# Ground-state properties of doubly magic nuclei from the unitary-model-operator approach with the chiral two- and three-nucleon forces

## TL;DR

This study applies the unitary-model-operator approach with chiral two- and three-nucleon forces to calculate ground-state energies and radii of doubly magic nuclei, demonstrating consistency with other ab initio methods and SRG scale independence.

## Contribution

First UMOA calculation incorporating both nucleon-nucleon and three-nucleon interactions based on chiral EFT with SRG evolution.

## Key findings

- Ground-state energies and radii agree with recent ab initio results.
- Calculated radii are largely independent of SRG resolution scale.
- SRG evolution minimally affects the radius operator.

## Abstract

The ground-state energies and radii for $^{4}$He, $^{16}$O, and $^{40}$Ca are calculated with the unitary-model-operator approach (UMOA). In the present study, we employ the similarity renormalization group (SRG) evolved nucleon-nucleon ($NN$) and three-nucleon ($3N$) interactions based on the chiral effective field theory. This is the first UMOA calculation with both $NN$ and $3N$ interactions. The calculated ground-state energies and radii are consistent with the recent {\it ab initio} results with the same interaction. We evaluate the expectation values with two- and three-body SRG evolved radius operators, in addition to those with the bare radius operator. With the aid of the higher-body evolution of radius operator, it is seen that the calculated radii tend to be SRG resolution-scale independent. We find that the SRG evolution gives minor modifications for the radius operator.