Covariance analysis for Energy Density Functionals and instabilities

Abstract

We present the covariance analysis of two successful nuclear energy density functionals, (i) a non-relativistic Skyrme functional built from a zero-range effective interaction, and (ii) a relativistic nuclear energy density functional based on density dependent meson-nucleon couplings. The covariance analysis is a useful tool for understanding the limitations of a model, the correlations between observables and the statistical errors. We show, for our selected test nucleus 208Pb, that when the constraint on a property A included in the fit is relaxed, correlations with other observables B become larger; on the other hand, when a strong constraint is imposed on A, the correlations with other properties become very small. We also provide a brief review, partly connected with the covariance analysis, of some instabilities displayed by several energy density functionals currently used in nuclear physics.

Accepted in JPhysG; Focus issue "Enhancing the interaction between nuclear experiment and theory through information and statistics" (ISNET)

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• The nuclear symmetry energy and the breaking of the isospin symmetry: how do they reconcile with each other?
• Nuclear charge and neutron radii and nuclear matter: trend analysis
• Implications of parity-violating electron scattering experiments on ${}^{48}$Ca (CREX) and ${}^{208}$Pb (PREX-II) for nuclear energy density functionals
• Constraints on the Neutron Skin and the Symmetry Energy from the Anti-analog Giant Dipole Resonance in 208Pb
• Challenges in Nuclear Structure Theory
• Impact of statistical uncertainties on the composition of the outer crust of a neutron star
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• Confirmation of $g_{\mathrm{A}}$ quenching using the revised spectrum-shape method for the analysis of the ${}^{113}$Cd $\beta$-decay as measured with the COBRA demonstrator
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• Stability of the manifold boundary approximation method for reductions of nuclear structure models
• Impact of error analysis on the composition the outer crust of a neutron star