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Driven by recent laboratory experiments and astronomical observations, significant advances have deepened our understanding of neutron-star physics. NICER's Pulse Profile Modeling has refined our knowledge of neutron star masses and radii, while gravitational-wave detections have revealed key insights into the structure of neutron stars. Particularly relevant is the extraction of the tidal deformability by the LIGO-Virgo collaboration and the most recent determination of stellar radii by NICER, both suggesting a relatively soft equation of state (EOS) at intermediate densities. Additionally, measurements from the PREX collaboration and from pulsar timing suggest instead that the EOS is stiff in the vicinity of saturation density and at the highest densities accessible to date. But how stiff can the EOS be at these very high densities? Recent events featuring compact objects near the "lower mass gap" have raised questions about the existence of very massive neutron stars. Motivated by this finding and in light of new refinements to theoretical models, we explore the possibility that these massive objects may indeed be rapidly rotating neutron stars. We explore how rotation affects both the maximum neutron star mass and their associated radii, and discuss the implications they may have on the equation of state., Comment: 8 pages and 3 figures. Submitted to Physical Review C

We study the impact of nuclear structure uncertainties on a measurement of the weak charge of $^{12}\mathrm{C}$ at the future MESA facility in Mainz. Information from a large variety of nuclear models, accurately calibrated to the ground-state properties of selected nuclei, suggest that a $0.3$% precision measurement of the parity-violating asymmetry at forward angles will not be compromised by nuclear structure effects, thereby allowing a world-leading determination of the weak charge of $^{12}\mathrm{C}$. Furthermore, we show that a combination of measurements of the parity-violating asymmetry at forward and backward angles for the same electron beam energy can be used to extract information on the nuclear weak charge distribution. We conclude that a $0.34$% precision on the weak radius of $^{12}\mathrm{C}$ may be achieved by performing a $3$% precision measurement of the parity-violating asymmetry at backward angles., Comment: 14 pages, 7 figure, 1 table. Matches the published version

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 [1], 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 in Ref.[1] 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. We expect that powerful reduced basis methods used recently to create efficient emulators will be essential to accomplish this task.

The recently completed PREX-2 campaign - which measured the weak form factor of lead at an optimal momentum transfer - has confirmed that the neutron skin of lead is relatively large and has provided a precise determination of the interior baryon density of a heavy nucleus. In turn, the measured form factor can be related to various nuclear and neutron-star properties. Astrophysical observations by the NICER mission have benefited from improvements in flux, energy resolution, and notably, timing resolution. NICER has the capability to measure pulse profile data, which enables simultaneous mass-radius determinations. During the next decade, measurements in astrophysics, gravitational wave astronomy, and nuclear physics are expected to provide a wealth of more precise data. In this review we provide an overview of the current state of neutron skin measurements and offer insights into the prospects for the future., Comment: submitted to Annual Reviews of Nuclear and Particle Science

The confluence of major theoretical, experimental, and observational advances are providing a unique perspective on the equation of state of dense neutron-rich matter -- particularly its symmetry energy -- and its imprint on the mass-radius relation for neutron stars. In this contribution we organize these developments in an equation of state density ladder. Of particular relevance to this discussion is the impact of the various rungs on the equation of state and the identification of possible discrepancies among the various methods. A preliminary analysis identifies a possible tension between laboratory measurements and gravitational-wave detections that could indicate the emergence of a phase transition in the stellar core.

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS., Comment: White paper prepared for the 2023 Long Range Plan. v3: Updated version as published in Progress in Particle and Nuclear Physics. Note: the published version does not include the executive summary; in the updated arXiv version, the executive summary is included as an appendix. v4: Corrected list of authors

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 predictions with properly estimated uncertainties for observables not included in the fit, specifically the neutron skin thickness of 208Pb and 48Ca, as reported by PREX and CREX collaborations. 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., Comment: 23 pages, 7 figures

The nuclear root-mean-square charge radius of $^{54}$Ni was determined with collinear laser spectroscopy to be $R(^{54}$Ni) = 3.737\,(3)~fm. In conjunction with the known radius of the mirror nucleus $^{54}$Fe, the difference of the charge radii was extracted as $\Delta R_{\rm ch}$ = 0.049\,(4)~fm. Based on the correlation between $\Delta R_{\rm ch}$ and the slope of the symmetry energy at nuclear saturation density ($L$), we deduced $20 \le L \le 70$\,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$\sigma$ error bands. Our result indicates the neutron-skin thickness of $^{48}$Ca as 0.15\,-\,0.19\,fm., Comment: 6 total pages, 3 figures

We present a feasibility study of a simultaneous sub-percent extraction of the weak charge and the weak radius of the ${}^{12}$C nucleus using parity-violating electron scattering, based on a largely model-independent assessment of the uncertainties. The corresponding measurement is considered to be carried out at the future MESA facility in Mainz with $E_{\rm beam} = 155$ MeV. We find that a combination of a $0.3\%$ precise measurement of the parity-violating asymmetry at forward angles with a $10\%$ measurement at backward angles will allow to determine the weak charge and the weak radius of ${}^{12}$C with $0.4\%$ and $0.5\%$ precision, respectively. These values could be improved to $0.3\%$ and $0.2\%$ for a $3\%$ backward measurement. This experimental program will have impact on precision low-energy tests in the electroweak sector and nuclear structure., Comment: 7 pages, 5 figures

Exotic nuclei, particularly those near the driplines, are at the core of one of the fundamental questions driving nuclear structure and astrophysics today: what are the limits of nuclear binding? Exotic nuclei play a critical role in both informing theoretical models as well as in our understanding of the origin of the heavy elements. Our purpose is to refine existing mass models through the training of an artificial neural network that will mitigate the large model discrepancies far away from stability. The basic paradigm of our two-pronged approach is an existing mass model that captures as much as possible of the underlying physics followed by the implementation of a Bayesian Neural Network (BNN) refinement to account for the missing physics. Bayesian inference is employed to determine the parameters of the neural network so that model predictions may be accompanied by theoretical uncertainties. Despite the undeniable quality of the mass models adopted in this work, we observe a significant improvement (of about 40%) after the BNN refinement is implemented. Indeed, in the specific case of the Duflo-Zuker mass formula, we find that the rms deviation relative to experiment is reduced from rms =0.503MeV to rms=0.286 MeV. These newly refined mass tables are used to map the neutron drip lines (or rather "drip bands") and to study a few critical r-process nuclei. The BNN approach is highly successful in refining the predictions of existing mass models. In particular, the large discrepancy displayed by the original "bare" models in regions where experimental data is unavailable is considerably quenched after the BNN refinement. This lends credence to our approach and has motivated us to publish refined mass tables that we trust will be helpful for future astrophysical applications.

The distribution of electric charge in atomic nuclei is fundamental to our understanding of the complex nuclear dynamics and a quintessential observable to validate nuclear structure models. We explore a novel approach that combines sophisticated models of nuclear structure with Bayesian neural networks (BNN) to generate predictions for the charge radii of thousands of nuclei throughout the nuclear chart. A class of relativistic energy density functionals is used to provide robust predictions for nuclear charge radii. In turn, these predictions are refined through Bayesian learning for a neural network that is trained using residuals between theoretical predictions and the experimental data. Although predictions obtained with density functional theory provide a fairly good description of experiment, our results show significant improvement (better than 40%) after BNN refinement. Moreover, these improved results for nuclear charge radii are supplemented with theoretical error bars. We have successfully demonstrated the ability of the BNN approach to significantly increase the accuracy of nuclear models in the predictions of nuclear charge radii. However, as many before us, we failed to uncover the underlying physics behind the intriguing behavior of charge radii along the calcium isotopic chain., Comment: 14 pages, 6 figures

The Garvey-Kelson relations (GKRs) are algebraic expressions originally developed to predict nuclear masses. In this letter we show that the GKRs provide a fruitful framework for the prediction of other physical observables that also display a slowly-varying dynamics. Based on this concept, we extend the GKRs to the study of nuclear charge radii. The GKRs are tested on 455 out of the approximately 800 nuclei whose charge radius is experimentally known. We find a rms deviation between the GK predictions and the experimental values of only 0.01 fm. This should be contrasted against some of the most successful microscopic models that yield rms deviations almost three times as large. Predictions - with reliable uncertainties - are provided for 116 nuclei whose charge radius is presently unknown., Comment: 4 pages and 3 figures

A new relation between the neutron skin of a heavy nucleus and the radius of a neutron star is proposed: the larger the neutron skin of the nucleus the larger the radius of the star. Relativistic models that reproduce a variety of ground-state observables can not determine uniquely the neutron skin of a heavy nucleus. Thus, a large range of neutron skins is generated by supplementing the models with nonlinear couplings between isoscalar and isovector mesons. We illustrate how the correlation between the neutron skin and the radius of the star can be used to place important constraints on the equation of state and how it may help elucidate the existence of a phase transition in the interior of the neutron star., Comment: 4 pages including 4 encapsulated postscript figures

Isoscalar monopole and dipole compressional modes are computed for a variety of closed-shell nuclei in a relativistic random-phase approximation to three different parametrizations of the Walecka model with scalar self-interactions. Particular emphasis is placed on the role of self-consistency which by itself, and with little else, guarantees the decoupling of the spurious isoscalar-dipole strength from the physical response and the conservation of the vector current. A powerful new relation is introduced to quantify the violation of the vector current in terms of various ground-state form-factors. For the isoscalar-dipole mode two distinct regions are clearly identified: (i) a high-energy component that is sensitive to the size of the nucleus and scales with the compressibility of the model and (ii) a low-energy component that is insensitivity to the nuclear compressibility. A fairly good description of both compressional modes is obtained by using a ``soft'' parametrization having a compression modulus of K=224 MeV., Comment: 28 pages and 10 figures; submitted to PRC

We study strangeness-changing response functions as an alternative description of hypernuclear structure. Hypernuclear states are treated in the same manner as any other conventional nuclear excitation that emerges from the response of the nuclear ground state to an external probe. The nuclear response is calculated using a random-phase approximation to an effective relativistic mean-field model that reproduces bulk properties of normal nuclei. The relevant meson-baryon vertices are constrained by imposing SU(3)-flavor symmetry, while the residual hyperon-particle - nucleon-hole interaction is assumed to be mediated by the two lightest S = -1 mesons: the pseudoscalar kaon and its vector partner the K*(892). We use this model to analyze the spectra of oxygen and calcium hypernuclei., Comment: RevTex, 17 pages, 8 figures

Nuclear matter is modeled directly in terms of its constituent quarks. A many-body string-flip potential is used that confines quarks within hadrons, enables the hadrons to separate without generating van der Waals forces, and is symmetric in all quark coordinates. We present variational Monte Carlo results for the ground-state properties of large, three-dimensional systems. A phase transition from nuclear to quark matter is observed which is characterized by a dramatic rearrangement of strings. We report on exact calculations of the dynamic response of many-quark systems in one spatial dimension. At low density and small momentum transfers the response is substantially larger than that of a free Fermi gas of quarks; this suggests that there is a coherent response from all the quarks inside the hadron. This coherence, however, is incomplete, as the response is suppressed relative to that of a free Fermi gas of nucleons due to the internal quark substructure of the hadron., Comment: 10 (LaTeX) pages with five figures; to appear in the proceedings of the Int. Symp. on Non-nucleonic Degrees of Freedom Detected in Nucleus, Osaka, Japan, September 2-5, 1996

We examine the effect of isospin-violating meson-nucleon coupling constants and of $\pi$-$\eta$ mixing on the binding-energy differences of mirror nuclei in a model that possesses no contribution from $\rho$-$\omega$ mixing. The ${}^{3}$He-${}^{3}$H binding-energy difference is computed in a nonrelativistic approach using a realistic wave function. We find the ${}^{3}$He-${}^{3}$H binding-energy difference very sensitive to the short-distance behavior of the nucleon-nucleon potential. We conclude that for the typically hard Bonn form factors such models can not account for the observed binding-energy difference in the three-nucleon system. For the medium-mass region (A=15--41) the binding-energy differences of mirror nuclei are computed using a relativistic mean-field approximation to the Walecka model. We obtain large binding-energy differences---of the order of several hundred keV---arising from the pseudoscalar sector. Two effects are primarily responsible for this new finding: a) the inclusion of isospin breaking in the pion-nucleon coupling constant, and b) the in-medium enhancement of the small components of the bound-state wave functions. We look for off-shell ambiguities in these results and find them to be large., Comment: 19 LaTeX pages and 2 postscript figures. Revisions/additions: Manuscript now includes a treatment of the binding-energy difference in the three-nucleon system as well as a study of possible off-shell ambiguities in the binding-energy differences of (A=15-41) mirror nuclei

We examine the effect of isospin-violating meson-nucleon coupling constants on low-energy pion-nucleon scattering. We compute the couplings in the context of a nonrelativistic quark model. The difference between the up and down constituent masses induces a coupling of the neutral pion to the proton that is slightly larger than the corresponding one for the neutron. This difference generates a large isospin-violating correction---proportional to the isospin-even contribution arising from the nucleon Born terms---to the charge-exchange ($\pi^{-}p \rightarrow \pi^{0}n$) amplitude. In contrast to the isospin-conserving case, this correction is not cancelled by $\sigma$-meson exchange; in our model there is no isospin-violating $NN\sigma$ coupling at $q^2=0$. As a result, we find a violation of the triangle identity consistent with the one reported by Gibbs, Ai, and Kaufmann from a recent analysis of pion-nucleon data., Comment: 9 pages, no figures