Inelastic neutron scattering cross sections for ${}^{76}\mathrm{Ge}$ relevant to background in neutrinoless double-$\beta$ decay experiments

The experimental signature in searches for the neutrinoless double-$\beta$ decay of ${}^{76}\mathrm{Ge}$ is a peak near 2039 keV in the spectrum. Given the low probability of the process, it is important that the background in this region be well understood. Inelastic scattering reactions with neutrons from muon-induced interactions and $(\alpha ,n)$ reactions in the surrounding materials or in the detector can provide contributions to the background. We have measured the production cross sections for $\gamma$ rays from the ${}^{76}\mathrm{Ge}(n,n^{\prime }\gamma )$ reaction in the 2039-keV region at incident neutron energies up to 4.9 MeV. In addition to determining that the cross sections of a previously known 2040.7-keV $\gamma$ ray from the 3952-keV level in ${}^{76}\mathrm{Ge}$ are rather small, we find that a larger contribution arises from a 2037.5-keV $\gamma$ ray which is attributed to a newly identified level at 3147 keV in ${}^{76}\mathrm{Ge}$. A third contribution is also possible from another new level at 3577 keV. These results indicate that the 2039-keV region in ${}^{76}\mathrm{Ge}$ neutrinoless double-$\beta$ decay searches is more complex than was previously thought.

Figure 1

Partial level scheme of $\gamma$ rays deexciting the 3951.89-keV level in ${}^{76}\mathrm{Ge}$ [16, 17]. The 2040.70-keV $\gamma$ ray is near the $Q$ value for the double-$\beta$ decay of ${}^{76}\mathrm{Ge}$ to ${}^{76}\mathrm{Se}$.

Figure 2

Gamma-ray spectrum from the ${}^{76}\mathrm{Ge}(n,n^{\prime }\gamma )$ reaction taken at an incident neutron energy of 3.7 MeV and a detection angle of ${90}^{\circ }$ showing a new 2037.5(3)-keV $\gamma$ ray. The inset shows the yield of this $\gamma$ ray from the $(n,n^{\prime }\gamma )$ excitation function data with incident neutron energies of 3.3 to 3.7 MeV.

Figure 3

Gamma-ray spectrum from the ${}^{76}\mathrm{Ge}(n,n^{\prime }\gamma )$ reaction taken at an incident neutron energy of 3.7 MeV and a detection angle of ${90}^{\circ }$ showing a new 2584.7(2)-keV $\gamma$ ray. The inset shows the yield of this $\gamma$ ray from the $(n,n^{\prime }\gamma )$ excitation function data with incident neutron energies of 3.2 to 3.7 MeV.

Figure 4

Experimental attenuation factor $F(\tau$) for the newly observed 3147-keV level as measured from the 2037.5-keV $\gamma$ ray. The top plot is from the first data run while the bottom plot is from the second data run.

Figure 5

Experimental attenuation factor $F(\tau$) for the newly observed 3147-keV level as measured from the 2584.7-keV $\gamma$ ray for the first and second experiments.

Figure 6

Widths of the 2037.5(5)-keV peak. The increase in width at 3.6 MeV likely corresponds to an unresolved doublet due to another $\gamma$ ray from the 3577-keV level.

Figure 7

Gamma-ray spectra from the ${}^{76}\mathrm{Ge}$($n,n^{\prime }\gamma$) reaction at an incident neutron energy of 4.5 MeV and a detection angle of ${125}^{\circ }$. The regions shown are centered around energies of $\gamma$ rays deexciting the 3951.89-keV level in ${}^{76}\mathrm{Ge}$.

Figure 8

Inelastic neutron scattering cross section for the 3951.89-keV level in ${}^{76}\mathrm{Ge}$ determined from the 3388.75-keV and 3951.70-keV $\gamma$-ray yields and branching ratios from Camp and Foster [16].

Figure 9

Inelastic neutron scattering cross section for the 2040.70-keV $\gamma$ ray based on the branching ratios found by Camp and Foster [16].

Figure 10

Experimental attenuation factor $F\left(\tau \right)$ for the 3951.89-keV level as measured from the 2843.50-, 3388.75-, and 3951.70-keV $\gamma$ rays. The plots shown are from the 4.5-MeV data taken during the first data run.