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DOE OSTI2024

How do mirror charge radii constrain density dependence of the symmetry energy?

It has recently been suggested that differences in the charge radii of mirror nuclei (Δ$R^{mirr}_{ch}$) 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 48 Ca and 208 Pb, Δ$R^{mirr}_{ch}$ in 36 Ca$-$ 36 S, 38 Ca$-$ 38 Ar, 41 Sc$-$ 41 Ca, 48 Ni$-$ 48 Ca, 52 Ni$-$ 52 Cr, and 54 Ni$-$ 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$R^{mirr}_{ch}$, $R_{skin}$ 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$R^{mirr}_{ch}$ $-$ $L$ 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$R^{mirr}_{ch}$ $-$ $L$ correlation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Global properties of nuclei at finite-temperature within the covariant energy density functional theory

In stellar environments nuclei appear at finite temperatures, becoming extremely hot in core-collapse supernovae and neutron-star mergers. However, due to theoretical and computational complexity, most model calculations of nuclear properties are performed at zero temperature, while those existing at finite temperatures are limited only to selected regions of the nuclide chart. In this study we perform the global calculation of nuclear properties for even-even 8 ≤ Z ≤ 104 nuclei at temperatures in range 0 ≤ T ≤ 2 MeV. Calculations are based on the finite-temperature relativistic Hartree-Bogoliubov model supplemented by the Bonche-Levit-Vautherin vapor subtraction procedure. We find that near the neutron-drip line the continuum states have significant contribution already at moderate temperature T ≈ 1 MeV, thus emphasizing the necessity of the vapor subtraction procedure. Results include neutron emission lifetimes, quadrupole deformations, neutron-skin thickness, proton and neutron pairing gaps, entropy and excitation energy. Up to the temperature T ≈ 1 MeV, the nuclear landscape is influenced only moderately by the finite-temperature effects, mainly by reducing the pairing correlations. Here, as the temperature increases further, the effects on nuclear structures become pronounced, reducing both the deformations and the shell effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Investigating the weak charge of 48 Ca using a dispersive optical model

A new nonlocal dispersive-optical-model analysis has been carried out for neutrons and protons in 48 Ca that reproduces the weak-form-factor measurement of CREX. In addition to elastic-scattering angular distributions, total and reaction cross sections, single-particle energies, the neutron and proton numbers, and the charge distribution, the CREX-measured weak form factor has been fit to extract the neutron and proton self-energies both above and below the Fermi energy. The resulting single-particle propagators yield a weak form factor of F w = 0.125 ± 0.05 and a neutron skin of R skin = 0.152 ± 0.05 fm, in good agreement with CREX. The rearrangement of the neutron distribution to accommodate such a thin neutron skin results in the high-momentum content of the neutrons exceeding that of the protons, in contrast to what is expected from high-energy two-nucleon knockout measurements by the CLAS collaboration and ab initio asymmetric matter calculations. The present analysis also emphasizes the importance of neutron experimental data in constraining weak charge observables necessary for a precise description of neutron densities. Notably, the neutron reaction cross section and further parity-violating experiments weak form factor measurements are essential to generate a unique way to determine the 48 Ca neutron distribution in this framework.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

The Symmetry Energy: Current Status of Ab Initio Predictions vs. Empirical Constraints

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.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Information content of the differences in the charge radii of mirror nuclei

Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy L. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, $ΔR$$^{mir}_{ch}$, is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability α D . In particular, this quantity correlates poorly with both the neutron skin and L. Here, we demonstrate that $ΔR$$^{mir}_{ch}$ is influenced by pairing correlations in the presence of low-lying proton continuum in the proton-rich mirror-partner nucleus. Considering the large theoretical uncertainties on $ΔR$$^{mir}_{ch}$, we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on L.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Bayesian uncertainty quantification for nuclear matter incompressibility

Within a Bayesian statistical framework using the standard Skyrme-Hartree-Fock model, the maximum a posteriori (MAP) values and uncertainties of nuclear matter incompressibility and isovector interaction parameters are inferred from the experimental data of giant resonances and neutron-skin thicknesses of typical heavy nuclei. Furthermore, with the uncertainties of the isovector interaction parameters constrained by the data of the isovector giant dipole resonance and the neutron-skin thickness, we have obtained K 0 = 223$^{+7}_{–8}$ MeV at 68% confidence level using the data of the isoscalar giant monopole resonance in 208 Pb measured at the Research Center for Nuclear Physics (RCNP), Japan, and at the Texas A&M University, USA. Although the corresponding 120 Sn data gives a MAP value for K 0 about 5 MeV smaller than the 208 Pb data, there are significant overlaps in their posterior probability distribution functions.

190 ≤ A ≤ 219↗

DOE OSTI2023

Probing nuclear structure with mean transverse momentum in relativistic isobar collisions

Transverse momentum (p⊥) generation in relativistic heavy-ion collisions is sensitive to the initial geometry and the final-state bulk evolution. We demonstrate with hydrodynamic calculations that the mean p⊥ ratio (R $\langle p⊥ \rangle$ ) between the highly similar isobar $^{96}_{44}$RU + $^{96}_{44}$RU and $^{96}_{44}$Zr + $^{96}_{44}$Zr collisions is insensitive to the bulk evolution and remains sensitive to the small difference in the initial nuclear structure (neutron skin and deformation) between the Ru and Zr nuclei. Here, we further find that nuclear deformation can produce an anticorrelation between R $\langle p⊥ \rangle$ and eccentricity (or elliptic flow) in central collisions. These findings suggest that the R $\langle p⊥ \rangle$ between the isobar systems can be used to measure the neutron skin thickness and deformation parameters, which can, in turn, constrain the nuclear symmetry energy slope parameter.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Implications of PREX-2 on the electric dipole polarizability of neutron-rich nuclei

Background: The recent announcement by the PREX collaboration of an unanticipated thick neutron skin in 208 Pb ($R^{208}_{skin}$) has challenged the understanding of neutron-rich matter in the vicinity of nuclear saturation density. Whereas earlier constraints indicate that the symmetry energy is relatively soft, the PREX-2 result seems to suggest the opposite. Purpose: To confront constraints on the symmetry energy obtained from measurements of the electric dipole polarizability against those informed by the PREX-2 measurement of $R^{208}_{skin}$ and by the correlations that it entails. Methods: Here, covariant energy density functionals informed by the properties of finite nuclei are used to compute the electric dipole response of 48 Ca, 68 Ni, 132 Sn, and 208 Pb. The set of functionals used in this work are consistent with experimental data, yet are flexible enough in that they span a wide range of values of $R^{208}_{skin}$ Results: It is found that theoretical predictions of the electric dipole polarizability that are consistent with the PREX-2 measurement systematically overestimate the corresponding values extracted from the direct measurements of the distribution of electric dipole strength. Conclusions: The neutron skin thickness of 208 Pb extracted from parity violating electron scattering and the electric dipole polarizability measured in photoabsorption experiments are two of the cleanest experimental tools used to constrain the symmetry energy around nuclear saturation density. However, the recent value of $R^{208}_{skin}$ that suggests a fairly stiff symmetry energy stands in stark contrast to the conclusions derived from the electric dipole polarizability. At present, I offer no solution to this dilemma.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Simulations, Modeling and Data Analysis of Parity Violating Electron Scattering Experiments

In the Standard Model (SM) of nuclear and particle physics, parity violation is incorporated through the representation of the weak interaction as a chiral gauge interaction. Only the left-handed components of particles and right-handed components of antiparticles participate in weak interactions in the Standard Model. This implies that parity is asymmetric for the weak interaction. Parity violating electron scattering (PVES) experiments are designed to probe the physics parameters related to the SM, with the possibility to discover physics beyond the SM (BSM) by measuring the parity violating asymmetry ¿¿¿ of longitudinally polarized electrons scattered off unpolarized targets with high precision. This dissertation will be focused on two PVES experiments, the next 208Pb Lead Radius Experiment (PREX-II), and the Measurement of a Lepton-Lepton Electroweak Reaction (MOLLER) experiment, as well as in some small sections, the Calcium Radius Experiment (CREX) and P2 experiment which are also PVES experiments). PREX-II and CREX experiments, performed in Hall A at the Thomas Jefferson National Accelerator Facility (Jefferson Lab), measured ¿¿¿ in the elastic scattering of longitudinally polarized electrons from 208Pb and 48Ca targets to provide a precise model independent determination of the neutron skin thickness of 208Pb and 48Ca nuclei, respectively. The MOLLER experiment, proposed to start in 2027 and also to be performed in Hall A at Jefferson Lab, is to measure ¿¿¿ of longitudinally polarized electrons scattered off unpolarized electrons (Møller scattering) to determine the weak charge of electrons ¿¿¿ and the weak mixing angle ¿¿ with high precision. As for the P2 experiment, which will be performed at the upcoming MESA accelerator in Mainz Germany, it is to measure the weak charge of proton ¿¿¿ using ¿¿¿ in the elastic electron-proton scattering of polarized electrons off unpolarized protons. The final results from the PREX-II experiment are presented as ¿¿¿=550±16 (¿¿¿¿)±8 (¿¿¿¿) parts-per-billion (ppb). Combining the PREX-I and PREX-II results, the neutron skin thickness from PREX experiments is determined as ¿¿-¿¿=0.283±0.071 ¿¿ in 208Pb. This thesis lists the software and computational contribution of the author to these PVES experiments, including writing scripts and software to help with the PREX-II/CREX experiments, analyzing data to provide useful information and systematic uncertainty for the PREX-II experiment, modeling and simulations for the MOLLER, and providing an alternative design of an electronic equipment for the P2 experiment.

Chen, Yufan↗

DOE OSTI2024

Simulations, Modeling and Data Analysis of Parity Violating Electron Scattering Experiments

Chen, Yufan↗

DOE OSTI2024

Probing nuclear structure of heavy ions at energies available at the CERN Large Hadron Collider

We perform high-statistics simulations to study the impacts of nuclear structure on the ratios of anisotropic flow observables in 208 Pb + 208 Pb and 129 Xe + 129 Xe collisions at the Large Hadron Collider. Even with 40% difference in atomic numbers between 208 Pb and 129 Xe nuclei, the ratios of anisotropic flow in the same centrality class between the two collision systems are strongly affected by the nuclear structure inputs in the initial state. The ratios of v 2 ⁡{4}/v 2 ⁡{2} in these collisions are sensitive to the nuclear skin thickness of the colliding nuclei, providing indirect constraints on the nuclei's neutron skin. In conclusion, our model predictions serve as a benchmark to compare with experimental measurements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Compiled properties of nucleonic matter and nuclear and neutron star models from nonrelativistic and relativistic interactions

Here, this paper compiles the model parameters and zero-temperature properties of an extensive collection of published theoretical nuclear interactions, including 255 nonrelativistic (Skyrme-like) forces, 270 relativistic mean field (RMF) and point-coupling (RMF-PC) forces, and 13 Gogny-like forces. This forms the most exhaustive tabulation of model parameters to date. The properties of uniform symmetric matter and pure neutron matter at the saturation density are determined. Symmetry properties found from the second-order term of a Taylor expansion in neutron excess are compared with the energy difference of pure neutron and symmetric nuclear matter at the saturation density. Selected liquid-droplet model parameters, including the surface tension and surface symmetry energy, are determined for semi-infinite surfaces. Theoretical liquid droplet model neutron skin thicknesses of the neutron-rich closed-shell nuclei 48 Ca and 208 Pb are compared with published theoretical Hartree-Fock and experimental results. A similar comparison is made between theoretical liquid-droplet and experimental values of dipole polarizabilities. In addition, radii, binding energies, moments of inertia and tidal deformabilities of 1.2⁢M ⊙ , 1.4⁢M ⊙ and 1.6⁢M ⊙ neutron stars are computed. An extensive correlation analysis of bulk matter, nuclear structure, and low-mass neutron star properties is performed and compared with nuclear experiments and astrophysical observations.

nuclear astrophysics↗

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 OSTI2020

Systematic Matter and Binding-Energy Distributions from a Dispersive Optical Model Analysis

We present the first systematic dispersive-optical-model analysis of 16,18 O, 40,48 Ca, 58,64 Ni, 112,124 Sn, and 208 Pb. In all systems, roughly half the total nuclear binding energy is associated with the most-bound 10% of the total nucleon density. The extracted neutron skins reveal interplay of asymmetry, Coulomb, and shell effects on the skin thickness. Here, our results indicate that optical-model fits on isotopic pairs are effective for constraining nuclear structural quantities otherwise difficult to observe experimentally.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Recent advances in chiral EFT based nuclear forces and their applications

During the past two decades, chiral effective field theory has evolved into a powerful tool to derive nuclear forces from first principles. Nearly all two-nucleon interactions have been worked out up to sixth order of chiral perturbation theory, while, with few exceptions, three-nucleon forces, which play a subtle, but crucial role in microscopic nuclear structure calculations, have been derived up to fifth order. We review the current status of these forces as well as their applications in nuclear many-body systems. While the ab initio description of light nuclei is generally very successful, we point out and analyze problems encountered with medium-mass nuclei. We also survey the construction of equations of state for symmetric nuclear matter and neutron-rich matter based on chiral forces. A focal point is the symmetry energy and its impact on neutron skins and systems of astrophysical relevance. The physics of neutron-rich systems, from nuclei to compact stars, is essentially determined by the density dependence of the symmetry energy. Here, we review the status of predictions in comparison with latest empirical constraints, with particular attention to those extracted from parity-violating electron scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗