Background: Theoretical approaches based on density functional theory provide the only tractable method to incorporate the wide range of densities and isospin asymmetries required to describe finite nuclei, infinite nuclear matter, and neutron stars.Purpose: A relativistic energy density functional (EDF) is developed to address the complexity of such diverse nuclear systems. Moreover, a statistical perspective is adopted to describe the information content of various physical observables.Methods: We implement the model optimization by minimizing a suitably constructed χ 2 objective function using various properties of finite nuclei and neutron stars. The minimization is then supplemented by a covariance analysis that includes both uncertainty estimates and correlation coefficients.Results: A new model, "FSUGold 2 ", is created that can well reproduce the ground-state properties of finite nuclei, their monopole response, and that accounts for the maximum neutron star mass observed up to date. In particular, the model predicts both a stiff symmetry energy and a soft equation of state for symmetric nuclear matter-suggesting a fairly large neutron-skin thickness in 208 Pb and a moderate value of the nuclear incompressibility. Conclusions:We conclude that without any meaningful constraint on the isovector sector, relativistic EDFs will continue to predict significantly large neutron skins. However, the calibration scheme adopted here is flexible enough to create models with different assumptions on various observables. Such a scheme-properly supplemented by a covariance analysis-provides a powerful tool to identify the critical measurements required to place meaningful constraints on theoretical models.

Recent progress in the determination of both masses and radii of neutron stars are starting to place stringent constraints on the dense matter equation of state. In particular, new theoretical developments together with improved statistical tools seem to favor stellar radii that are significantly smaller than those predicted by models using purely nucleonic equations of state. Given that the underlying equation of state must also account for the observation of 2M neutron stars, theoretical approaches to the study of the dense matter equation of state are facing serious challenges. In response to this challenge, we compute in a model-independent way the underlying equation of state associated with an assumed mass-radius template similar to the "common radius" assumption used in recent studies. Once such a mass-radius template is adopted, the equation of state follows directly from the implementation of Lindblom's algorithm; assumptions on the nature or composition of the dense stellar core are not required. By analyzing mass-radius profiles with a maximum mass consistent with observation and common radii in the 8 to 11 km range, a lower limit on the stellar radius of a 1.4M neutron star of RNS 10.7 km is obtained in order to prevent the equation of state from violating causality. How does subatomic matter organize itself and what phenomena emerge is one of the overarching questions guiding the field of nuclear physics [1]. In the case of atomic nuclei, the quest to answer this question requires understanding the nature of the nuclear force and the limits of nuclear existence. In the case of extended nucleonic matter, this involves elucidating the nature of neutron stars and dense nuclear matter. In this letter we focus on the latter.Owing to the long-range nature of the Coulomb force, extended nucleonic matter must be electrically neutral. As a result, dense nuclear matter must be by necessity neutron-rich. This is because the electronic contribution to the energy increases rapidly with density, so electron capture becomes energetically advantageous. Given that such extreme conditions of density and isospin asymmetry can not be realized in terrestrial experiments, neutron stars have become unique laboratories for the exploration of dense matter. This situation has created a strong synergy between nuclear physics and astrophysics, that has been cemented even further through an intimate interplay between theory, experiment, and observation [2]. Indeed, powerful telescopes operating at a variety of wavelengths drive new theoretical and experimental efforts which in turn suggest new observations. A recent example of such a unique synergy is how accurate measurements of massive neutron stars [3,4] have informed nuclear models that fall under the general rubric of density functional theory. Density functional theory (DFT) offers a comprehensive-and likely unique-framework to describe strongly interacting nu- * Electronic address: wc09c@my.fsu.edu † Electronic address: jpiekarewicz@fsu.edu clear many-body systems rangin...

openAccessArticle: Truecover date: 2015-09-02pii: S0370-2693(15)00530-4Harvest Date: 2016-01-06 13:08:33issueName:Page Range: 284-284href scidir: http://www.sciencedirect.com/science/article/pii/S0370269315005304pubType

Background: 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.Purpose: To 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.Methods: 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.Results: 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. Conclusions: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.

How might a smooth probability distribution be estimated, with accurately quantified uncertainty, from a limited amount of sampled data? Here we describe a field-theoretic approach that addresses this problem remarkably well in one dimension, providing an exact nonparametric Bayesian posterior without relying on tunable parameters or large-data approximations. Strong non-Gaussian constraints, which require a non-perturbative treatment, are found to play a major role in reducing distribution uncertainty. A software implementation of this method is provided.