Benchmarking projected generator coordinate method for nuclear Gamow-Teller transitions

TL;DR

This paper extends the projected generator coordinate method to accurately describe Gamow-Teller transitions and double beta decay in nuclei, benchmarking against exact solutions and other computational approaches.

Contribution

The work introduces a minimal extension of PGCM for GT transitions and $2 uetaeta$ decay, validated through benchmarking against exact and other advanced nuclear models.

Findings

Benchmarking shows good agreement with exact solutions for calcium and titanium isotopes.

The extended PGCM accurately predicts $2 uetaeta$ decay matrix elements.

Comparison with other methods highlights the effectiveness of the proposed approach.

Abstract

In this work, we aim to achieve a minimal extension of the quantum-number projected generator coordinate method (PGCM) to describe Gamow-Teller (GT) transition strengths in even-even nuclei and to compute the NME of $2\nu\beta\beta$ decay. Within the PGCM framework, the wave functions of odd-odd nuclei are constructed as superpositions of neutron and proton quasiparticle configurations built on quasiparticle vacua constrained to have, on average, odd neutron and odd proton particle numbers. The angular momentum and particle numbers associated with the underlying mean-field states are restored through projection techniques. Using a shell-model Hamiltonian defined in the $fp$ shell, we assess the validity of this approach by benchmarking GT transitions in calcium and titanium isotopes, as well as the $2\nu\beta\beta$ decay of $^{48}$Ca to $^{48}$Ti, against exact solutions. For comparison, we also confront our results with those obtained from configuration-interaction calculations employing different particle-hole truncation schemes, both with and without in-medium similarity renormalization group (IMSRG) evolution.