Search for double-$\beta$ decay processes in ${}^{106}$Cd with the help of a ${}^{106}$CdWO${}_4$ crystal scintillator

A search for double $\beta$ processes in ${}^{106}$Cd was carried out at the Gran Sasso National Laboratories of the INFN (Italy) with the help of a ${}^{106}$CdWO${}_4$ crystal scintillator (215 g) enriched in ${}^{106}$Cd up to 66$\%$. After 6590 h of data taking, new improved half-life limits on the double $\beta$ decay processes in ${}^{106}$Cd were established at the level of ${10}^{19}$–${10}^{21}$ yr; in particular, $T_{1/2}^{2\nu \varepsilon {\beta }^{+}}⩾2.1\times {10}^{20}$ yr, $T_{1/2}^{2\nu 2{\beta }^{+}}⩾4.3\times {10}^{20}$ yr, and $T_{1/2}^{0\nu 2\varepsilon }⩾1.0\times {10}^{21}$ yr. The resonant neutrinoless double-electron captures to the 2718-, 2741-, and 2748-keV excited states of ${}^{106}$Pd are restricted to $T_{1/2}^{0\nu 2K}⩾4.3\times {10}^{20}$ yr, $T_{1/2}^{0\nu K{L}_1}⩾9.5\times {10}^{20}$ yr, and $T_{1/2}^{0\nu K{L}_3}⩾4.3\times {10}^{20}$ yr, respectively (all limits at 90$\%$ confidence level). A possible resonant enhancement of the $0\nu 2\varepsilon$ processes is estimated in the framework of the quasiparticle random phase approximation (QRPA) approach. Radioactive contamination of the ${}^{106}$CdWO${}_4$ crystal scintillator is reported.

Figure 1

Simplified decay scheme of ${}^{106}$Cd [52] (levels at 1904–2714 keV are omitted). Energies of the excited levels and of the emitted $\gamma$ quanta are in keV. Relative intensities of $\gamma$ quanta are given in parentheses.

Figure 2

Energy spectrum measured with the ${}^{106}$CdWO${}_4$ scintillator over 6590 h in the low-background setup. Inset: Decay of $\beta$ active ${}^{113}$Cd${}^m$ dominates at an energy of $<$0.65 MeV (data over 283 h).

Figure 3

The $\alpha$ peaks of ${}^{224}$Ra, ${}^{220}$Rn, and ${}^{216}$Po selected by the time-amplitude analysis of data accumulated over 9454 h with the ${}^{106}$CdWO${}_4$ detector. The obtained half-lives of ${}^{220}$Rn (${64}_{-12}^{+19}$ s) and ${}^{216}$Po (${175}_{-11}^{+13}$ ms) are in agreement with the table values (55.6 s and 145 ms, respectively [67]).

Figure 4

Shape indicators (see text) versus the energy accumulated over 6590 h with the ${}^{106}$CdWO${}_4$ crystal scintillator in the low-background setup. Three $\sigma$ intervals for shape indicator values corresponding to $\gamma$ quanta ($\beta$ particles) and $\alpha$ particles are depicted. Events with shape indicator values greater than $\approx$3.8 can be explained by the overlap of events (mainly of $\beta$ decays of ${}^{113}$Cd${}^m$ in the crystal), while the population of events in the energy interval $\approx$1.8–3.8 MeV with shape indicators outside of the $\gamma$($\beta$) region are caused by the decays of the fast ${}^{212}$Bi–${}^{212}$Po subchain of ${}^{228}$Th. Inset: Distribution of the shape indicators demonstrates the efficiency of pulse-shape discrimination among $\gamma$($\beta$), $\alpha$, and overlapped pulses.

Figure 5

Energy distribution of $\alpha$ events (points) selected by the pulse-shape analysis of data accumulated over 6590 h with the ${}^{106}$CdWO${}_4$ detector together with the fit (solid line) by a model which includes $\alpha$ decays from the ${}^{232}$Th and ${}^{238}$U families.

Figure 6

(a) Energy spectrum of ${}^{212}$$\mathrm{Bi}{\to }^{212}$$\mathrm{Po}{\to }^{208}$Pb events in the ${}^{106}$CdWO${}_4$ scintillator selected by means of the pulse-shape and of the front-edge analyses (see text) from data accumulated over 6590 h together with the fit (dashed line) of the simulated distribution. (b) Time distribution of ${}^{212}$Po $\alpha$ decay selected by the front-edge analysis. The fit of the time distribution gives a half-life, $T_{1/2}=(0.26\pm 0.03)\mu$s, in agreement with the table value for ${}^{212}$Po (0.299 $\mu$s [67]).

Figure 7

Energy spectrum of $\beta$($\gamma$) events accumulated over 6590 h in the low-background setup with the ${}^{106}$CdWO${}_4$ crystal scintillator (points) together with the background model [solid (black) superimposed line]. The main components of the background are shown: the $\beta$ spectrum of the internal ${}^{113}$Cd${}^m$, the distributions of ${}^{40}$K, ${}^{228}$Th, ${}^{238}$U, and ${}^{207}$Bi (deposited on the crystal surface), and the contribution from external $\gamma$ quanta from PMTs and the copper box (“ext $\gamma$”) under these experimental conditions.

Figure 8

Simulated response functions of the ${}^{106}$CdWO${}_4$ detector to $2\varepsilon$, $\varepsilon {\beta }^{+}$, and $2{\beta }^{+}$ processes in ${}^{106}$Cd.

Figure 9

Part of the energy spectrum of $\gamma$ and $\beta$ events accumulated with the ${}^{106}$CdWO${}_4$ detector over 6590 h (circles) and its fit in the energy interval 780–2800 keV (solid line) together with the excluded distributions of $2\nu \varepsilon {\beta }^{+}$ and $0\nu \varepsilon {\beta }^{+}$ decay of ${}^{106}$Cd.

Figure 10

Calculated half-life for resonant $0\nu 2\varepsilon$ capture decay of ${}^{106}$Cd to the excited level 2718 keV of ${}^{106}$Pd as a function of parameter $x$ (see text) for different values of the effective neutrino mass. Dashed line and arrow show the value of $x$ derived from recent measurements of $Q_{2\beta }$ in ${}^{106}$Cd [32].