  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.
