Two-neutrino double-$\beta$ decay of ${}^{150}\mathrm{Nd}$ to excited final states in ${}^{150}\mathrm{Sm}$

Background: Double-$\beta$ decay is a rare nuclear process in which two neutrons in the nucleus are converted to two protons with the emission of two electrons and two electron antineutrinos.

Purpose: We measured the half-life of the two-neutrino double-$\beta$ decay of ${}^{150}\mathrm{Nd}$ to excited final states of ${}^{150}\mathrm{Sm}$ by detecting the deexcitation $\gamma$ rays of the daughter nucleus.

Method: This study yields the first detection of the coincidence $\gamma$ rays from the $0{}_1^{+}$ excited state of ${}^{150}\mathrm{Sm}$. These $\gamma$ rays have energies of 333.97 and 406.52 keV and are emitted in coincidence through a $0_1^{+}\to 2_1^{+}\to 0_{\mathrm{gs}}^{+}$ transition.

Results: The enriched ${\mathrm{Nd}}_2{\mathrm{O}}_3$ sample consisted of 40.13 g ${}^{150}\mathrm{Nd}$ and was observed for 642.8 days at the Kimballton Underground Research Facility, producing 21.6 net events in the region of interest. This count rate gives a half-life of $T_{1/2}=[1.{07}_{-0.25}^{+0.45}\left(\mathrm{stat}\right)\pm 0.07\left(\mathrm{syst}\right)]\times {10}^{20}$ yr. The effective nuclear matrix element was found to be $0.0465{}_{-0.0054}^{+0.0098}$. Finally, lower limits were obtained for decays to higher excited final states.

Conclusions: Our half-life measurement agrees within uncertainties with another recent measurement in which no coincidence was employed. Our nuclear matrix element calculation may have an impact on a recent neutrinoless double-$\beta$ decay nuclear matrix element calculation which implies that the decay to the first excited state in ${}^{150}\mathrm{Sm}$ is favored over that to the ground state.

Figure 1

Level scheme of ${}^{150}\mathrm{Nd}$ double-$\beta$ decay to excited states of ${}^{150}\mathrm{Sm}$.

Figure 2

Diagram of present double-$\beta$ decay setup. Not pictured are the oxygen-free high-conductivity copper plates between the NaI annulus and the lead shield. (Not to scale. Please refer to text for dimensions.)

Figure 3

Photograph of ${\mathrm{Nd}}_2{\mathrm{O}}_3$ sample (bluish powder) encased in polycarbonate and Tedlar.

Figure 4

(a) Diagram showing the electronics for the primary coincidence between the HPGe detectors. (b) Diagram showing the electronics for the veto detectors surrounding the HPGe detectors. See Sec. 2c for details.

Figure 5

The reduction of the 511-keV $\gamma$-ray line and the asymmetric peak from inelastic neutron scattering on ${}^{74}\mathrm{Ge}$ and ${}^{72}\mathrm{Ge}$ is evident. The labeled peaks in the spectrum are identified as electron-positron annihilation (511.00 keV), the $\beta$ decay of ${}^{208}\mathrm{Tl}$ to 208Pb (583.19 keV), the $\beta$ decay of ${}^{214}\mathrm{Bi}$ to ${}^{214}\mathrm{Po}$ (609.32 keV, 768.36 keV), and the $\beta$ decay of ${}^{212}\mathrm{Bi}$ to ${}^{212}\mathrm{Po}$ (727.33 keV).

Figure 6

An example of a two-dimensional spectrum taken at KURF for about 250 days. Energy in detector 2 is plotted against energy in detector 1. Bins are $1\times 1\mathrm{keV}$. See text for an explanation of the features of the plot.

Figure 7

(a) A slice of the two-dimensional spectrum of Fig. 6. The dashed line shows 333.97 keV. The resulting projected full-energy spectrum in coincidence with 333.97 keV is shown in (b). Here the energy scale is 4 keV per bin. Here it can be seen that a cross section of the two-dimensional spectrum containing the diagonal and vertical lines can result in peaks in the projection spectrum. Prominent peaks are labeled. Note that the 1460.82-keV peak (from the ${}^{40}\mathrm{K}$ decay) occurs at 1126.85 keV in the 333.97-keV coincidence data, because it is a result of the full energy being shared between both detectors.

Figure 8

Coincidence data for decays to the $0{}_1^{+}$ state. Spectrum (a) is in coincidence with 333.97 keV, and spectrum (b) is in coincidence with 406.52 keV. The coincidence-energy window in spectra (a) and (b) is $\pm 2.50$ keV for detector 2 and $\pm 3.00$ keV for detector 1. These values are based on measurements with calibration sources and the background lines referred to in Sec. 2f, which also provide information on the pulse-height stability.

Figure 9

The level diagram for ${}^{102}\mathrm{Rh}$. Note the $0_1^{+}\to 2_1^{+}\to 0_{\mathrm{gs}}^{+}$ decay which emits a 468.64-keV $\gamma$ ray in coincidence with a 475.10-keV $\gamma$ ray. These were used for coincidence efficiency measurements.

Figure 10

Coincidence detection efficiency data obtained as a function of $r$ for the $E_{\gamma 1}=333.97$ keV and $E_{\gamma 2}=406.52$ keV coincidence. The data were taken with the${}^{102}\mathrm{Rh}$ source ($E_{\gamma 1}=468.64$ keV and $E_{\gamma 2}=475.10$ keV) and then corrected for detection efficiency and attenuation differences between the two $\gamma$-ray pairs involved, and a geometric correction was applied. The curve through the data presents a least-squares fit. The upper and lower curves indicate the $\pm 6.8$% scale uncertainty associated with our data.

Figure 11

A comparison of the 742.81-keV $\gamma$-ray peak from the decay of ${}^{234m}\mathrm{Pa}$ to surrounding peaks.

Figure 12

Same as Fig. 8 with nearby background peaks labeled. The origin of the peaks at 328.00 and 338.32 keV in panel (b) are discussed in Sec. 3a and the origin of the shared-energy peaks at 727.33 and 768.36 keV in panels (a) and (b) are discussed in Sec. 3b.

Figure 13

Coincidence data for the background runs taken over 180.76 days with no sample inserted are shown in spectra (a) and (b). Coincidence data for the ${\mathrm{ThO}}_2$ data taken over 1.10 days are shown in spectra (c) and (d). In all spectra, the coincidence window is $\pm 3.00$ keV.

Figure 14

The decay scheme of ${}^{150}\mathrm{Pm} \beta$ decay after $\left(p,n\right)$ activation of ${}^{150}\mathrm{Nd}$.

Figure 15

Coincidence data for the higher excited states. Spectra (a) and (b) are in coincidence with 333.97 and 712.21 keV, respectively, (c) and (d) are in coincidence with 333.97 and 859.87 keV, respectively, and (e) and (f) are in coincidence with 333.97 and 921.2 keV, respectively. The coincidence-energy window is $\pm 3.00$ keV.