Potential neutron-induced γ -ray background on natural tellurium relevant to Te 130 0 ν β β decay searches at the CUORE and SNO + detectors

Gamma-ray production cross-section data have been obtained for the inelastic neutron scattering reactions $^{126,128,130}\mathrm{Te}(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ at five neutron energies between 3.6 and 10 MeV. We report data for the $\ensuremath{\gamma}$-ray energy region relevant to $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{130}\mathrm{Te}$ with a ${Q}_{\ensuremath{\beta}\ensuremath{\beta}}$ 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 $\ensuremath{\gamma}$-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 $\ensuremath{\gamma}$-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 $\ensuremath{\gamma}$-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 $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay searches of $^{130}\mathrm{Te}$, because it matches its ${Q}_{\ensuremath{\beta}\ensuremath{\beta}}$ value.