We explore neutron skin predictions for $^{208}$Pb in relation to the symmetry pressure in various microscopic models based on realistic nucleon-nucleon potentials and either the Dirac-Brueckner-Hartree-Fock approach or the conventional Brueckner-Hartree-Fock framework implemented with three-body forces. We also discuss the correlation between the neutron skin and the radius of a fixed-mass neutron star.
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.
We discuss the difference between neutron halos and neutron skins matching to our usual thinking of a skin as being connected to a body whereas a halo is, in some sense, disconnected from the body. We emphasize that the existence of one or more neutrons behaving incoherently with respect to the rest of the nucleons in a nucleus can match the picture of a neutron halo.
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.
We discuss neutron matter calculations based on chiral effective field theory interactions and their predictions for the symmetry energy, the neutron skin of 208 Pb, and for the radius of neutron stars.
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 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.
This paper presents an analysis of neutron skins based on fully microscopic equations of state, including chiral two- and three-nucleon forces consistently at N3LO. Other theoretical predictions and recent constraints are also addressed, such as those from the PREX II experiment and the latest parity-violating electron scattering measurement of the 27Al neutron skin.
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.
Interplay of effects of neutron skins in coordinate space and proton skins in momentum space on hard photons emission in heavy-ion collisions around Fermi Energy
The nucleon density distributions and the thickness of pure neutron matter in Ca isotopes were systematically studied using the Skyrme-Hartree-Fock model (SHF) from the $β$-stability line to the neutron drip-line. The pure neutron matter, related with the neutron skin or halo, was shown to depend not only on the Fermi levels of the neutrons but also on the orbital angular momentum of the valence neutrons. New definitions for the thickness of pure neutron matter are 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…
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…
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 …
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.
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 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…
The neutron matter equation of state is calculated from two-neutron forces up to fifth order of the chiral expansion and the order-by-order convergence of the predictions is investigated. Based on these equations of state, the binding energies and the neutron and proton density distributions in 208Pb and 48Ca are derived, with particular attention to the neutron skins, the focal point of this paper. Anticipating future experiments which will provide reliable information on the weak charge density in nuclei, the theoretical uncertainties and the possibility of constraining the size of few-neutr…
We present predictions of the binding energy per nucleon and the neutron skin thickness in highly neutron-rich isotopes of Oxygen, Magnesium, and Aluminum. The calculations are carried out at and below the neutron drip line as predicted by our model. The nuclear properties are obtained via an energy functional whose input is the equation of state of isospin-asymmetric infinite matter. The latter is based on a microscopic derivation of the energy per particle in neutron matter applying chiral few-nucleon forces together with a phenomenological model for the equation of state of symmetric nuclea…
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.
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.
A nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in $^{48}$Ca. Elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, and the charge distribution have been fitted to extract the neutron and proton self-energies both above and below the Fermi energy. From the single-particle propagator resulting from these self-energies we have determined the charge and neutron matter distributions in $^{48}$Ca. A neutron skin of 0.249$\pm$0.023~fm is deduced. The energy dependence of the to…
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.
We analyze the influence of the single-particle structure on the neutron density distribution and the neutron skin in Ca, Ni, Zr, Sn, and Pb isotopes. The nucleon density distributions are calculated in the Hartree-Fock+BCS approach with the SLy4 Skyrme force. A close correlation is found between the quantum numbers of the valence neutrons and the changes in the position and the diffuseness of the nuclear surface, which in turn affect the neutron skin thickness. Neutrons in the valence orbitals with low principal quantum number and high angular momentum mainly displace the position of the neut…
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 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 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.
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…
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. Ne…
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…
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 use the Isospin Quantum Molecular Dynamics model (IQMD) to analyze the centrality dependence of the isospin ratio of pions, $π^-/π^+$. We find that the density dependence of the asymmetry potential, the Pauli blocking of the $Δ$-decay and the thickness of the neutron skin influence in different ways this observable. Using the centrality dependence of this ratio at different beam energies we can disentangle the different contributions and open the way for their experimental determination.
Very lately, the PREX and the CREX collaboration present skin values, $r_{\rm skin}^{208}({\rm newPREX2}) =0.278 \pm 0.078\ {\rm (exp)} \pm 0.012\ {\rm (theor.)}\,{\rm fm}$ and $r_{\rm skin}^{48}=0.121 \pm 0.026\ {\rm (exp)} \pm 0.024\ {\rm (model)}$, respectively. We recently determined a neutron-skin value $r_{\rm skin}^{208}=0.278 \pm 0.035$fm from measured reaction cross sections $σ_{\rm R}({\rm exp})$ of p+$^{208}$Pb scattering in a range of incident energies $10 \lsim E_{\rm in} \lsim 100$ MeV where the chiral (Kyushu) $g$-matrix folding model is reliable for $^{12}$C+$^{12}$C scattering…
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…
Correlations between the behavior of the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the Pygmy Dipole Resonance (PDR) in 68Ni and 132Sn have been investigated by using different Random Phase Approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint…
We address two questions pertaining to the uniqueness and usefulness of a new observable: (i) Considering the current theoretical knowledge, what novel information does new measurement bring in? (ii) How can new data reduce uncertainties of current theoretical models? We illustrate these points by studying the radius of the neutron distribution of a heavy nucleus, a quantity related to the equation of state for neutron matter that determines properties of nuclei and neutron stars. By systematically varying parameters of two theoretical models and studying the resulting confidence ellipsoid, we…
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 …
We present the first Bayesian inference of neutron star crust properties to incorporate neutron skin data, including the recent PREX measurement of the neutron skin of $^{208}$Pb, combined with recent chiral effective field theory predictions of pure neutron matter with statistical errors. Using a compressible liquid drop model with an extended Skyrme energy-density functional, we obtain the most stringent constraints to date on the transition pressure $P_{\rm cc}=0.33^{+0.07}_{-0.07}$ MeV fm$^{-3}$ and chemical potential $μ_{\rm cc}=12.6^{+1.8}_{-1.9}$ MeV (which control the mass, moment of i…
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 …
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…
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…
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…
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…
Dipole excitations below the neutron threshold in neutron rich Sn isotopes are studied theoretically in the Quasiparticle-Phonon Model with HFB single particle input. Of special interest are the low-lying two-phonon 1- states and the Pygmy Dipole Resonance (PDR). The evolution of low-energy dipole excitations with neutron excess is investigated over the Sn isotopic chain including the experimentally unknown regions close to 132Sn. A dependence of the PDR strengths and centroid energies on the neutron skin thickness is found. Despite significant multi-phonon contributions to mean energies and t…
The static dipole polarizability, $α_{\rm D}$, in ${}^{208}$Pb has been recently measured with high-resolution via proton inelastic scattering at the Research Center for Nuclear Physics (RCNP). This observable is thought to be intimately connected with the neutron skin thickness, $r_{\rm skin}$, of the same nucleus and, more fundamentally, it is believed to be associated with the density dependence of the nuclear symmetry energy. The impact of $r_{\rm skin}$ on $α_{\rm D}$ in ${}^{208}$Pb is investigated and discussed on the basis of a large and representative set of relativistic and non-relat…
A Fock space representation of the monopole part of the Coulomb potential is presented. Quantum effects show through a small orbital term in $l(l+1)$. Once it is averaged out, the classical electrostatic energy emerges as an essentially exact expression, which makes it possible to eliminate the Nolen-Schiffer anomaly, and to estimate neutron skins and the evolution of radii along yrast states of mirror nuclei. The energy differences of the latter are quantitatively reproduced by the monopole term and a schematic multipole one.
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…
[Background] We constructed the Kyushu chiral $g$-matrix and confirmed its reliability at $30 \lesssim E_{\rm in} \lesssim 100 $~MeV and $250 \lesssim E_{\rm in} \lesssim 400$~MeV for $^{12}$C scattering. Reaction cross section data of $^{4}$He scattering are available for some nuclides including $^{208}$Pb. PREX II collaboration reported a thick neutron skin for $^{208}$Pb. [Purpose] Our purpose is to deduce neutron skin thicknesses of $^{208}$Pb and some other nuclides from reaction cross sections calculated in terms of the double folding model with the $g$-matrix. [Methods] We fold the $g$-…
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…
We investigated effects of pairing correlations on the neutron skin thickness and the symmetry energy of finite nuclei. In this calculation we used Hartree-Fock-Bogoliubov (HFB) method with Skyrme forces and effective pairing interactions. The results have been compared with available experimental data, Hartree-Fock (HF) results as well as the predictions by droplet model (DM). Finally, our discussion was extended to study of the pairing interaction in nuclear matter. Roles of isospin T = 0 pairing in the nuclear matter were also discussed.
