Accurate calibration of relativistic mean-field models: correlating observables and providing meaningful theoretical uncertainties

Abstract

Theoretical uncertainties in the predictions of relativistic mean-field models are estimated using a chi-square minimization procedure that is implemented by studying the small oscillations around the chi-square minimum. By diagonalizing the matrix of second derivatives, one gains access to a wealth of information---in the form of powerful correlations---that would normally remain hidden. We illustrate the power of the {\sl covariance analysis} by using two relativistic mean-field models: (a) the original linear Walecka model and (b) the accurately calibrated FSUGold parametrization. In addition to providing meaningful theoretical uncertainties for both model parameters and predicted observables, the covariance analysis establishes robust correlations between physical observables. In particular, we show that whereas the correlation coefficient between the slope of the symmetry energy and the neutron-skin thickness of Lead is indeed very large, a 1% measurement of the neutron radius of Lead may only be able to constrain the slope of the symmetry energy to about 30%.

15 pages, 3 figures, 3 tables

References in corpus (11)

• Shapiro delay measurement of a two solar mass neutron star
• Neutron-Rich Nuclei in Heaven and Earth
• Nuclear symmetry energy probed by neutron skin thickness of nuclei
• Neutron skin of 208Pb, nuclear symmetry energy, and the parity radius experiment
• Relativistic effective interaction for nuclei, giant resonances, and neutron stars
• Incompressibility of neutron-rich matter
• Pygmy Resonances and Neutron Skins
• Surface Symmetry Energy of Nuclear Energy Density Functionals
• Asymmetric nuclear matter and neutron-skin in extended relativistic mean field model
• Why is Tin so soft?
• Validating relativistic models of nuclear structure against theoretical, experimental, and observational constraints

Cited by in corpus (51)

• Equations of state for supernovae and compact stars
• Error Estimates of Theoretical Models: a Guide
• Building relativistic mean field models for finite nuclei and neutron stars
• Nuclear energy density optimization: Shell structure
• Towards Understanding Astrophysical Effects of Nuclear Symmetry Energy
• Neutron skins of atomic nuclei: per aspera ad astra
• Energy density functional for nuclei and neutron stars
• Critical Density and Impact of $\Delta (1232)$ Resonance Formation in Neutron Stars
• Information content of the low-energy electric dipole strength: correlation analysis
• Covariant energy density functionals: nuclear matter constraints and global ground state properties
• Neutron skins and neutron stars
• Neutron-proton effective mass splitting in neutron-rich matter at normal density from analyzing nucleon-nucleus scattering data within an isospin dependent optical model
• Propagation of uncertainties in the Skyrme energy-density-functional model
• Nuclear Theory and Science of the Facility for Rare Isotope Beams
• Impact of the neutron star crust on the tidal polarizability
• Living on the edge of stability, the limits of the nuclear landscape
• Neutron skin uncertainties of Skyrme energy density functionals
• Generic Constraints on the Relativistic Mean-Field and Skyrme-Hartree-Fock Models from the Pure Neutron Matter Equation of State
• Information content of the weak-charge form factor
• Symmetry Energy Constraints from Giant Resonances: A Theoretical Overview
• Symmetry energy in nuclear density functional theory
• Nuclear charge and neutron radii and nuclear matter: trend analysis
• Constraining compact star properties with nuclear saturation parameters
• Information content of the differences in the charge radii of mirror nuclei
• Covariance analysis for Energy Density Functionals and instabilities
• Neutron star structure and collective excitations of finite nuclei
• Effect of topological defects on "nuclear pasta" observables
• Nuclear fourth-order symmetry energy and its effects on neutron star properties in the relativistic Hartree-Fock theory
• Sensitivity of the fusion cross section to the density dependence of the symmetry energy
• Challenges in Nuclear Structure Theory
• Sloppy nuclear energy density functionals: effective model reduction
• Magnetization of neutron star matter
• CREX- and PREX-II-motivated relativistic interactions and their implications for the bulk properties of nuclear matter and neutron stars
• Information and statistics: a new paradigm in theoretical nuclear physics
• Observational constraint from the heaviest pulsar PSR J0952-0607 on the equation of state of dense matter in relativistic mean field model
• Uncertainty quantification in nuclear shell model
• Optimizing relativistic energy density functionals: covariance analysis
• Non-parametric Bayesian approach to extrapolation problems in configuration interaction methods
• Quantifying Correlations Between Isovector Observables and the Density Dependence of Nuclear Symmetry Energy away from Saturation Density
• Propagation of uncertainties in the nuclear DFT models
• Uncertainty propagation within the UNEDF models
• Giant monopole energies from a constrained relativistic mean-field approach
• Moments of inertia of neutron stars in relativistic mean field theory: the role of the isovector scalar channel
• Uncertainty Quantification for Neutrino Opacities in Core-Collapse Supernovae and Neutron Star Mergers
• Pure Neutron Matter Constraints and Nuclear Symmetry Energy
• Sensitivity of predictions in an effective model -- application to the chiral critical end point position in the Nambu--Jona-Lasinio model
• Pygmies, giants, and skins as laboratory constraints on the equation of state of neutron-rich matter
• Direct Inference of Nuclear Equation-of-State Parameters from Gravitational-Wave Observations
• Pygmies, Giants, and Skins
• Analytic insights on the information content of new observables
• Uncertainty evaluation and correlation analysis of single-particle energies in phenomenological nuclear mean field: An investigation of propagating uncertainties for independent model parameters