# Optimizing the relativistic energy density functional with nuclear ground state and collective excitation properties

## TL;DR

This paper develops a new relativistic energy density functional, DD-PCX, that accurately models nuclear ground states and collective excitations, using experimental data to better constrain nuclear matter properties.

## Contribution

It introduces the DD-PCX functional, combining ground state and excitation data in a unified framework with covariance analysis for uncertainty estimation.

## Key findings

- Accurately describes nuclear ground state properties and excitations.
- Constrains symmetry energy near saturation density.
- Provides statistical uncertainties for model parameters.

## Abstract

We introduce a new relativistic energy density functional constrained by the ground state properties of atomic nuclei along with the isoscalar giant monopole resonance energy and dipole polarizability in $^{208}$Pb. A unified framework of the relativistic Hartree-Bogoliubov model and random phase approximation based on the relativistic density-dependent point coupling interaction is established in order to determine the DD-PCX parameterization by $\chi^2$ minimization. This procedure is supplemented with the co-variance analysis in order to estimate statistical uncertainties in the model parameters and observables. The effective interaction DD-PCX accurately describes the nuclear ground state properties including the neutron-skin thickness, as well as the isoscalar giant monopole resonance excitation energies and dipole polarizabilities. The implementation of the experimental data on nuclear excitations allows constraining the symmetry energy close to the saturation density, and the incompressibility of nuclear matter by using genuine observables on finite nuclei in the $\chi^2$ minimization protocol, rather than using pseudo-observables on the nuclear matter, or by relying on the ground state properties only, as it has been customary in the previous studies.