First limit on neutrinoless quadruple $\beta$ decay of ${}^{150}\mathrm{Nd}$ to the $0_1^{+}$ state of ${}^{150}\mathrm{Gd}$

Background: Observation of lepton number violation via detection of neutrinoless double $\beta$ decay requires that the neutrino be a Majorana particle. If the neutrino is a Dirac particle, a potential lepton-number violating process is neutrinoless quadruple $\beta$ decay. Only a few nuclei can undergo neutrinoless quadruple $\beta$ decay; one of these nuclei is ${}^{150}\mathrm{Nd}$.

Purpose: This study yields the first half-life limit of the neutrinoless quadruple $\beta$ decay to the excited $0_1^{+}$ state of ${}^{150}\mathrm{Gd}$.

Methods: We searched for neutrinoless quadruple $\beta$ decay events to excited final states of ${}^{150}\mathrm{Gd}$ by detecting the deexcitation $\gamma$ rays of the daughter nucleus in coincidence. These $\gamma$ rays have energies of 569.031 and 638.050 keV, and are emitted in coincidence through a $0_1^{+}\to 2_1^{+}\to 0_{gs}^{+}$ transition.

Results: The enriched ${\mathrm{Nd}}_2{\mathrm{O}}_3$ sample consisted of $40.33\pm 0.02$ g ${}^{150}\mathrm{Nd}$ and was observed for 642.8 days at the Kimballton Underground Research Facility. A half-life limit for the decay to the $0_1^{+}$ state of ${}^{150}\mathrm{Gd}$ was found to be $T_{1/2}>1.76\times {10}^{20}$ years (90% CL).

Conclusions: We report the first search for this decay to excited final states. Though the predicted half-life of this decay is many orders of magnitudes larger, constraining this value experimentally is vital to check for potential enhancements to the decay rate.

Figure 1

Level scheme of ${}^{150}\mathrm{Nd}0\nu 4\beta$ decay to ${}^{150}\mathrm{Gd}$.

Figure 2

Setup diagram for the double-$\beta$ decay apparatus. Please see text for details.

Figure 3

The potential background peak at 569.70 keV is shown in a single-detector spectrum. Also note the lack of any excess of counts at 640 keV. See text for details of the origin of the background radiation.

Figure 4

(a) The two-dimensional spectrum shows the ${\mathrm{ThO}}_2$ data where no events are in coincidence above background in our region of interest (indicated by the dashed lines at 569.05 and 638.05 keV). (b) The singles spectrum for the ${\mathrm{ThO}}_2$ data shows no peak at 569 keV. See text for details.

Figure 5

Coincidence data for decays to the $0_1^{+}$ state in ${}^{150}\mathrm{Gd}$. Spectrum (a) is in coincidence with 569.03 keV, and spectrum (b) is in coincidence with 638.05 keV. The coincidence-energy window in spectra (a) and (b) is 2.50 keV for detector 2 and 3.00 keV for detector 1. Events within the region of interest are colored red.