Cosmic-ray muons and especially their secondaries break apart nuclei (spallation) and produce fast neutrons and beta-decay isotopes, which are backgrounds for low-energy experiments. In Super-Kamiokande, these beta decays are the dominant background in 6--18 MeV, relevant for solar neutrinos and the diffuse supernova neutrino background. In a previous paper, we showed that these spallation isotopes are produced primarily in showers, instead of in isolation. This explains an empirical spatial correlation between a peak in the muon Cherenkov light profile and the spallation decay, which Super-Kamiokande used to develop a new spallation cut. However, the muon light profiles that Super-Kamiokande measured are grossly inconsistent with shower physics. We show how to resolve this discrepancy and how to reconstruct accurate profiles of muons and their showers from their Cherenkov light. We propose a new spallation cut based on these improved profiles and quantify its effects. Our results can significantly benefit low-energy studies in Super-Kamiokande, and will be especially important for detectors at shallower depths, like the proposed Hyper-Kamiokande.
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