Observation of annual modulation induced by $\gamma$ rays from ($\alpha$, $\gamma$) reactions at the Soudan Underground Laboratory

Annual modulation of $\gamma$ rays from ($\alpha$, $\gamma$) reactions in the Soudan Underground Lab has been observed using a 12-liter scintillation detector. This significant annual modulation, measured over 4 years, can mimic the signature for dark matter and can also generate potential background events for neutrinoless double-$\beta$ decay experiments. The measured annual modulation of the event rate from ($\alpha$, $\gamma$) reactions is strongly correlated with the time-varying radon concentration observed independently in the Lab. The $\alpha$ flux from radon decay is simulated starting from the measured radon concentration, and the $\gamma$-ray flux is determined using the convolution of the $\alpha$ flux and the cross sections for ($\alpha$, $\gamma$) reactions. The calculated $\gamma$-ray flux is sufficient to generate the measured event rate that exhibits an annual modulation.