# Probing chiral interactions up to next-to-next-to-next-to-leading order in medium-mass nuclei

## TL;DR

This study uses advanced chiral interactions and in-medium similarity renormalization group methods to analyze ground-state energies and charge radii of medium-mass nuclei, revealing insights into nuclear interactions and their uncertainties.

## Contribution

It introduces a comprehensive analysis of chiral NN and 3N interactions up to N$^3$LO in medium-mass nuclei using IM-SRG, including a study of their sensitivity and evolution effects.

## Key findings

- N$^2$LO and N$^3$LO results overlap within uncertainties.
- Ground-state energies are systematically underbound.
- Charge radii are larger than experimental values but show improved agreement.

## Abstract

We study ground-state energies and charge radii of closed-shell medium-mass nuclei based on novel chiral nucleon-nucleon (NN) and three-nucleon (3N) interactions, with a focus on exploring the connections between finite nuclei and nuclear matter. To this end, we perform in-medium similarity renormalization group (IM-SRG) calculations based on chiral interactions at next-to-leading order (NLO), N$^2$LO, and N$^3$LO, where the 3N interactions at N$^2$LO and N$^3$LO are fit to the empirical saturation point of nuclear matter and to the triton binding energy. Our results for energies and radii at N$^2$LO and N$^3$LO overlap within uncertainties, and the cutoff variation of the interactions is within the EFT uncertainty band. We find underbound ground-state energies, as expected from the comparison to the empirical saturation point. The radii are systematically too large, but the agreement with experiment is better. We further explore variations of the 3N couplings to test their sensitivity in nuclei. While nuclear matter at saturation density is quite sensitive to the 3N couplings, we find a considerably weaker dependence in medium-mass nuclei. In addition, we explore a consistent momentum-space SRG evolution of these NN and 3N interactions, exhibiting improved many-body convergence. For the SRG-evolved interactions, the sensitivity to the 3N couplings is found to be stronger in medium-mass nuclei.