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An overview of neutron skin predictions obtained using an empirical nonlocal dispersive optical model (DOM) is presented. The DOM links both scattering and bound-state experimental data through a subtracted dispersion relation which allows for fully consistent, data-informed predictions for nuclei where such data exist. Large skins were predicted for both 48Ca ( R skin 48 = 0.25 ± 0.023 fm in 2017) and 208Pb ( R skin 208 = 0.25 ± 0.05 fm in 2020). Whereas the DOM prediction in 208Pb is within 1 σ of the subsequent PREX-2 measurement, the DOM prediction in 48Ca is over 2 σ larger than the thin neutron skin resulting from CREX. From the moment it was revealed, the thin skin in 48Ca has puzzled the nuclear-physics community as no adequate theories simultaneously predict both a large skin in 208Pb and a small skin in 48Ca. The DOM is unique in its ability to treat both structure and reaction data on the same footing, providing a unique perspective on this R skin puzzle. It appears vital that more neutron data be measured in both the scattering and bound-state domain for 48Ca to clarify the situation. [ABSTRACT FROM AUTHOR]

We studied the photoproduction of dileptons from strong electromagnetic fields generated by the nucleus in relativistic heavy-ion collisions. The production of dileptons is calculated based on the Equivalent Photon Approximation (EPA) method, which depends on the strength of the electromagnetic fields and the density of protons in the nucleus. With the EPA method, we construct the connections between dilepton photoproduction and the electromagnetic form factors in the nucleus. Finally, the nuclear proton densities can be determined with the dilepton photoproduction, which is employed to extract the neutron skin in the nucleus. Our calculations indicate that the dilepton photoproduction varies evidently with different proton densities in the nucleus, suggesting a deeper symmetry underlying the connections between proton density (or the neutron skin) and the dilepton photoproduction. This offers a new way to study the neutron skin in the nucleus. [ABSTRACT FROM AUTHOR]

The concept of symmetry under various transformations of quantities describing basic natural phenomena is one of the fundamental principles in the mathematical formulation of physical laws. Starting with Noether's theorems, we highlight some well–known examples of global symmetries and symmetry breaking on the particle level, such as the separation of strong and electroweak interactions and the Higgs mechanism, which gives mass to leptons and quarks. The relation between symmetry energy and charge symmetry breaking at both the nuclear level (under the interchange of protons and neutrons) and the particle level (under the interchange of u and d quarks) forms the main subject of this work. We trace the concept of symmetry energy from its introduction in the simple semi-empirical mass formula and liquid drop models to the most sophisticated non-relativistic, relativistic, and ab initio models. Methods used to extract symmetry energy attributes, utilizing the most significant combined terrestrial and astrophysical data and theoretical predictions, are reviewed. This includes properties of finite nuclei, heavy-ion collisions, neutron stars, gravitational waves, and parity–violating electron scattering experiments such as CREX and PREX, for which selected examples are provided. Finally, future approaches to investigation of the symmetry energy and its properties are discussed. [ABSTRACT FROM AUTHOR]

We have obtained the constraints on the density dependence of the symmetry energy from neutron-skin thickness data by parity-violating electron scatterings and neutron-star observables using a Bayesian approach, based on the standard Skyrme-Hartree-Fock (SHF) model and its extension as well as the relativistic mean-field (RMF) model. While the neutron-skin thickness data (neutron-star observables) mostly constrain the symmetry energy at subsaturation (suprasaturation) densities, they may more or less constrain the behavior of the symmetry energy at suprasaturation (subsaturation) densities, depending on the energy-density functional form. Besides showing the final posterior density dependence of the symmetry energy, we also compare the slope parameters of the symmetry energy at 0.10 fm−3 as well as the values of the symmetry energy at twice saturation density from three effective nuclear interactions. The present work serves as a comparison study based on relativistic and non-relativistic energy-density functionals, for constraining the nuclear symmetry energy from low to high densities using a Bayesian approach. [ABSTRACT FROM AUTHOR]

An overview of neutron skin predictions obtained using an empirical nonlocal dispersive optical model (DOM) is presented. The DOM links both scattering and bound-state experimental data through a subtracted dispersion relation which allows for fully consistent, data-informed predictions for nuclei where such data exist. Large skins were predicted for both 48Ca (Rskin48=0.25±0.023 fm in 2017) and 208Pb (Rskin208=0.25±0.05 fm in 2020). Whereas the DOM prediction in 208Pb is within 1σ of the subsequent PREX-2 measurement, the DOM prediction in 48Ca is over 2σ larger than the thin neutron skin resulting from CREX. From the moment it was revealed, the thin skin in 48Ca has puzzled the nuclear-physics community as no adequate theories simultaneously predict both a large skin in 208Pb and a small skin in 48Ca. The DOM is unique in its ability to treat both structure and reaction data on the same footing, providing a unique perspective on this Rskin puzzle. It appears vital that more neutron data be measured in both the scattering and bound-state domain for 48Ca to clarify the situation.

It has recently been suggested that differences in the charge radii of mirror nuclei (ΔRchmirr) are strongly correlated with the neutron-skin thickness (Rskin) of neutron-rich nuclei and with the slope of the symmetry energy (L). To test this assumption, we present ab initio calculations of Rskin in 48Ca and 208Pb, ΔRchmirr in 36Ca−36S, 38Ca−38Ar, 41Sc−41Ca, 48Ni−48Ca, 52Ni−52Cr, and 54Ni−54Fe mirror pairs, and L. Employing the recently developed 34 chiral interaction samples, identified by the history matching approach, we conduct rigorous statistical analysis of correlations among ΔRchmirr, Rskin and L, accounting for quantified uncertainties from low-energy constants of chiral interaction, chiral effective field theory truncation and many-body method approximation. The ab initio results reveal an appreciable ΔRchmirr−L correlation in fp-shell mirror pairs. However, contrary to previous studies, the present calculation finds that the studied sd-shell mirror pairs do not exhibit any ΔRchmirr−L correlation.

We studied the photoproduction of dileptons from strong electromagnetic fields generated by the nucleus in relativistic heavy-ion collisions. The production of dileptons is calculated based on the Equivalent Photon Approximation (EPA) method, which depends on the strength of the electromagnetic fields and the density of protons in the nucleus. With the EPA method, we construct the connections between dilepton photoproduction and the electromagnetic form factors in the nucleus. Finally, the nuclear proton densities can be determined with the dilepton photoproduction, which is employed to extract the neutron skin in the nucleus. Our calculations indicate that the dilepton photoproduction varies evidently with different proton densities in the nucleus, suggesting a deeper symmetry underlying the connections between proton density (or the neutron skin) and the dilepton photoproduction. This offers a new way to study the neutron skin in the nucleus.

The concept of symmetry under various transformations of quantities describing basic natural phenomena is one of the fundamental principles in the mathematical formulation of physical laws. Starting with Noether’s theorems, we highlight some well–known examples of global symmetries and symmetry breaking on the particle level, such as the separation of strong and electroweak interactions and the Higgs mechanism, which gives mass to leptons and quarks. The relation between symmetry energy and charge symmetry breaking at both the nuclear level (under the interchange of protons and neutrons) and the particle level (under the interchange of u and d quarks) forms the main subject of this work. We trace the concept of symmetry energy from its introduction in the simple semi-empirical mass formula and liquid drop models to the most sophisticated non-relativistic, relativistic, and ab initio models. Methods used to extract symmetry energy attributes, utilizing the most significant combined terrestrial and astrophysical data and theoretical predictions, are reviewed. This includes properties of finite nuclei, heavy-ion collisions, neutron stars, gravitational waves, and parity–violating electron scattering experiments such as CREX and PREX, for which selected examples are provided. Finally, future approaches to investigation of the symmetry energy and its properties are discussed.

To improve the constraints of symmetry energy at subsaturation density, measuring and accumulating more neutron skin data for neutron-rich unstable nuclei is naturally required. Aiming to probe the neutron skin of unstable nuclei by using low-intermediate-energy heavy-ion collisions, we develop a new version of an improved quantum molecular dynamics model, in which the neutron skin of the initial nucleus and the mean-field potential in nucleon propagation are consistently treated. Our calculations show that the three observables, such as the cross-sections of the primary projectile-like residues with A > 100 ( σ A > 100 ), the difference of σ A > 100 between 132 Sn + 124 Sn and 124 Sn + 124 Sn systems ( δ σ A > 100 ), and the neutron-to-proton yield ratio ( R (n / p) ) in the transverse direction, could be used to measure the neutron skin of the unstable nuclei and to constrain the slope of the symmetry energy in the future. [ABSTRACT FROM AUTHOR]

Background:: The cross sections of the isovector spin-dipole resonances (SDR) in the Sb isotopes have been measured. Within the model used, the neutron-skin thicknesses rskin(exp) deduced 0.12±0.06 fm for 116Sn, 0.13±0.06 fm for 118Sn, 0.18±0.07 fm for 120Sn, 0.22±0.07 fm for 122Sn, 0.19±0.07 fm for 124Sn. We tested the chiral (Kyushu) g-matrix folding model for 12C+12C scattering, and found that the Kyushu g-matrix folding model is reliable for reaction cross sections σR in 30˜

Infinite nuclear matter is a suitable laboratory to learn about nuclear forces in many-body systems. In particular, modern theoretical predictions of neutron-rich matter are timely because of recent and planned experiments aimed at constraining the equation of state of isospin-asymmetric matter. For these reasons, we have taken a broad look at the equation of state of neutron-rich matter and the closely related symmetry energy, which is the focal point of this article. Its density dependence is of paramount importance for a number of nuclear and astrophysical systems, ranging from neutron skins to the structure of neutron stars. We review and discuss ab initio predictions in relation to recent empirical constraints. We emphasize and demonstrate that free-space nucleon–nucleon data pose stringent constraints on the density dependence of the neutron matter equation of state, which essentially determines the slope of the symmetry energy at saturation. [ABSTRACT FROM AUTHOR]

It has recently been suggested that differences in the charge radii of mirror nuclei (Δ R ch mirr) are strongly correlated with the neutron-skin thickness (R skin) of neutron-rich nuclei and with the slope of the symmetry energy (L). To test this assumption, we present ab initio calculations of R skin in 48Ca and 208Pb, Δ R ch mirr in 36Ca − 36 S, 38Ca − 38 Ar, 41Sc − 41 Ca, 48Ni − 48 Ca, 52Ni − 52 Cr, and 54Ni − 54 Fe mirror pairs, and L. Employing the recently developed 34 chiral interaction samples, identified by the history matching approach, we conduct rigorous statistical analysis of correlations among Δ R ch mirr , R skin and L , accounting for quantified uncertainties from low-energy constants of chiral interaction, chiral effective field theory truncation and many-body method approximation. The ab initio results reveal an appreciable Δ R ch mirr − L correlation in fp -shell mirror pairs. However, contrary to previous studies, the present calculation finds that the studied sd -shell mirror pairs do not exhibit any Δ R ch mirr − L correlation. [ABSTRACT FROM AUTHOR]

The physics of radioactive nuclear beams is one of the frontiers of nuclear physics. New phenomena and physics appear in exotic nuclei far from the β-stability line. The neutron skin is an exotic phenomena in unstable nuclei and is closely correlated with the properties of the equation of state (EOS) of asymmetric nuclear matter and neutron stars. This study sought to examine previous studies on the effect of the neutron skin on nuclei-nuclei collisions to identify good observables for determining the neutron skin thickness, which could in turn be used to investigate the EOS of asymmetric nuclear matter. Various theoretical models are used to study the effect of neutron skin in nuclei-nuclei collisions. The statistical abrasion-ablation (SAA) and isospin-dependent quantum molecular dynamics (IQMD) models are used to study the neutron abrasion cross-section, neutron/proton ratio, and t/3He ratios. A nuclear structure model is used to investigate the relation between the neutron skin and α-cluster formation, α decay, nuclear surface, and nuclear temperature. Strong correlations have been found between the neutron skin thickness and neutron abrasion cross-section, neutron/proton ratio, and t/3He ratios, photo production, and other quantities. By measuring quantities that have a strong correlation with the neutron skin, the skin thickness can be obtained. The EOS of asymmetric nuclear matter and properties of neutron stars can be studied or constrained by using the obtained neutron skin data. Further investigations are necessary for determining observables that are useful for determining the neutron skin thickness from experimental measurements.

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. 1 3 9 ± 0. 0 5 8  fm. [ABSTRACT FROM AUTHOR]

To improve the constraints of symmetry energy at subsaturation density, measuring and accumulating more neutron skin data for neutron-rich unstable nuclei is naturally required. Aiming to probe the neutron skin of unstable nuclei by using low-intermediate-energy heavy-ion collisions, we develop a new version of an improved quantum molecular dynamics model, in which the neutron skin of the initial nucleus and the mean-field potential in nucleon propagation are consistently treated. Our calculations show that the three observables, such as the cross-sections of the primary projectile-like residues with A>100 (σA>100), the difference of σA>100 between 132Sn + 124Sn and 124Sn + 124Sn systems (δσA>100), and the neutron-to-proton yield ratio (R(n/p)) in the transverse direction, could be used to measure the neutron skin of the unstable nuclei and to constrain the slope of the symmetry energy in the future.

Assuming that the core of a large finite nucleus in which the neutron number (N) is quite large compared to the proton number (Z), is composed of neutron-proton pairs (which are deutrons and bosons) and the unpaired neutrons stay in the surface region (neutron skin region), A model is proposed in which the deutrons in the core interact with the neutrons in the surface region. The nucleus is considered as an assembly of a mixture of interacting bosons (deutrons) and fermions (neutrons) and the model Hamiltonian is diagonalized to calculate the quasi-particle energy of the interacting system. The low value of the quasi-particle energy per neutron when compared to the large binding fraction can lead to a march towards the dripline for the neutrons. [ABSTRACT FROM AUTHOR]

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 a direct variational method based on Fermi-like trial functions.

Infinite nuclear matter is a suitable laboratory to learn about nuclear forces in many-body systems. In particular, modern theoretical predictions of neutron-rich matter are timely because of recent and planned experiments aimed at constraining the equation of state of isospin-asymmetric matter. For these reasons, we have taken a broad look at the equation of state of neutron-rich matter and the closely related symmetry energy, which is the focal point of this article. Its density dependence is of paramount importance for a number of nuclear and astrophysical systems, ranging from neutron skins to the structure of neutron stars. We review and discuss ab initio predictions in relation to recent empirical constraints. We emphasize and demonstrate that free-space nucleon–nucleon data pose stringent constraints on the density dependence of the neutron matter equation of state, which essentially determines the slope of the symmetry energy at saturation.

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 a direct variational method based on Fermi-like trial functions. [ABSTRACT FROM AUTHOR]

Abstract A thick neutron skin emerges from the first determination of root mean square radii of the proton distributions for 17−22N from charge changing cross section measurements around 900 A MeV at GSI. Neutron halo effects are signalled for 22N from an increase in the proton and matter radii. The radii suggest an unconventional shell gap at N = 14 arising from the attractive proton–neutron tensor interaction, in good agreement with shell model calculations. Ab initio , in-medium similarity re-normalization group, calculations with a state-of-the-art chiral nucleon–nucleon and three-nucleon interaction reproduce well the data approaching the neutron drip-line isotopes but are challenged in explaining the complete isotopic trend of the radii. [ABSTRACT FROM AUTHOR]

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 Δrnp as a sum of skin- and halo-like terms is obtained. The contribution of halo and skin terms to Δrnp are found to be approximately equal.

Predictions are presented for proton skins based on isospin-asymmetric equations of state derived microscopically from high-precision chiral few-nucleon interactions. Moreover, the relation between the neutron skin of a nucleus and the difference between the proton radii of the corresponding mirror nuclei is investigated.

We report predictions for the neutron skin in 208Pb using chiral two- and three-body interactions at increasing orders of chiral effective field theory and varying resolution scales. Closely related quantities, such as the slope of the symmetry energy, are also discussed. The sensitivity of the skin to just pure neutron matter pressure when going from order 2 to order 4 of chiral effective theory is singled out in a set of calculations that employ an empirical equation of state for symmetric nuclear matter.

The cross sections of the isovector spin-dipole resonances (SDR) in the Sb isotopes have been measured. Within the model used, the neutron-skin thicknesses r skin (exp) deduced 0. 12 ± 0. 06 fm for 116Sn, 0. 13 ± 0. 06 fm for 118Sn, 0. 18 ± 0. 07 fm for 120Sn, 0. 22 ± 0. 07 fm for 122Sn, 0. 19 ± 0. 07 fm for 124Sn. We tested the chiral (Kyushu) g -matrix folding model for 12C+12C scattering, and found that the Kyushu g -matrix folding model is reliable for reaction cross sections σ R in 30 ˜ < E in ˜ < 100 MeV and 250 ˜ < E in ˜ < 400 MeV. We determine neutron skin thickness r skin (exp) , using measured σ R of 4He+116,120,224Sn scattering. The results are r skin (exp) = 0. 242 ± 0. 140 fm for 116Sn, r skin (exp) = 0. 377 ± 0. 140 fm for 120Sn, r skin (exp) = 0. 180 ± 0. 142 fm for 124Sn. The σ R are available for proton scattering on 116,118,120,122,124Sn with high accuracy of 2 ∼ 3 % as a function of incident energy E in. Our aim is to determine r skin (exp) for 116,118,120,122,124Sn with small errors by using the Kyushu g -matrix folding model. Our model is the Kyushu g -matrix folding model with the densities scaled from the D1S-GHFB+AMP neutron density, where D1S-GHFB+AMP stands for Gogny-D1S HFB (D1S-GHFB) with the angular momentum projection (AMP). The proton radii of D1S-GHFB+AMP agree with those calculated with the isotope shift method based on the electron scattering. We then scale the D1S-GHFB+AMP neutron densities so as to reproduce the σ R (exp). In 30 ˜ < E in ˜ < 65 MeV , we determine r skin (exp) from measured σ R. The values are r skin (exp) = 0. 118 ± 0. 021 fm for 116Sn, 0. 112 ± 0. 021 fm for 118Sn, 0. 124 ± 0. 021 fm for 120Sn, 0. 156 ± 0. 022 fm for 124Sn. As for 122Sn, the skin value in 30 ˜ < E in ˜ < 50 MeV is 0. 122 ± 0. 024 fm. Our results are consistent with the previous values. [ABSTRACT FROM AUTHOR]

The isovector particle densities and surface tension coefficients for the average binding energy in the approximation of a sharp edge proton-neutron asymmetric nucleus are used for analytical calculations of its neutron skin and isovector stiffness coefficients. They are significantly different from the well-known ones for the most Skyrme forces. The energies and energy-weighted sum rules of the isovector giant dipole resonances obtained within the Fermi-liquid drop model are in good agreement with the experimental data.

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 r 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. [ABSTRACT FROM AUTHOR]

We report predictions for the neutron skin in 208Pb using chiral two- and three-body interactions at increasing orders of chiral effective field theory and varying resolution scales. Closely related quantities, such as the slope of the symmetry energy, are also discussed. The sensitivity of the skin to just pure neutron matter pressure when going from order 2 to order 4 of chiral effective theory is singled out in a set of calculations that employ an empirical equation of state for symmetric nuclear matter. [ABSTRACT FROM AUTHOR]

The mass-dependent symmetry energy coefficients a(A) has been extracted by analysing the heavy nuclear mass differences reducing the uncertainties as far as possible in our previous work. Taking advantage of the obtained symmetry energy coefficient a(A) and the density profiles obtained by switching off the Coulomb interaction in Pb, we calculated the slope parameter L of the symmetry energy at the density of 0.11 fm. The calculated L ranges from 40.5 MeV to 60.3 MeV. The slope parameter L of the symmetry energy at the density of 0.11 fm is also calculated directly with Skyrme interactions for nuclear matter and is found to have a fine linear relation with the neutron skin thickness of Pb, which is the difference of the neutron and proton rms radii of the nucleus. With the linear relation the neutron skin thickness Δ R of Pb is predicted to be 0.15-0.21 fm. [ABSTRACT FROM AUTHOR]