Covariance analysis for Energy Density Functionals and instabilities

TL;DR

This paper applies covariance analysis to two nuclear energy density functionals to understand their limitations, correlations between observables, and instabilities, providing insights into model reliability and parameter constraints.

Contribution

It introduces covariance analysis to compare non-relativistic and relativistic nuclear energy density functionals and examines how constraints affect observable correlations.

Findings

Relaxing constraints increases correlations between observables.

Imposing strong constraints reduces correlations.

The study reviews instabilities in current energy density functionals.

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.