This study measured the ${}^{10}\mathrm{Be}$ and ${}^{26}\mathrm{Al}$ 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 $8.79\times {10}^{12}$ positive muons over $\sim 120\mathrm{days}$ with an energy of 160 GeV extracted at the COMPASS experiment line at CERN-SPS. The experiment revealed the ${}^{10}\mathrm{Be}$ and ${}^{26}\mathrm{Al}$ production rates in the synthetic silica plates as $(1.8\pm 0.1)\times {10}^{-7}$ and $(1.3\pm 0.08)\times {10}^{-6}\text{atoms}/\mathrm{muon}/({\mathrm{g}}_{\mathrm{SiO}2}/{\mathrm{cm}}^2)$, respectively. In addition, we obtained the production rates in the granite core as approximately $(4.1\pm 0.2)\times {10}^{-7}$ and $(4.0\pm 0.3)\times {10}^{-6}\mathrm{atoms}/\mathrm{muon}/({\mathrm{g}}_{\text{quartz}}/{\text{cm}}^2)$ for ${}^{10}\mathrm{Be}$ and ${}^{26}\mathrm{Al}$, 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 ${}^{10}\mathrm{Be}$ and ${}^{26}\mathrm{Al}$ 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 ${}^{10}\mathrm{Be}$ and ${}^{26}\mathrm{Al}$ 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 ${}^{26}\mathrm{A}\mathrm{l}/{}^{10}\mathrm{B}\mathrm{e}$ also exhibited characteristics of both spallation types. We conclude that the production cross sections of ${}^{10}\mathrm{Be}$ and ${}^{26}\mathrm{Al}$ for the target atoms of oxygen and silicon were $9.2\pm 0.6\mathrm{\mu }\mathrm{b}$ and $132.3\pm 7.7\mathrm{\mu }\mathrm{b}$ via direct muon-induced spallation in the synthetic silica, and $27.2\pm 1.9\mathrm{\mu }\mathrm{b}$ and $486\pm 44\mathrm{\mu }\mathrm{b}$ including secondary particle-induced spallation in the granite quartz, respectively. Additionally, the depth profiles of ${}^{10}\mathrm{Be}$ and ${}^{26}\mathrm{Al}$ 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 $5000{\mathrm{g}/\mathrm{cm}}^2$. 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.

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• Galactic disks
• High-energy accelerators & colliders
• Interstellar medium
• Normal galaxies
• Particle accelerators
• Particle-beam sources
• Solar system & its planets
• Supernova remnants
• 20 ≤ A ≤ 38
• A ≤ 5
• Interplanetary magnetic field
• Nuclear mass ranges
• Cosmic ray & astroparticle detectors
• Cosmic rays & astroparticles
• Particle sources & targets