# Variational approximations to exact solutions in shell-model valence spaces: calcium isotopes in the pf-shell

## TL;DR

This paper evaluates the accuracy of mean-field and beyond-mean-field methods in shell-model calculations for calcium isotopes, demonstrating near-exact results when advanced techniques and collective coordinates are used.

## Contribution

It introduces a comprehensive comparison of self-consistent mean-field and advanced projection methods against exact shell-model solutions in the pf-shell.

## Key findings

- High accuracy of beyond-mean-field methods with particle-number and angular-momentum restoration
- Explicit inclusion of quadrupole and neutron-neutron pairing improves results
- Excellent agreement with exact diagonalization for calcium isotopes

## Abstract

We study the performance of self-consistent mean-field and beyond-mean-field approximations in shell-model valence spaces. In particular, Hartree-Fock-Bogolyubov, particle-number variation after projection and projected generator coordinate methods are applied to obtain ground-state and excitation energies for even-even and odd-even Calcium isotopes in the pf-shell. The standard (and non-trivial) KB3G nuclear effective interaction has been used. The comparison with the exact solutions -- provided by the full diagonalization of the Hamiltonian -- shows an outstanding agreement when particle-number and angular-momentum restorations are performed and both quadrupole and neutron-neutron pairing degrees of freedom are explicitly explored as collective coordinates.