Novel way of evaluating $g_A$ quenching in $\beta^+$/EC decays : Introducing the Branching-Ratio Method (BRM)

TL;DR

The paper introduces the Branching-Ratio Method (BRM), a new approach for accurately determining the effective axial coupling constant $g_A^{eff}$ in forbidden non-unique $eta^+$/EC decays, enhancing nuclear physics modeling.

Contribution

The novel BRM constrains $g_A^{eff}$ by using branching ratios of $eta^+$ and EC decays, reducing ambiguities and improving nuclear decay analysis.

Findings

Applied BRM to $^{59}$Ni decay with three different shell-model Hamiltonians.

Demonstrated effects of nuclear structure variations on $g_A^{eff}$ determination.

Showed BRM's potential for testing nuclear Hamiltonians in complex decay processes.

Abstract

The novel Branching-Ratio Method (BRM) for the determination of effective value $g_{\rm A}^{\rm eff}$ of the weak axial coupling $g_{\rm A}$ for forbidden non-unique (FNU) $\beta^+$/electron-capture(EC) decays is introduced. The method offers new possibilities for testing the fitness of nuclear Hamiltonians in modeling the physics of complex $\beta^+$/EC decays. The constraint of simultaneously reproducing the branching to $\beta^+$ and EC transitions offers an additional constraint in tackling the problem of $g_{\rm A}^{\rm eff}$ determination. In the BRM the ambiguity in the choice of the values of $g_{\rm A}^{\rm eff}$ and s-NME (small relativistic vector nuclear matrix element) is lifted when constraints of the branching ratios of $\beta^+$ and EC decays are applied. As an example, in the present work we apply BRM to the case of second FNU $\beta^+$/EC decay of $^{59}$Ni. This decay is treated with three different nuclear shell-model (NSM) Hamiltonians demonstrating the effects of different nuclear-structure aspects in application of the BRM.