Covariance analysis for energy density functionals and instabilities

We present the covariance analysis of two successful nuclear energy density functionals (EDFs), (i) a non-relativistic Skyrme functional built from a zero-range effective interaction, and (ii) a relativistic nuclear EDF 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 Pb-208, 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 EDFs currently used in nuclear physics.