# Towards the global description of nuclear charge radii: exploring the Fayans energy density functional

## TL;DR

This study compares Fayans and Skyrme energy density functionals in nuclear density functional theory to understand charge radii and odd-even effects, highlighting the impact of gradient-dependent surface and pairing terms on predictive accuracy.

## Contribution

It introduces a systematic analysis of the Fayans functional's components and their influence on nuclear observables, especially charge radii and odd-even staggering effects.

## Key findings

- Fayans functional accurately describes odd-even staggering in energies and radii.
- Adding differential radii data increases the gradient term coupling constants significantly.
- Fayans and Skyrme functionals have similar nuclear matter parameters when fitted to comparable datasets.

## Abstract

In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction. We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar datasets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. Detailed analysis is carried out for medium-mass and heavy semi-magic nuclei with a particular focus on the Ca chain. By making the surface and pairing terms dependent on density gradients, the Fayans functional offers the superb simultaneous description of odd-even staggering effects in energies and charge radii. Conversely, when the data on differential radii are added to the pool of fit-observables, the coupling constants determining the strengths of the gradient terms of Fayans functional are increased by orders of magnitude. The Skyrme functional optimized in this work with the generalized Fayans pairing term offers results of similar quality. We quantify these findings by performing correlation analysis based on the statistical linear regression technique. The nuclear matter parameters characterizing Fayans and Skyrme functionals optimized to similar datasets are fairly close.