Optimizing relativistic energy density functionals: covariance analysis

TL;DR

This paper applies covariance analysis to relativistic energy density functionals to evaluate parameter stability, uncertainties, and correlations, enhancing the understanding of model robustness and predictive power in nuclear physics.

Contribution

It introduces a comprehensive statistical framework for analyzing the stability and uncertainties of parameters in relativistic energy density functionals.

Findings

Identified weakly and strongly constrained parameter combinations.

Quantified uncertainties of nuclear matter and finite nucleus observables.

Assessed the stability of the density functional in nuclear matter.

Abstract

The stability of model parameters for a class of relativistic energy density functionals, characterized by contact (point-coupling) effective inter-nucleon interactions and density-dependent coupling parameters, is analyzed using methods of statistical analysis. A set of pseudo-observables in infinite and semi-infinite nuclear matter is used to define a quality measure $\chi^2$ for subsequent analysis. We calculate uncertainties of model parameters and correlation coefficients between parameters, and determine the eigenvectors and eigenvalues of the matrix of second derivatives of $\chi^2$ at the minimum. This allows to examine the stability of the density functional in nuclear matter, and to deduce weakly and strongly constrained combinations of parameters. In addition, we also compute uncertainties of observables that are not included in the calculation of $\chi^2$: binding energy of asymmetric nuclear matter, surface thickness of semi-infinite nuclear matter, binding energies and charge radii of finite nuclei.