M1 dipole strength from projected generator coordinate method calculations in the sd-shell valence space

TL;DR

This paper evaluates the projected generator coordinate method (PGCM) for calculating M1 dipole strength in sd-shell nuclei, benchmarking its performance against exact diagonalization to improve understanding of low-energy gamma-ray strength functions.

Contribution

It demonstrates PGCM's capability to reproduce exact diagonalization results for M1 transitions in sd-shell nuclei, highlighting its potential as an improved theoretical tool.

Findings

PGCM accurately reproduces $1^{+}$ states and M1 transitions.

PGCM offers advantages over QRPA by restoring symmetries.

Benchmarking with ${}^{24}$Mg shows promising results.

Abstract

The low-energy enhancement observed in the deexcitation $\gamma$-ray strength functions, attributed to magnetic dipole (M1) radiations, has spurred theoretical efforts to improve on its description. Among the most widely used approaches are the quasiparticle random-phase approximation (QRPA) and its extensions. However, these methods often struggle to reproduce the correct behavior of the M1 strength at the lowest $\gamma$ energies. An alternative framework, the projected generator coordinate method (PGCM), offers significant advantages over QRPA by restoring broken symmetries and incorporating both vibrational and rotational dynamics within a unified description. Due to these features, PGCM has been proposed as a promising tool to study the low-energy M1 strength function in atomic nuclei. However, comprehensive investigations employing this method are lacking. The PGCM is presently used within the frame of sd-shell valence space calculations based on the USDB shell-model interaction to benchmark its performance against the solutions obtained via exact diagonalization. The reliability of two different sets of generator coordinates in the PGCM calculations is gauged using ${}^{24}$Mg as a test case. The ability of the PGCM to reproduce results from exact diagonalization in the sd valence space is demonstrated for $1^{+}$ states and M1 transitions. Future work will need to assess whether the proposed method can be applied systematically and extended to large-scale calculations while maintaining a reasonable computational cost.