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

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.