Production rates of long-lived radionuclides Be10 and Al26</…

This study measured the ¹⁰Be and ²⁶Al production cross sections of muon-induced long-lived radionuclides to investigate the long-term variations in high-energy cosmic ray muon yields and high-energy galactic cosmic rays over a few million years. We exposed targets consisting of synthetic silica plates and quartz samples in a 1-m-long granite core to a beam containing 8.79×10¹² positive muons over ~120 days with an energy of 160 GeV extracted at the COMPASS experiment line at CERN-SPS. The experiment revealed the ¹⁰Be and ²⁶Al production rates in the synthetic silica plates as (1.8±0.1)×10^-7 and (1.3±0.08)×10^-6 atoms/muon/(gSiO2/cm²), respectively. In addition, we obtained the production rates in the granite core as approximately (4.1±0.2)×10^-7 and $(4.0±{}0.3)×{}{10}^{{-}6} atoms/muon/{{0ex}{0ex}}({g}quartz/{cm}²)$ for $¹⁰Be$ and $²⁶Al$, respectively, although those rates varied with location. Furthermore, we performed full muon exposure simulations for the identical experimental setup using two simulators, phits and fluka, to examine the ¹⁰Be and ²⁶Al production rates obtained in the muon beam experiment. The experimental rates are approximately 2--3 times higher than the simulated ones. Although the simulations are complex and depend on many models. Additionally, the phits and fluka analysis of the particle contributions to the ¹⁰Be and ²⁶Al production rates indicated that the positive muons and secondary particles produce those nuclides at a constant rate and an increasing rate with respect to granite core location, respectively, suggesting direct muon-induced spallation and secondary particle-induced spallation. The experimental production ratio ²⁶Al/¹⁰Be also exhibited characteristics of both spallation types. We conclude that the production cross sections of ¹⁰Be and ²⁶Al for the target atoms of oxygen and silicon were 9.2±0.6 μb and 132.3±7.7 μb via direct muon-induced spallation in the synthetic silica, and 27.2±1.9 μb and 486±44 μb including secondary particle-induced spallation in the granite quartz, respectively. Additionally, the depth profiles of ¹⁰Be and ²⁶Al concentrations in rocks estimated from the known total muon flux deep underground and this study's cross sections were comparable to those of the concentrations measured at depths greater than 5000 g/cm². Overall, our study showed that these cross sections revealed by the high-energy muon beam experiment are a valuable tool for estimating variations in high-energy galactic cosmic rays over a few million years using in situ rocks and simulators.