Gamow-Teller strength in $^{48}$Ca and $^{78}$Ni with the charge-exchange subtracted second random-phase approximation

TL;DR

This paper introduces a self-consistent subtracted second random-phase approximation method for charge-exchange processes, improving predictions of Gamow-Teller strength and beta-decay rates in key nuclei without ad hoc quenching, with implications for double-beta decay calculations.

Contribution

It develops a novel self-consistent subtracted second RPA approach for charge-exchange, enhancing accuracy in modeling Gamow-Teller excitations in doubly-magic nuclei.

Findings

Better agreement with experimental Gamow-Teller strength in $^{48}$Ca.

Accurate beta-decay rate prediction for $^{78}$Ni.

Long high-energy tail in spectrum due to two-particle--two-hole configurations.

Abstract

We develop a fully self-consistent subtracted second random-phase approximation for charge-exchange processes with Skyrme energy-density functionals. As a first application, we study Gamow-Teller excitations in the doubly-magic nucleus $^{48}$Ca, the lightest double-$\beta$ emitter that could be used in an experiment, and in $^{78}$Ni, the single-beta-decay rate of which is known. The amount of Gamow-Teller strength below 20 or 30 MeV is considerably smaller than in other energy-density-functional calculations and agrees better with experiment in $^{48}$Ca, as does the beta-decay rate in $^{78}$Ni. These important results, obtained without \textit{ad hoc} quenching factors, are due to the presence of two-particle -- two-hole configurations. Their density progressively increases with excitation energy, leading to a long high-energy tail in the spectrum, a fact that may have implications for the computation of nuclear matrix elements for neutrinoless double-$\beta$ decay in the same framework.