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At least 73 records · Page 4

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↗

Accurate Determination of the Neutron Skin Thickness of Pb 208 through Parity-Violation in Electron Scattering

We report a precision measurement of the parity-violating asymmetry A PV in the elastic scattering of longitudinally polarized electrons from 208 Pb. We measure A PV = 550 ± 16 (stat) ±8 (syst) parts per billion, leading to an extraction of the neutral weak form factor F W (Q 2 = 0.00616 GeV 2 ) = 0.368 ± 0.013. Combined with our previous measurement, the extracted neutron skin thickness is R n -R p = 0.283 ± 0.071 fm. The result also yields the first significant direct measurement of the interior weak density of 208 Pb: ρ$^0_W$ = -0.0796 ± 0.0036(exp) ± 0.0013(theo) fm -3 leading to the interior baryon density ρ$^0_b$ = 0.1480 ± 0.0036(exp) ± 0.0013(theo) fm -3 . Finally, the measurement accurately constrains the density dependence of the symmetry energy of nuclear matter near saturation density, with implications for the size and composition of neutron stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Precision Determination of the Neutral Weak Form Factor of Ca 48

In this work, we report a precise measurement of the parity-violating asymmetry $A_{\rm PV}$ in the elastic scattering of longitudinally polarized electrons from $^{48}{\rm Ca}$. We measure $A_{\rm PV} =2668\pm 106\ {\rm (stat)}\pm 40\ {\rm (syst)}$ parts per billion, leading to an extraction of the neutral weak form factor $F_{\rm W} (q=0.8733$ fm$^{-1}) = 0.1304 \pm 0.0052 \ {\rm (stat)}\pm 0.0020\ {\rm (syst)}$ and the charge minus the weak form factor $F_{\rm ch} - F_{\rm W} = 0.0277\pm 0.0055$. The resulting neutron skin thickness $R_n-R_p=0.121 \pm 0.026\ {\rm (exp)} \pm 0.024\ {\rm (model)}$~fm is relatively thin yet consistent with many model calculations. The combined CREX and PREX results will have implications for future energy density functional calculations and on the density dependence of the symmetry energy of nuclear matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Measurement of the $\textit{B}(\textit{E}2 ↑)$ strengths of 36 Ca and 38 Ca

In this work, the $B(E2, 0^+_1 → 2^+_1)$ strengths of 36 Ca and 38 Ca are measured to be 131(20) $e^2\text{fm}^4$ and 101(11) $e^2\text{fm}^4$, respectively. The $\textit{B}(\textit{E}2)$ value for 36 Ca required a measurement of the p/γ branching ratio because the 2 + state is proton unbound. This branching ratio is $B_p$=0.087(8). These $\textit{B}(\textit{E}2)$ and branching-ratio values can be reproduced in the shell-model with the ZMB2 interaction, an interaction that predicts the $\textit{Z} = 20 \textit{sd}$-shell closure is incomplete with large proton pf-shell occupancies in the ground state. These occupancies are at odds with other shell-model and energy-density-functional calculations of 36 Ca. New data are used to provide an update on constraints of the density dependence of the symmetry energy through mirror charge-radii differences as well as to help reduce uncertainties of the astrophysical important 35 K(p,γ) reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Semi-classical approximation description of static properties of nuclei

In this report, we present recent development in semi-classical description of static properties of nuclei. By employing the Wigner transform, we derive simple semiclassical approximations for evaluating properties of nuclear system. We present results of calculations of static properties, using the energy density functional associated with Skyrme effective nucleon–nucleon interaction. In particular, we consider properties of the Wigner distribution function, line of beta stability, Coulomb and symmetry energies, deformation energies, equation of state, nuclear radii, and single-particle level density.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Probing neutron-skin thickness with free spectator neutrons in ultracentral high-energy isobaric collisions

We show that the yield ratio of free spectator neutrons produced in high-energy 96 Zr+ 96 Zr to 96 Ru+ 96 Ru collisions is a clean probe of the neutron-skin thickness of colliding nuclei and the slope parameter L of the symmetry energy. The idea is demonstrated based on the proton and neutron density distributions via a state-of-the-art Skyrme-Hartree-Fock-Bogolyubov calculation. Among spectator nucleons given by the Glauber model, free spectator neutrons include those from direct production that survive from clusterization as well as those from deexcitation of heavy clusters described by the popular GEMINI model. More free neutrons are produced in collisions of 96 Zr nucleus due to its larger neutron skin, compared to those produced in collisions of 96 Ru nucleus with a smaller neutron skin. The difference of the free spectator neutron yield is further increased with the increasing difference of the neutron-skin thickness between 96 Zr and 96 Ru with a larger L value, and the increase in ultracentral collisions is particularly insensitive to model details and experimental uncertainties. Since the production of free spectator neutrons is not affected by the complicated dynamics in the mid-rapidity region, the ratio of their multiplicities in ultracentral isobaric collisions is a robust observable for constraining the neutron skin and L value.

79 ASTRONOMY AND ASTROPHYSICS↗

Probing the Neutron Skin with Ultrarelativistic Isobaric Collisions

Particle production in ultrarelativistic heavy ion collisions depends on the details of the nucleon density distributions in the colliding nuclei. We demonstrate that the charged hadron multiplicity distributions in isobaric collisions at ultrarelativistic energies provide a novel approach to determine the poorly known neutron density distributions and thus the neutron skin thickness in finite nuclei, which can in turn put stringent constraints on the nuclear symmetry energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Neutron matter from local chiral effective field theory interactions at large cutoffs

Neutron matter is an important many-body system that provides valuable constraints for the equation of state (EOS) of neutron stars. Neutron-matter calculations employing chiral effective field theory (EFT) interactions have been extensively used for this purpose. Among the various many-body methods, quantum Monte Carlo (QMC) methods stand out due to their nonperturbative nature and the achievable precision. However, QMC methods require local interactions as input, which leads to the appearance of stronger regulator artifacts compared to nonlocal interactions. To circumvent this, we employ large-cutoff interactions derived within chiral EFT (400 MeV ≤ Λ 𝑐 ≤ 700MeV) for studies of pure neutron matter. These interactions have been adjusted to nucleon-nucleon scattering phase shifts, the triton binding energy, as well as the triton 𝛽-decay half-life. We find that regulator artifacts significantly decrease with increasing cutoff, leading to a significant reduction of uncertainties in the neutron-matter EOS. We discuss implications for the symmetry energy and demonstrate how our new calculations lead to a reduction in the theoretical uncertainty of predicted neutron-star radii by up to 30% for low-mass stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Charge radii of exotic neon and magnesium isotopes

We compute the charge radii and ground-state energies of even-mass neon and magnesium isotopes from neutron number N = 8 to the dripline. Our calculations are based on nucleon-nucleon and three-nucleon potentials from chiral effective field theory that include Δ isobars. These potentials yield an accurate saturation point and symmetry energy of nuclear matter. We use the coupled-cluster method and start from an axially symmetric reference state. Binding energies and two-neutron separation energies largely agree with data, and the dripline in neon is accurate. The computed charge radii are accurate for many isotopes where data exist. Finer details, such as isotope shifts, however, are not accurately reproduced. These chiral potentials indicate a subshell closure at N = 14 for the radii (but not for two-neutron separation energies) and a decrease in charge radii at N = 8 (observed in neon and predicted for magnesium). Furthermore, they yield a continued increase of charge radii as neutrons are added beyond N = 14 yet underestimate the large increase at N = 20 in magnesium.

20 ≤ A ≤ 38↗

Information Content of the Parity-Violating Asymmetry in Pb 208

The parity-violating asymmetry A PV in 208 Pb, recently measured by the PREX-2 Collaboration, is studied using modern relativistic (covariant) and nonrelativistic energy density functionals. We first assess the theoretical uncertainty on A PV which is intrinsic to the adopted approach. To this end, we use quantified functionals that are able to accommodate our previous knowledge on nuclear observables such as binding energies, charge radii, and the dipole polarizability α D of 208 Pb. We then add the quantified value of A PV together with α D to our calibration dataset to optimize new functionals. Based on these results, we predict a neutron skin thickness in 208 Pb r skin = 0.19 ± 0.02 fm and the symmetry-energy slope L = 54 ± 8 MeV. These values are consistent with other estimates based on astrophysical data and are significantly lower than those recently reported using a particular set of relativistic energy density functionals. Here, we also make a prediction for the A PV value in 48 Ca that will be soon available from the CREX measurement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A theoretical overview of isospin and EOS effects in heavy-ion reactions at intermediate energies

The isospin dependence of in-medium nuclear effective interactions is a fundamental issue in nuclear physics and has broad ramifications in astrophysics. Its uncertainties, especially the difference of neutron-proton interactions in the isosinglet and isotriplet channels, affect significantly the density and momentum dependence of the isovector single-nucleon potential and nucleon-nucleon short-range correlation in neutron-rich matter. Consequently, the neutron-proton effective mass splitting and the density dependence of nuclear symmetry energy are still rather uncertain. Heavy-ion reactions, especially those involving rare isotopes, are a useful tool for probing the isospin dependence of nuclear effective interactions through 1) the neutron-skin in coordinate and proton-skin in momentum of the initial state of colliding nuclei, 2) the density and momentum dependence of especially the isovector nuclear mean-field as well as 3) the isospin dependence of in-medium nucleon-nucleon cross sections. Observations of neutron stars especially since GW1710817 have also helped us significantly in understanding the isospin dependence of nuclear effective interactions. We summarize here a review talk on these issues given at the 2021 International Workshop on multi-facets of EOS and Clustering. For details we refer the readers to the original publications and references therein.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

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)↗

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↗

Quarkyonic matter equation of state in beta-equilibrium

Quark matter may appear due to a hadronic-quark transition in the core of a hybrid star. Quarkyonic matter is an approach in which both quarks and nucleons appear as quasiparticles in a crossover transition, and provides an explicit realization of early ideas concerning quark matter (e.g., the MIT bag model). This description has recently been employed by McLerran and Reddy to model chargeless (pure neutron) matter with an approach that has the virtue that the speed of sound rises quickly at a neutron-quark transition so as to satisfy observational constraints on the neutron star maximum mass (≳ 2 $M_⊙$) and the radius of a 1.4 $M_⊙$ star ($R_{1.4}$ ≲ 13.5 km). Traditional models involving first-order transitions result in softer pressure-energy density relations that have difficulty satisfying these constraints except with very narrow choices of parameters. Here, we propose a variation of quarkyonic matter involving protons and leptons whose energy can be explicitly minimized to achieve both chemical and beta equilibrium, which cannot be done in the chargeless formulation. Quarkyonic stellar models are able to satisfy observed mass and radius constraints with a wide range of model parameters, avoiding the obligatory fine-tuning of conventional hybrid star models, including requiring the transition density to be very close to the nuclear saturation density. Our formulation fits experimental and theoretical properties of the nuclear symmetry energy and pure neutron matter, and contains as few as three free parameters. This makes it an ideal tool for the study of high-density matter that is an efficient alternative to piecewise polytrope or spectral decomposition methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗

Indirect methods in nuclear astrophysics with relativistic radioactive beams

Reactions with radioactive nuclear beams at relativistic energies have opened new doors to clarify the mechanisms of stellar evolution and cataclysmic events involving stars and during the big bang epoch. Numerous nuclear reactions of astrophysical interest cannot be assessed directly in laboratory experiments. Ironically, some of the information needed to describe such reactions, at extremely low energies (e.g., keVs), can only be studied on Earth by using relativistic collisions between heavy ions at GeV energies. In this contribution, we make a short review of experiments with relativistic radioactive beams and of the theoretical methods needed to understand the physics of stars, adding to the knowledge inferred from astronomical observations. We continue by introducing a more detailed description of how the use of relativistic radioactive beams can help to solve astrophysical puzzles and several successful experimental methods. State-of-the-art theories are discussed at some length with the purpose of helping us understand the experimental results reported. The review is not complete and we have focused most of it to traditional methods aiming at the determination of the equation of state of symmetric and asymmetric nuclear matter and the role of the symmetry energy. Whenever possible, under the limitations of our present understanding of experimental data and theory, we try to pinpoint the information still missing to further understand how stars evolve, explode, and how their internal structure might be. We try to convey the idea that in order to improve microscopic theories for many-body calculations, nuclear structure, nuclear reactions, and astrophysics, and in order to constrain and allow for convergence of our understanding of stars, we still need considerable improvements in terms of accuracy of experiments and the development of new and dedicated nuclear facilities to study relativistic reactions with radioactive beams.

79 ASTRONOMY AND ASTROPHYSICS↗

Bayes goes fast: Uncertainty quantification for a covariant energy density functional emulated by the reduced basis method

A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the calibration is enabled by the emulation of the high-fidelity model through the implementation of a reduced basis method (RBM)—a set of dimensionality reduction techniques that can speed up demanding calculations involving partial differential equations by several orders of magnitude. The RBM emulator we build—using only 100 evaluations of the high-fidelity model—is able to accurately reproduce the model calculations in tens of milliseconds on a personal computer, an increase in speed of nearly a factor of 3,300 when compared to the original solver. Besides the analysis of the posterior distribution of parameters, we present model calculations for masses and radii with properly estimated uncertainties. We also analyze the model correlation between the slope of the symmetry energy L and the neutron skin of 48 Ca and 208 Pb. The straightforward implementation and outstanding performance of the RBM makes it an ideal tool for assisting the nuclear theory community in providing reliable estimates with properly quantified uncertainties of physical observables. Such uncertainty quantification tools will become essential given the expected abundance of data from the recently inaugurated and future experimental and observational facilities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Bayesian mixture model approach to quantifying the empirical nuclear saturation point

The equation of state (EOS) in the limit of infinite symmetric nuclear matter exhibits an equilibrium density, $n_0 \approx 0.16 \, \mathrm{fm}^{-3}$, at which the pressure vanishes and the energy per particle attains its minimum, $E_0 \approx -16 \, \mathrm{MeV}$. Although not directly measurable, the nuclear saturation point $(n_0,E_0)$ can be extrapolated by density functional theory (DFT), providing tight constraints for microscopic interactions derived from chiral effective field theory (EFT). However, when considering several DFT predictions for $(n_0,E_0)$ from Skyrme and Relativistic Mean Field (RMF) models together, a discrepancy between these model classes emerges at high confidence levels that each model prediction's uncertainty cannot explain. How can we leverage these DFT constraints to rigorously benchmark nuclear saturation properties of chiral interactions? To address this question, we present a Bayesian mixture model that combines multiple DFT predictions for $(n_0,E_0)$ using an efficient conjugate prior approach. The inferred posterior distribution for the saturation point's mean and covariance matrix follows a Normal-inverse-Wishart class, resulting in posterior predictives in the form of correlated, bivariate $t$-distributions. The DFT uncertainty reports are then used to mix these posteriors using an ordinary Monte Carlo approach. At the 95\% credibility level, we estimate $n_0 \approx 0.157 \pm 0.010 \, \mathrm{fm}^{-3}$ and $E_0 \approx -15.97 \pm 0.40 \, \mathrm{MeV}$ for the marginal (univariate) $t$-distributions. Combined with chiral EFT calculations of the pure neutron matter EOS, we obtain bivariate normal distributions for the nuclear symmetry energy and its slope parameter evaluated at $n_0$: $S_v \approx 32.0 \pm 1.1 \, \mathrm{MeV}$ and $L\approx 52.6\pm 8.1 \, \mathrm{MeV}$ (95\%), respectively. Furthermore, our Bayesian framework is publicly available, so practitioners can readily use and extend our results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗