# The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay

## TL;DR

This paper introduces a novel method combining generator-coordinate techniques with vibrational modes to improve nuclear structure calculations, especially for neutrinoless double-beta decay matrix elements, benchmarking against full shell model results.

## Contribution

It develops a new approach integrating vibrational modes into GCM, enhancing accuracy in nuclear excitation spectra and decay matrix elements.

## Key findings

- Improved excitation spectra with few vibrational modes.
- Significant enhancement of neutrinoless double-beta decay matrix elements.
- Benchmarking shows better results than standard GCM.

## Abstract

Good many-body methods for medium and heavy nuclei are important. Here we combine ideas from standard generator-coordinate methods (GCM) and the so-called Monte Carlo shell model, and set forth a novel approach: starting from a mean-field solution (Hartree-Fock-Bogoliubov), we create a set of non-orthogonal basis states, by using low-lying vibrational quasiparticleTamm-Dancoff modes, and then project onto states of good angular momentum and particle number. The results we benchmark against full shell model calculations. Even with just a few such modes we find improvement over standard GCM calculations in excitation spectra. We also find significant improvement in $0\nu\beta\beta$ nuclear matrix elements.