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 Laboratory was 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 laboratory. 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.

Figure 1

Plot of $\sqrt[]{a_0\times a_1}$ vs $X/l$ [16, 22]. $\mathrm{Here}\sqrt{a_0\times a_1}$ represents the total energy deposited in the detector, where $a_0$ and $a_1$ are the charges collected at the two ends of the detector, and $X/l$ describes the relative position of the particle in the detector, where $l$ is the attenuation length and $X$ is the distance between the midpoint of the detector and the point where a high-energy event is deposited.

Figure 2

Annual modulation of $\gamma$ flux in the Soudan Underground Laboratory. The $x$ axis is calendar time from 28 August 2011 to 8 October 2014 (covering $\sim 4$ years), while the $y$ axis represents the percent change in $\gamma$-ray intensity measured by the scintillator detector. The blue line is the best fit sinusoidal modulation to the black circles, which represent selected $\gamma$ events. Also plotted is the percent change in radon concentration for the same period of time, where the data (magenta dots) were collected by MINOS and the red line is a best fit using Eq. (2).

Figure 3

Radon modulation data (red) from the MINOS Collaboration [13] plotted against temperature (black) and humidity (blue). The green line is an Eq. (2) fit to the radon concentration seasonal variation over 10 years, giving a slightly different period and phase than the 4-year fit.

Figure 4

Correlation of the percentage variation of $\gamma$-ray flux ($y$ axis) versus the percentage variation of radon rates ($x$ axis) at SUL. The correlation coefficient between $\gamma$ rays and radon is found to be $(73.9\pm 21.7)$%.

Figure 5

Calculation of cross section of the ($\alpha ,\gamma$) reaction, when incident $\alpha$ particle has an energy 4 MeV for different targets, using the talys code [35]. The green (upper) line is the cross section plot for the aluminum target, the blue (middle) line is for silicon, and the red (lower) line is for the oxygen target.

Figure 6

The $\gamma$-ray flux from the ($\alpha ,\gamma$) reaction on the aluminum walls of the detector. The red (upper) line is the $\gamma$ yield due to thoron daughter and light green (lower) line is the $\gamma$ yield due to radon daughter. The higher $\gamma$ yield in aluminum in the region from 2 to 8 MeV is not surprising since the reaction cross section is largest at low energy.

Figure 7

The $\gamma$-ray flux from ($\alpha ,\gamma$) reaction in silicon (rock component). The red (upper) line is the $\gamma$ yield due to thoron daughter and light green (lower) line is the $\gamma$ yield due to radon daughter. The $\gamma$-ray yields depend strongly on the silicon present in rock cavities inside the mine. With increasing $\gamma$-ray energies, the flux gradually decreases.

Figure 8

The $\gamma$-ray flux from ($\alpha ,\gamma$) reaction with oxygen (air and rock component). The red (upper) line is the $\gamma$ yield due to thoron daughter and light green (lower) line is the $\gamma$ yield due to radon daughter.