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DOE OSTI2026

Neutron skins probed in proton knockout from neutron-rich nuclei

Proton-induced quasifree knockout reactions provide a powerful probe of nuclear single-particle structure and reaction dynamics in both stable and neutron-rich nuclei. Here, in this work, we develop a unified theoretical framework for the calculation of inclusive (𝑝, 2⁢𝑝) and sequential (𝑝, 3⁢𝑝) reaction cross sections and fragment momentum distributions at intermediate and relativistic energies. The approach is based on a probabilistic extension of Glauber multiple-scattering theory combined with microscopic nuclear densities obtained from Hartree-Fock-Bogoliubov calculations using Skyrme energy-density functionals. We focus in particular on the sensitivity of total cross sections and longitudinal momentum dispersions to neutron-skin thickness along isotopic chains. Our results indicate that both (𝑝, 2⁢𝑝) and (𝑝, 3⁢𝑝) reactions exhibit a systematic decrease of cross section and momentum width with increasing neutron excess, reflecting enhanced attenuation and surface bias induced by neutron skins. The effect is significantly stronger for two-proton removal, suggesting that (𝑝, 3⁢𝑝) reactions may offer enhanced sensitivity to isovector nuclear structure. These findings establish proton-induced knockout reactions as complementary hadronic probes of neutron skins and the density dependence of the nuclear symmetry energy.

direct reactions↗
DOE OSTI2024

Impact of tensor couplings with scalar mixing on covariant energy density functionals

The recent pioneering campaigns conducted by the Lead Radius Experiment (PREX) and the Calcium Radius Experiment (CREX) Collaborations have uncovered major deficiencies in the theoretical description of some fundamental properties of atomic nuclei. Following a recent refinement to the isovector sector of covariant energy density functionals we present here additional improvements to the functional by including both tensor couplings and an isoscalar-isovector mixing term in the scalar sector. Motivated by the distinct surface properties of calcium and lead, we expect that the tensor terms that generate derivative couplings will help break the linear correlation between the neutron skin thickness of these two nuclei. Moreover, the addition of these new terms mitigates most of the problems identified by Reed et al. in describing the properties of both finite nuclei and neutron stars. While significant progress has been made in reconciling the PREX-CREX results without compromising other observables, the final resolution awaits the completion of a proper calibration for this new class of functionals. As a result, we expect that powerful reduced basis methods used recently to create efficient emulators will be essential to accomplish this task.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Exploring the sensitivity of charge-exchange ( p , n ) reactions to the neutron density distribution

The determination of the nuclear neutron properties suffers from uncontrolled uncertainties, which have attracted considerable attention recently, such as in the context of the PREX experiment. Our aim is to analyze the sensitivity of charge-exchange (p,n) reactions to the neutron density distribution ρ n and constrain the neutron characteristics in the nuclear structure models. Method: By combing the folding and the mean-field models, the nucleon-nucleus (N,A) potential can be obtained from the nuclear density distribution. Further, the (p,p) and (p,n) cross sections for 48 Ca and 208 Pb are calculated following the distorted-wave Born approximation method. As a result, compared with the (p,p) cross section, the effects of ρ n variation on the (p,n) cross section are significant, which is due to the impact of isovector properties. Based on the global folding model analyses of data, it is found that 48 Ca and 208 Pb have relatively large neutron skin thickness ΔR np . Results illustrate that the charge-exchange (p,n) reaction is a sensitive probe of ρ n . The results in this paper can offer useful guides for future experiments of neutron characteristics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Density dependence of the symmetry energy in the post–PREX-CREX era

The recently published CREX results suggest a rather peculiar picture for the density dependence of the symmetry energy. Whereas PREX favors a large neutron skin thickness in 208 Pb, thereby suggesting a stiff equation of state, CREX suggests instead a much softer equation of state. This discrepancy has caused a large spur in the theoretical community, since no model has been able to simultaneously reproduce within 1σ the PREX and CREX results. Motivated by a novel correlation between a CREX observable and a combination of bulk symmetry energy parameters, we calibrate three new covariant energy density functionals that reproduce binding energies and charge radii of spherical nuclei—and also accommodate the constraints imposed by PREX and CREX. Given that these models suggest a stiff equation of state at high densities, predictions for neutron star properties are also discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Density dependence of the symmetry energy in the post–PREX-CREX era

The recently published CREX results suggest a rather peculiar picture for the density dependence of the symmetry energy. Whereas PREX favors a large neutron skin thickness in 208 Pb, thereby suggesting a stiff equation of state, CREX suggests instead a much softer equation of state. Here, this discrepancy has caused a large spur in the theoretical community, since no model has been able to simultaneously reproduce within 1σ the PREX and CREX results. Motivated by a novel correlation between a CREX observable and a combination of bulk symmetry energy parameters, we calibrate three new covariant energy density functionals that reproduce binding energies and charge radii of spherical nuclei—and also accommodate the constraints imposed by PREX and CREX. Given that these models suggest a stiff equation of state at high densities, predictions for neutron star properties are also discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Proton Distribution Radii of 16–24 O: Signatures of New Shell Closures and Neutron Skin

The root mean square radii of the proton density distribution in 16–24 O derived from measurements of charge changing cross sections with a carbon target at ~900A MeV together with the matter radii portray thick neutron skin for 22–24 O despite 22,24 O being doubly magic. Imprints of the shell closures at N=14 and 16 are reflected in local minima of their proton radii that provide evidence for the tensor interaction causing them. The radii agree with ab initio calculations employing the chiral NNLO sat interaction, though skin thickness predictions are challenged. Furthermore, shell model predictions agree well with the data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Determination of the Al 27 Neutron Distribution Radius from a Parity-Violating Electron Scattering Measurement

In this paper, we report the first measurement of the parity-violating elastic electron scattering asymmetry on 27 Al. The 27 Al elastic asymmetry is $A_{\text{PV}}$ = 2.16 ± 0.11(stat) ± 0.16(syst) ppm, and was measured at $\langle Q^2\rangle$ = 0.02357 ± 0.00010 GeV$^2$, $\angleθ_{\text{lab}}$ = 7.61° ± 0.02°, and $\langle E_{\text{lab}}$ = 1.157 GeV with the Q weak apparatus at Jefferson Lab. Predictions using a simple Born approximation as well as more sophisticated distorted-wave calculations are in good agreement with this result. From this asymmetry the 27 Al neutron radius $R_n$ = 2.89 ± 0.12 fm was determined using a many-models correlation technique. The corresponding neutron skin thickness $R_n – R_p$ = –0.04 ± 0.12 fm is small, as expected for a light nucleus with a neutron excess of only 1. This result thus serves as a successful benchmark for electroweak determinations of neutron radii on heavier nuclei. A tree-level approach was used to extract the 27 Al weak radius $R_w$ = 3.00 ± 0.15 fm, and the weak skin thickness $R_{\text{wk}} – R_{\text{ch}}$ = –0.04 ± 0.15 fm. The weak form factor at this $Q^2$ is $F_{\text{wk}}$ = 0.39 ± 0.04.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Electric and magnetic dipole strength in 112,114,116,118,120,124 Sn

Background: There is renewed interest in electric dipole strength distributions for a variety of reasons including the extraction of the dipole polarizability related to properties of the symmetry energy and a measure for the neutron skin thickness, understanding the structure of low-energy $\textit{E}$1 strength in nuclei with neutron excess, and establishing the systematics of the isovector giant dipole resonance (IVGDR). Inelastic proton scattering at energies of a few hundred MeV and very forward angles including 0° has been established as a tool for the study of electric and magnetic dipole strength distributions in nuclei. Purpose: The present work aims at a systematic investigation of the electric and magnetic dipole strength distributions in the chain of stable even-mass tin isotopes. Methods: Inelastic proton scattering experiments were performed at the Research Center for Nuclear Physics, Osaka, with a 295-MeV beam covering laboratory angles 0°–6° and excitation energies 6–22 MeV. Cross sections due to $\textit{E}$1 and $\textit{M}$1 excitations were extracted with a multipole decomposition analysis (MDA) and then converted to reduced transition probabilities with the “virtual photon method” for $\textit{E}$1 and the “unit cross section method” for $\textit{M}$1 excitations, respectively. Including a theory-aided correction for the high-excitation-energy region not covered experimentally, the electric dipole polarizability was determined from the $\textit{E}$1 strength distributions. Results: In this work, total photoabsorption cross sections derived from the $\textit{E}$1 and $\textit{M}$1 strength distributions show significant differences compared to those from previous ($\textit{γ, xn}$) experiments in the energy region of the IVGDR. The widths of the IVGDR deduced from the present data with a Lorentz parametrization show an approximately constant value of about 4.5 MeV in contrast to the large variations between isotopes observed in previous work. The IVGDR centroid energies are in good correspondence to expectations from empirical systematics of their mass dependence. Furthermore, a study of the dependence of the IVGDR energies on bulk matter properties is presented. The $\textit{E}$1 strengths below neutron threshold show fair agreement in this work with results from ($\textit{γ, γ'}$) experiments on 112,116,120,124 Sn in the energy region between 6 and 7 MeV, where also isoscalar $\textit{E}$1 strength was found for 124 Sn. At higher excitation energies, large differences are observed, pointing to a different nature of the excited states with small ground-state branching ratios. The isovector spin-$\textit{M}$1 strengths exhibit a broad distribution between 6 and 12 MeV in all studied nuclei. Conclusions: The present results contribute to the solution of a variety of nuclear structure problems including the systematics of the energy and width of the IVGDR, the structure of low-energy $\textit{E}$1 strength in nuclei, new constraints to energy density functionals (EDFs) aiming at a systematic description of the dipole polarizability across the nuclear chart, from which properties of the symmetry energy can be derived, and the systematics of the isovector spin-$\textit{M}$1 strength in heavy nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Neutron Skin Measurement of208Pb Using Parity-Violating Electron Scattering

Nuclear stability requires large nuclei to have more neutrons than protons. While the central core of the nucleus is composed of symmetric nuclear matter, the extra neutrons in heavy nuclei are pushed out to the surface of the nucleus, forming a pure outer neutron skin layer. While the proton distribution inside a nucleus has been accurately measured using electromagnetic probes, previous measurements of neutron distributions in complex nuclei have suffered a lack of systematic precision. PREX-2 and CREX use Parity-Violating electron Scattering (PVeS), as an electroweak interaction probe, to measure the neutron distributions in208Pb and48Ca, respectively. Making use of elastic scattering of longitudinally polarized electrons from unpolarized (isotopically pure) targets, PREX-2 and CREX measure the asymmetry in scattering rates between opposite beam polarization states. Since both experiments share the same exact measurement concept and apparatus, much of this dissertation applies to both PREX-2 and CREX. However, the presented asymmetry analysis and neutron skin extraction are only for PREX-2. PREX-2 measures the parity-violating asymmetry, APV, for 953 MeV electrons scattered elastically from208Pb at?5°in the lab. The final result is APV= 550.00±16.09(stat.)±8.16(syst.)ppb. From this measurement, we report the neutron skin thickness in208Pb nuclei to be, Rskin= 0.278±0.078(exp.)±0.012(model) fm. This measurement has broad implications throughout the physics community, increasing our knowledge in neutron star structure, the equation of state of nuclear matter, nuclear baryon density, nuclear electric dipole polarizability, and more. Key Words: Neutron skin, electroweak interaction, PREX-2, CREX, parity-violating asymmetry, neutron star, quartz detector, weak charge radius, symmetry energy, Hall A, Jefferson Lab

Adhikari, Devi↗
DOE OSTI2022

Free spectator nucleons in ultracentral relativistic heavy-ion collisions as a probe of neutron skin

Besides the yield ratio of free spectator neutrons produced in ultracentral 96 Zr + 96 Zr to 96 Ru + 96 Ru collisions, we propose that the yield ratio N n /N p of free spectator neutrons to protons in a single collision system at the BNL Relativistic Heavy Ion Collider or the CERN Large Hadron Collider can be a more sensitive probe of the neutron-skin thickness Δrnp and the slope parameter L of the symmetry energy. Here, the idea is demonstrated based on the proton and neutron density distributions of colliding nuclei obtained from Skyrme-Hartree-Fock-Bogolyubov calculations, and on a Glauber model that provides information of spectator matter. The final spectator particles are produced from direct emission, clusterization by a minimum spanning tree algorithm or a Wigner function approach, and deexcitation of heavy clusters by gemini. A larger Δr np associated with a larger L value increases the isospin asymmetry of spectator matter and thus leads to a larger N n /N p , especially in ultracentral collisions where the multiplicity of free nucleons are free from the uncertainties of cluster formation and deexcitation. We have further shown that the double ratio of N n /N p in isobaric collision systems or in collisions by isotopes helps to cancel the detecting efficiency for protons. Effects from nuclear deformation and electromagnetic excitation are studied, and they are found to be subdominant compared to the expected sensitivity to Δr np .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Bayesian refinement of covariant energy density functionals

The last five years have seen remarkable progress in our quest to determine the equation of state of neutron rich matter. Here, recent advances across the theoretical, experimental, and observational landscape have been incorporated in a Bayesian framework to refine existing covariant energy density functionals previously calibrated by the properties of finite nuclei. In particular, constraints on the maximum neutron star mass from pulsar timing, on stellar radii from the NICER mission, on tidal deformabilities from the LIGO-Virgo collaboration, and on the dynamics of pure neutron matter as predicted from chiral effective field theories have resulted in significant refinements to the models, particularly to those predicting a stiff symmetry energy. Still, even after these improvements, we find it challenging to reproduce simultaneously the neutron skin thickness of both 208 Pb and 48 Ca recently reported by the PREX/CREX collaboration.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

The Neutron Skin of 48 Ca and 208 Pb: A Critical Analysis

We discuss the neutron skins of 48 Ca and 208 Pb. We review and critically examine modern predictions and empirical constraints, with special attention to the different interpretations of the findings from the PREX-II experiment and the recently reported value of the neutron skin in 48 Ca extracted from the CREX experiment. We argue that, in the spirit of the ab initio philosophy, the path to understanding the behavior of dense neutron-rich matter must not circumvent fundamental nuclear forces. Based only on that argument, a thick neutron skin in 208 Pb is highly unlikely.

chiral effective field theory↗
DOE OSTI2021

Charge Radius of Neutron-Deficient Ni 54 and Symmetry Energy Constraints Using the Difference in Mirror Pair Charge Radii

he nuclear root-mean-square charge radius of Ni 54 was determined with collinear laser spectroscopy to be R ( Ni 54 ) = 3.737 ( 3 ) fm . In conjunction with the known radius of the mirror nucleus Fe 54 , the difference of the charge radii was extracted as Δ R ch = 0.049 ( 4 ) fm . Based on the correlation between Δ R ch and the slope of the symmetry energy at nuclear saturation density ( L ), we deduced 21 ≤ L ≤ 88 MeV . The present result is consistent with the L from the binary neutron star merger GW170817, favoring a soft neutron matter EOS, and barely consistent with the PREX-2 result within 1 σ error bands. Our result indicates the neutron-skin thickness of Ca 48 as 0.15–0.21 fm.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Implications of PREX-2 on the Equation of State of Neutron-Rich Matter

Laboratory experiments sensitive to the equation of state of neutron rich matter in the vicinity of nuclear saturation density provide the first rung in a “density ladder” that connects terrestrial experiments to astronomical observations. In this context, the neutron skin thickness of 208 Pb ($R$ $^{208}_{skin}$) provides a stringent laboratory constraint on the density dependence of the symmetry energy. In turn, an improved value of $R$ $^{208}_{skin}$ has been reported recently by the PREX collaboration. Exploiting the strong correlation between $R$ $^{208}_{skin}$ and the slope of the symmetry energy L within a specific class of relativistic energy density functionals, we report a value of L = (106 ± 37) MeV—which systematically overestimates current limits based on both theoretical approaches and experimental measurements. Here, the impact of such a stiff symmetry energy on some critical neutron-star observables is also examined.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Relativistic Hybrid Stars with Sequential First-order Phase Transitions in Light of Multimessenger Constraints

In this work, we consider the properties of compact stars in which quark matter has low- and high-density phases that are separated by a first-order phase transition. Thus, unlike the commonly considered case of a single phase transition from hadronic to quark matter, our models of hybrid stars contain sequential phase transitions from hadronic matter to low- and then to high-density quark matter phases. We extend our previous study of the parameter space of hybrid stars with a single phase transition to those with sequential phase transitions, taking into account the constraints on the mass and radius of neutron stars from the NICER experiment, the experimental inferences of the neutron skin thickness of the lead nucleus by the PREX-II experiment, and constraints on the tidal deformability from the gravitational-wave event GW170817. We determine the range of the masses for which both twin and triplet configurations, i.e., identical-mass stars with two and three different values of radii, arise.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Probing the Symmetry Energy with the Spectral Pion Ratio

Many neutron star (NS) properties, such as the proton fraction within a NS, reflect the symmetry energy contributions to the Equation of State that dominate when neutron and proton densities differ strongly. To constrain these contributions at supra-saturation densities, we measure the spectra of charged pions produced by colliding rare isotope tin (Sn) beams with isotopically enriched Sn targets. Here, using ratios of the charged pion spectra measured at high transverse momenta, we deduce the slope of the symmetry energy to be 42 < $L$ < 117 MeV. This value is slightly lower but consistent with the $L$ values deduced from a recent measurement of the neutron skin thickness of 208 Pb.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Electric Dipole Polarizability of Neutron Rich Nuclei

We report that insights into the equation of state of neutron rich matter obtained from the neutron skin thickness of 208 Pb are in sharp conflict with earlier measurements of the electric dipole polarizability. A set of accurately calibrated energy density functionals are used to highlight the tension and to articulate how a highly-intense Gamma Factory may help resolve the present dilemma.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Precise measurement of nuclear interaction cross sections towards neutron-skin determination with R 3 B

The R 3 B (Reactions with Relativistic Radioactive Beams) experiment as a major instrument of the NUSTAR collaboration for the research facility FAIR in Darmstadt is designed for kinematically complete studies of reactions with high-energy radioactive beams. Part of the broad physics program of R 3 B is to constrain the asymmetry term in the nuclear equation-of-state and hence improve the description of highly asymmetric nuclear matter (e.g., in neutron stars). For a precise determination of the neutron-skin thickness – an observable which is directly correlated with the symmetry energy in theoretical calculations – by measuring absolute fragmentation cross sections, it is essential to quantify the uncertainty and challenge the reaction model under stable conditions. During the successful FAIR Phase-0 campaign of R 3 B, we precisely measured the energy dependence of total interaction cross sections in 12 C + 12 C collisions, for a direct comparison with calculations based on the eikonal reaction theory.

Ponnath, L. (ORCID:0000000286742624)↗