Study of Cosmogenic Neutron Production for $\sim$360 GeV Muons

The China Jinping underground Laboratory (CJPL) is an excellent location for studying solar, terrestrial, and supernova neutrinos due to its 2400-meter vertical rock overburden. Its unparalleled depth gives an opportunity to investigate the cosmic-ray muons with exceptionally high average energy at $\sim360$ GeV. This paper details a study of muon-related backgrounds based on 1178 days of data collected by the 1-ton prototype neutrino detector used for the Jinping Neutrino Experiment (JNE) since 2017. The apparent effects of detectors' finite size on the measured result are first discussed in detail. The analysis of 493 cosmic-ray muon candidates and $13.6\pm5.7$ cosmogenic neutron candidates, along with a thorough evaluation of detection efficiency and uncertainties, gives a muon flux of $(3.56\pm0.16_{\mathrm{stat.}}\pm0.10_{\mathrm{syst.}})\times10^{-10}~\mathrm{cm}^{-2}\mathrm{s^{-1}}$ and a cosmogenic neutron yield of $(3.37\pm 1.41_{\mathrm{stat.}}\pm 0.31_{\mathrm{sys.}}) \times 10^{-4}~\mathrm{\mu}^{-1} \mathrm{g}^{-1} \mathrm{cm}^{2}$ in LAB-based liquid scintillator.