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

Abstract

In recent years, interest in experimental studies of $β$-decay electron spectra -- often referred to as $β$ spectra -- has been growing. This is particularly true for $β$ transitions where the electron spectra are sensitive to the effective value of the weak axial coupling, $g_{\rm A}$. 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 $β$-decays, with the goal of estimating the effective $g_{\rm A}$ 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 $g_{\rm A}$ 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.

Figures (12)

• Figure 1: Photo and a sketch of the experimental setup. The position of the $^{133}$Ba calibration source in form of wire can also be identified. The optical coupling between the RZC crystal scintillator and the 3-inch ultra-low-background PMT was guaranteed by optical couplant. The crystal and the PMT were secured by PTFE tape as shown in the photo (not in the sketch).
• Figure 2: Top: Example of scintillation pulse profile of an event with energy 200.6 keV recorded by the 14-bit digitizer over a time window of 80 $\mu$s. The amplitude is in arbitrary unit. The photoelectrons of the pulse are resolved by the electronics. Bottom: Average pulse profile calculated by considering 4000 scintillation pulses with energy in the range (190--210) keV; in the plot the red curve is the result of the fit (see text).
• Figure 3: The experimental spectrum (black histogram) measured in presence of the $^{133}$Ba source is shown alongside the whole simulated model (red histogram). This simulation was performed considering a PTFE source holder with 1 mm thickness and a $^{133}$Ba source wire with 2 mm diameter, which provided the best agreement with the experimental data. Additionally, the measured $\beta$ spectrum from $^{87}$Rb (see later) is also displayed (blue histogram). The given labels represent the energy in keV of the main $^{133}$Ba gammas or the X-rays from the daughter $^{133}$Cs.
• Figure 4: Mean time of the pulses measured in a 5 $\mu$s time window by the RZC detector for all the collected events as a function of their energy. The red curves correspond to the 4$\sigma$ intervals around the mean time values of scintillation pulses for $\beta/\gamma$ band events. Mainly pile-up events are ruled out by removing events out of the region delimited by the red curves. This procedure implies a negligible dead-time of about 0.1%.
• Figure 5: Left: mean time distributions of events with energy above 320 keV. Three populations are shown: the red histogram has been obtained by considering events below the lower red curve of Fig. \ref{['fig:mean']} (84 $\alpha$ events); the blue histogram has been obtained by considering events in between the red curves of Fig. \ref{['fig:mean']} (37 $\beta/\gamma$ events); the green histogram are events above red band mostly due to pile-ups (7 events). Right: the energy spectrum of the $\beta/\gamma$ band and $\alpha$ events measured above 320 keV and the background model (red line), based on the ICP-MS data reported in Table \ref{['conc']}, considering in particular the contributions from $^{238}$U, $^{232}$Th and $^{235}$U chains and from $^{40}$K.