scissor like motion against a deformed proton-neutron core.
The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference betwe…
We study the effects of correlations beyond the independent particle model in the evaluation of neutron skins of various neutron-rich doubly magic nuclei. We consider short- and long-range correlations to take into account the presence of the strongly repulsive core of the bare nucleon-nucleon interaction and collective nuclear phenomena, respectively. Despite the strong sensitivity on the structure of the nucleus considered, our results indicate that, in general, correlations increase the values of the neutron skins.
The neutron skin thickness of nuclei is a sensitive probe of the nuclear symmetry energy having multiple implications for nuclear and astrophysical studies. However, precision measurements of this observable are difficult. 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 b…
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.
We present recent investigations on dipole and quadrupole excitations in spherical skin nuclei, particular exploring their connection to the thickness of the neutron skin. Our theoretical method relies on density functional theory, which provides us with a proper link between nuclear many-body theory of the nuclear ground state and its phenomenological description. For the calculation of the nuclear excited states we apply QPM theory. A new quadrupole mode related to pygmy quadrupole resonance (PQR) in tin isotopes is suggested.
Some aspects, both experimental and theoretical, of extracting the neutron skin $ΔR$ from properties of isovector giant resonances are discussed. Existing proposals are critically reviewed. The method relying on the energy difference between the GTR and IAS is shown to lack sensitivity to $ΔR$. A simple explanation of the linear relation between the symmetry energy and the neutron skin is also given.
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…
Character of the low-energy $E1$ excitations is investigated by analyzing transition densities obtained from the RPA calculations in the doubly-magic nuclei. We propose a decomposition method of the $E1$ excitations into the $pn$ mode (i.e. oscillation between protons and neutrons) and the skin mode (oscillation of the neutron skin against the inner core) via the transition densities, by which their mixing is handled in a straightforward manner. Crossover behavior of the $E1$ excitations is found, from the skin mode at low energy to the $pn$ mode at higher energy. The ratio of the skin-mode st…
Proton and neutron density profiles of 760 nuclei in the mass region of A=16-304are analyzed using the Skyrme energy density for the parameter set SLy4. Simple formulae are obtained to fit the resulting radii and diffuseness data. These formulae may be useful to estimate the values of the unmeasured radii, and especially in extrapolating charge radius values for nuclei which are far from the valley of stability or to perform analytic calculations for bound and/or scattering problems. The obtained neutron and proton root-mean-square radii and the neutron skin thicknesses are in agreement with t…
In this paper, I have discussed the numerical predictions for the neutron-skin thickness (NST) of various finite nuclei starting from $^{40}$Ca to $^{238}$U using recently developed effective relativistic mean-field models G3 and IOPB-I \cite{G3, IOPB}. The calculated results are compared with the PREX-II data, and the experiment has been done with antiprotons at CERN. Further, I have also calculated the dimensional tidal deformability of a canonical neutron star 1.4$M_\odot$ and compared it with the recent observation of GW1701817.
Systematic studies of dipole and other multipole excitations in stable and exotic nuclei are discussed theoretically. Exploring the relation of the strengths of low-energy dipole and quadrupole pygmy resonances to the thickness of the neutron (proton) skin a close connection between static and dynamic properties of the nucleus is observed. The fine structure of low-energy dipole strength in 138Ba nucleus is revealed from E1 and spin-flip M1 strengths distributions.
The electric quadrupole response is investigated theoretically by HFB and QPM calculations along the Sn isotopic chain with special emphasis on excitations above the first collective state and below the particle threshold. Depending on the asymmetry, additional strength clustering as a group of states similar to the known PDR mode is found. The spectral distributions and electric response functions are discussed. The transition densities of these Pygmy Quadrupole Resonances (PQR) states are closely related to the neutron excess and showing special features being compatible with an oscillation …
We examine a method to determine the neutron-skin thickness of nuclei using data on the charge-exchange anti-analog giant dipole resonance (AGDR). Calculations performed using the relativistic proton-neutron quasiparticle random-phase approximation (RQRPA) reproduce the isotopic trend of the excitation energies of the AGDR, as well as that of the spin-flip giant dipole resonances (IVSGDR), in comparison to available data for the even-even isotopes 112-124Sn. It is shown that the excitation energies of the AGDR, obtained using a set of density-dependent effective interactions which span a range…
The neutron skin of nuclei is an important fundamental property, but its accurate measurement faces many challenges. Inspired by charge symmetry of nuclear forces, the neutron skin of a neutron-rich nucleus is related to the difference between the charge radii of the corresponding mirror nuclei. We investigate this relation within the framework of the Hartree-Fock-Bogoliubov method with Skyrme interactions. Predictions for proton skins are also made for several mirror pairs in the middle mass range. For the first time the correlation between the thickness of the neutron skin and the characteri…
The influence of the diffuse surface layer of a finite nucleus on the mean square radii and their isotopic shift is investigated. We present the calculations within the Gibbs-Tolman approach using the experimental values of the nucleon separation energies. Results are compared with that obtained by means of direct variational method based on Fermi-like trial functions.
An alternative way to constrain the density dependence of the symmetry energy with the slope of the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z^{2/3} is proposed. The linear dependence of the neutron skin thickness on the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement experimentally and the extended Thomas-Fermi approach incorporated the Skyrme energy density functional theoretically. An obviously linear relationship between the slope paramet…
We study several structure properties of finite nuclei using relativistic mean-field Lagrangians constructed according to the Brown-Rho scaling due to the chiral symmetry restoration at high densities. The models are consistent with current experimental constraints for the equations of state of symmetric matter at both normal and supra-normal densities and of asymmetric matter at sub-saturation densities. It is shown that these models can successfully describe the binding energies and charge radii of finite nuclei. Compared to calculations with usual relativistic mean-field models, these model…
We studied the charge radius ($r_{c}$), neutron radius ($r_n$), and neutron skin-thickness ($Δr=r_n-r_p$) over a chain of isotopes from C to Zr with the stable region to the neutron drip line. Theoretical calculations are done with axially deformed self-consistent relativistic mean-field theory (RMF) with effective nonlinear NL3 and NL3* interactions. The theoretically estimated values are compared with available experimental data and a reasonable agreement are noted. We additionally assessed the two-neutron separation energy ($S_{2n}$) to mark the drip line nuclei of the considered isotopic s…
The Relativistic Mean Field (RMF) theory is applied to the analysis of ground-state properties of Ne, Na, Cl and Ar isotopes. In particular, we study the recently established proton skin in Ar isotopes and neutron skin in Na isotopes as a function of the difference between the proton and the neutron separation energy. We use the TMA effective interaction in the RMF Lagrangian, and describe pairing correlation by the density-independent delta-function interaction. We calculate single neutron and proton separation energies, quadrupole deformations, nuclear matter radii and differences between pr…
The Gamow-Teller resonances (GTR) and isobaric analog states (IAS) of a sequence of even-even Sn target nuclei are calculated by using the framework of the relativistic Hartree-Bogoliubov model plus proton-neutron quasiparticle random-phase approximation. The calculation reproduces the experimental data on ground-state properties, as well as the excitation energies of the isovector excitations. It is shown that the isotopic dependence of the energy spacings between the GTR and IAS provides direct information on the evolution of neutron skin-thickness along the Sn isotopic chain. A new method i…
We study the finite temperature Hartree-Fock-BCS approximation for selected stable Sn nuclei with zero-range Skyrme forces. Hartree Fock BCS approximation allows for a straightforward interpretation of the results since it involves u and v's which are not matrices as in HFB. Pairing transitions from superfluid to the normal state are studied with respect to the temperature. The temperature dependence of the nuclear radii and neutron skin are also analyzed. An increase of proton and neutron radii is obtained in neutron rich nuclei especially above the critical temperature. Using different Skyrm…
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.
Nuclei with large neutron-to-proton ratios have neutron skins, which manifest themselves in an excess of neutrons at distances greater than the radius of the proton distribution. In addition, some drip-line nuclei develop very extended halo structures. The neutron halo is a threshold effect; it appears when the valence neutrons occupy weakly bound orbits. In this study, nuclear skins and halos are analyzed within the self-consistent Skyrme-Hartree-Fock-Bogoliubov and relativistic Hartree-Bogoliubov theories for spherical shapes. It is demonstrated that skins, halos, and surface thickness can b…
Low-energy dipole excitations have been investigated theoretically in N=50, several N=82 isotones and the Z=50 Sn isotopes. For this purpose a method incorporating both HFB and multi-phonon QPM theory is applied. A concentration of one-phonon dipole strength located below the neutron emission threshold has been calculated in these nuclei. The analysis of the corresponding neutron and proton dipole transition densities allows to assign a genuine pattern to the low-energy excitations and making them distinct from the conventional GDR modes. Analyzing also the QRPA wave functions of the states we…
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 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…
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…
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.
We study the correlation between the thickness of the neutron skin in finite nuclei and the nuclear symmetry energy for isotopic chains of even-even Ni, Sn, and Pb nuclei in the framework of the deformed self-consistent mean-field Skyrme HF+BCS method. The symmetry energy, the neutron pressure and the asymmetric compressibility in finite nuclei are calculated within the coherent density fluctuation model using the symmetry energy as a function of density within the Brueckner energy-density functional. The mass dependence of the nuclear symmetry energy and the neutron skin thickness are also st…
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…
A study of the charge and matter densities and the corresponding rms radii for even-even isotopes of Ni, Kr, and Sn has been performed in the framework of deformed self-consistent mean field Skyrme HF+BCS method. The resulting charge radii and neutron skin thicknesses of these nuclei are compared with available experimental data, as well as with other theoretical predictions. The formation of a neutron skin, which manifests itself in an excess of neutrons at distances greater than the radius of the proton distribution, is analyzed in terms of various definitions. Formation of a proton skin is …
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…
In heavy nuclei the spatial distribution of protons and neutrons is different. At CERN SPS energies production of $π^+$ and $π^-$ differs for $pp$, $pn$, $np$ and $nn$ scattering. These two facts lead to an impact parameter dependence of the $π^+$ to $π^-$ ratio in $^{208}Pb + ^{208}Pb$ collisions. A recent experiment at CERN seems to confirm qualitatively these predictions. It may open a possibility for determination of neutron density distribution in nuclei.
The complex nature of the nuclear forces generates a broad range and diversity of observational phenomena. Heavy nuclei, though orders of magnitude less massive than neutron stars, are governed by the same underlying physics, which is enshrined in the nuclear equation of state. Heavy nuclei are expected to develop a neutron-rich skin where many neutrons collect near the surface. Such a skin thickness is strongly sensitive to the poorly-known density dependence of the symmetry energy near saturation density. An accurate and model-independent determination of the neutron-skin thickness of heavy …
It has been recently suggested that differences in the charge radii of mirror nuclei are proportional to the neutron-skin thickness of neutron-rich nuclei and to the slope of the symmetry energy $L$ [B.A. Brown Phys. Rev. Lett. 119, 122502 (2017)]. The determination of the neutron skin has important implications for nuclear physics and astrophysics. Although the use of electroweak probes provides a largely model-independent determination of the neutron skin, the experimental challenges are enormous. Thus, the possibility that differences in the charge radii of mirror nuclei may be used as a su…
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…
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…
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.
Neutron-rich nuclei and neutron skins from chiral low-resolution interactions
Université Paris-Saclay（巴黎萨克雷大学）；CNRS/IN2P3, IJCLab（法国国家科学研究中心/欧洲核子研究组织，IJCLab）；Helmholtz Forschungsakademie Hessen für FAIR (HFHF)（黑森州亥姆霍兹FAIR研究院）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（德国重离子研究中心）；ExtreMe Matter Institute EMMI（极端物质研究所）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）；Technische Universität Darmstadt（达姆施塔特工业大学）
The model dependence in the correlations of the neutron-skin thickness in heavy nuclei with various symmetry energy parameters is analyzed by using several families of systematically varied microscopic mean field models. Such correlations show a varying degree of model dependence once the results for all the different families are combined. Some mean field models associated with similar values of the symmetry energy slope parameter at saturation density $L$, and pertaining to different families, yield a greater-than-expected spread in the neutron-skin thickness of the $^{208}$Pb nucleus. The e…
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: 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…
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…
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…
Neutron skin thickness ($R_{np}$) of the atomic nuclei $^{48}$Ca, $^{132}$Sn and $^{208}$Pb are considered in the KIDS (Korea:IBS-Daegu-Sungkyunkwan) density functional formalism. Model parameters most relevant to $R_{np}$ are constrained from standard nuclear data and neutron star properties determined from modern observations. Mean values of $R_{np}$ are obtained as 0.161, 0.220 and 0.160 fm for $^{48}$Ca, $^{132}$Sn and $^{208}$Pb, respectively, and the corresponding standard deviations are 0.011, 0.020 and 0.021 fm. Correlations between $R_{np}$ of the three nuclei are considered, and we f…
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 information on pygmy resonances reveals new aspects on the isospin dynamics of the nucleus with important astrophysical consequences. In this connection, the precise knowledge of nuclear response functions plays a key role in the determination of photonuclear reactions cross sections which are of importance for the synthesis of heavy neutron-rich elements. For that purpose, a theoretical method based on density functional theory and multi-phonon approach is applied for investigations of nuclear excitations with different multipolarities and energies in stable and exotic nuclei. The possibl…
