Abstract
We report the measured production rates of unstable isotopes $^9$Li and $^8$He produced by cosmic muon spallation on $^{12}$C using two identical detectors of the RENO experiment. Their beta-decays accompanied by a neutron make a significant contribution to backgrounds of reactor antineutrino events in precise determination of the smallest neutrino mixing angle. The mean muon energy of its near (far) detector with an overburden of 120 (450) m.w.e. is estimated as 33.1 +- 2.3 (73.6 +- 4.4) GeV. Based on roughly 3100 days of data, the cosmogenic production rate of $^9$Li ($^8$He) isotope is measured to be 44.2 +- 3.1 (10.6 +- 7.4) per day at near detector and 10.0 +- 1.1 (2.1 +- 1.5) per day at far detector. This corresponds to yields of $^9$Li ($^8$He), 4.80 +- 0.36 (1.15 +- 0.81) and 9.9 +- 1.1 (2.1 +- 1.5) at near and far detectors, respectively, in a unit of 10$^{-8}$ $\mu^{-1}$ g${^-1}$ cm${^2}$. Combining the measured $^9$Li yields with other available underground measurements, an excellent power-law relationship of the yield with respect to the mean muon energy is found to have an exponent of $\alpha$ = 0.75 +- 0.05.
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