Electron spectral shape of the third-forbidden ${\hat{I}}^2$-decay of ${}^{87}$Rb measured using a Rb${}_2$ZrCl${}_6$ crystal scintillator

Abstract

In recent years, interest in experimental studies of ${\hat{I}}^2$-decay electron spectra -- often referred to as ${\hat{I}}^2$ spectra -- has been growing. This is particularly true for ${\hat{I}}^2$ transitions where the electron spectra are sensitive to the effective value of the weak axial coupling, $g_{\mathrm{A}}$. Such measurements serve as important benchmarks for nuclear physics calculations and can also be used to characterize background in astroparticle physics experiments. In this work, a dedicated experiment has been carried out to investigate the spectral shape of the third-forbidden ${}^{87}$Rb ${\hat{I}}^2$-decays, with the goal of estimating the effective $g_{\mathrm{A}}$ value for this transition and of deriving the T${}_{1/2}$ value. This was done by comparing the experimental spectral shape with the estimates from various phenomenological models. The ${}^{87}$Rb source was embedded directly within the detector material of a new Rb${}_2$ZrCl${}_6$ crystal scintillator; the data taking was performed deep underground at Gran Sasso National Laboratory. The obtained experimental half-life value for the studied process is T${}_{1/2}=5.08(13)\times$ 10${}^{10}$ yr; while a $g_{\mathrm{A}}$ value in the range 0.4 to 0.6 is obtained when accounting for uncertainties and depending on the model adopted as discussed in detail in the text.

28 pages, 12 figures, 6 tables; accepted for publication on Eur. Phys. J. A