Potential neutron-induced $\gamma$-ray background on natural tellurium relevant to ${}^{130}\mathrm{Te}$ $0\nu \beta \beta$ decay searches at the CUORE and $\mathrm{SNO}+$ detectors

Gamma-ray production cross-section data have been obtained for the inelastic neutron scattering reactions ${}^{126,128,130}\mathrm{Te}(n,n^{\prime }\gamma )$ at five neutron energies between 3.6 and 10 MeV. We report data for the $\gamma$-ray energy region relevant to $0\nu \beta \beta$ decay of ${}^{130}\mathrm{Te}$ with a $Q_{\beta \beta }$ value of 2527.515 keV, assuming natural-abundance tellurium, as used at CUORE and $\mathrm{SNO}+$. The natural abundance of ${}^{130}\mathrm{Te}$, ${}^{128}\mathrm{Te}$, and ${}^{126}\mathrm{Te}$ is 34%, 32%, and 19%, respectively. For CUORE the $\gamma$-ray cascades from the excited state in ${}^{130}\mathrm{Te}$ at 2527.06 keV and in ${}^{126}\mathrm{Te}$ at 2533.85 keV are of concern. For $\mathrm{SNO}+$, accounting for its inferior energy resolution, an additional four levels are important in ${}^{130}\mathrm{Te}$, an additional nine levels in ${}^{128}\mathrm{Te}$, and an additional eight levels in ${}^{126}\mathrm{Te}$. Of these, we report neutron-induced $\gamma$-ray production cross sections for the strongest transitions: the 2581.15 keV level in ${}^{130}\mathrm{Te}$, the 2494.20, 2508.06, and 2630.14 keV levels in ${}^{128}\mathrm{Te}$, and the 2496.83 and 2585.46 keV level in ${}^{126}\mathrm{Te}$. The largest cross-section values were found for cascade $\gamma$-ray transitions to the ground state, while direct transitions to the ground state are very weak and were not observed in the present work. Both the CUORE and $\mathrm{SNO}+$ detectors, however, may not be able to distinguish between cascade transitions and direct transitions to the ground state, making the neutron-induced excitation of the 2527.06 keV state of ${}^{130}\mathrm{Te}$ in particular a potential problem for $0\nu \beta \beta$ decay searches of ${}^{130}\mathrm{Te}$, because it matches its $Q_{\beta \beta }$ value.

Figure 1

Schematic of the experimental setup showing the neutron source, shielding wall, collimator, and the two clover HPGe detectors, which are positioned at ${\theta }_{\gamma }={90}^{\circ }$ and ${127}^{\circ }$ relative to the incident pulsed neutron beam. The clover HPGe detectors measure $\gamma$ rays originating from the neutron-illuminated natural tellurium target. A small liquid scintillator located downstream at $0^{\circ }$ monitors the neutron beam. Data were also taken with the two clover HPGe detectors placed at ${\theta }_{\gamma }={72}^{\circ }$ and ${109}^{\circ }$.

Figure 2

Time-of-flight (TOF) spectrum generated by deuteron time pick-off signals and HPGe detector signals. Time increases from left to right. The strong peak is due to the neutron TOF between the deuterium gas cell and the tellurium target disk plus negligible TOF contributions from the deuteron beam (from the time pick-off unit to the deuterium gas cell) and from $\gamma$ rays (generated in the tellurium target and detected in a HPGe detector).

Figure 3

Gamma-ray spectrum measured with 6 MeV neutrons in the energy region of interest for $0\nu \beta \beta$ decay of ${}^{130}\mathrm{Te}$. The arrow at 2527.515 keV indicates where a hypothetical $0\nu \beta \beta$ event would be located. In agreement with Ref. [30], the decay of the 2527.06 state in ${}^{130}\mathrm{Te}$ is not observed, because there is no direct branching to the ground state. The ${}^{130}\mathrm{Te}$ ground-state transition at 2607.31 keV is clearly seen, as is the ${}^{126}\mathrm{Te}$ ground-state transition at 2503.2 keV, and less strong the ${}^{128}\mathrm{Te}$ ground-state transition at 2508.04 keV.

Figure 4

Gamma-ray energy spectrum of one clover HPGe detector in the 1600 keV to 1800 keV energy range. The peaks labeled are from the decay of neutron-induced excitations of levels in ${}^{130}\mathrm{Te}$ and ${}^{128}\mathrm{Te}$, respectively, as indicated in the partial level schemes below the peaks. The peaks not labeled are due to background. The incident neutron energy is 6 MeV.

Figure 5

Same as Fig. 4, but for the $\gamma$-ray energy region between approximately 1100 keV and 1200 keV, showing the deexcitation $\gamma$ ray of 1172.45 keV, originating from the decay of the 2533.85 keV level in ${}^{126}\mathrm{Te}$.

Figure 6

Gamma-ray spectrum in the energy region between 750 keV and 900 keV obtained from 6 MeV neutron-induced excitation of the 846.78 keV level in ${}^{56}\mathrm{Fe}$ used for neutron fluence determination.

Figure 7

Neutron-induced production cross sections of 1687.56 keV and 1741.64 keV $\gamma$ rays, resulting from the decay of the 2527.06 keV and 2581.85 keV levels of ${}^{130}\mathrm{Te}$, as a function of incident neutron energy.

Figure 8

Neutron-induced production cross sections of 1750.94 keV, 1764.83 keV, and 1886.92 keV $\gamma$ rays, resulting from the decay of the 2494.20 keV, 2508.06 keV, and 2630.14 keV levels of ${}^{128}\mathrm{Te}$, as a function of incident neutron energy.

Figure 9

Neutron-induced production cross sections of 1919.09 keV, 1172.45 keV, and 720.64 keV $\gamma$ rays, resulting from the decay of the 2585.46 keV, 2533.85 keV, and 2496.83 keV levels of ${}^{126}\mathrm{Te}$, as a function of incident neutron energy.

Figure 10

Angular dependence of the ratio of ${}^{130}\mathrm{Te}$ and ${}^{56}\mathrm{Fe}$ yields measured with 4.5 MeV incident neutrons. Here, the decay $\gamma$ rays of the 2527.06 keV level in ${}^{130}\mathrm{Te}$ and the 846.78 keV level in ${}^{56}\mathrm{Fe}$ were used.