Generator-coordinate reference states for spectra and $0\nu\beta\beta$ decay in the in-medium similarity renormalization group

TL;DR

This paper introduces a combined IMSRG and GCM approach using symmetry-restored reference states to improve the calculation of spectra and neutrinoless double-beta decay matrix elements, showing better results than previous methods.

Contribution

The paper develops a novel IMSRG+GCM method with symmetry-restored states for more accurate spectra and decay matrix elements, benchmarked against shell-model results.

Findings

Improved spectra over previous IMSRG and GCM methods.

Slight enhancement in $0 uetaeta$ matrix element accuracy.

Benchmarking against shell-model results confirms method validity.

Abstract

We use a reference state based on symmetry-restored states from deformed mean-field or generator-coordinate-method (GCM) calculations in conjunction with the in-medium similarity-renormalization group (IMSRG) to compute spectra and matrix elements for neutrinoless double-beta ($0\nu\beta\beta$) decay. Because the decay involves ground states from two nuclei, we use evolved operators from the IMSRG in one nucleus in a subsequent GCM calculation in the other. We benchmark the resulting IMSRG+GCM method against complete shell-model diagonalization for both the energies of low-lying states in $^{48}$Ca and $^{48}$Ti and the $0\nu\beta\beta$ matrix element for the decay of $^{48}$Ca, all in a single valence shell. Our approach produces better spectra than either the IMSRG with a spherical-mean-field reference or GCM calculations with unevolved operators. For the $0\nu\beta\beta$ matrix element the improvement is slight, but we expect more significant effects in full ab-initio calculations.