  Cosmic-ray-muon spallation-induced radioactive isotopes with $\beta$ decays
are one of the major backgrounds for solar, reactor, and supernova relic
neutrino experiments. Unlike in scintillator, production yields for cosmogenic
backgrounds in water have not been exclusively measured before, yet they are
becoming more and more important in next generation neutrino experiments
designed to search for rare signals. We have analyzed the low-energy trigger
data collected at Super-Kamiokande-IV in order to determine the production
rates of $^{12}$B, $^{12}$N, $^{16}$N, $^{11}$Be, $^9$Li, $^8$He, $^9$C,
$^8$Li, $^8$B and $^{15}$C. These rates were extracted from fits to time
differences between parent muons and subsequent daughter $\beta$'s by fixing
the known isotope lifetimes. Since $^9$Li can fake an inverse-beta-decay
reaction chain via a $\beta + n$ cascade decay, producing an irreducible
background with detected energy up to a dozen MeV, a dedicated study is needed
for evaluating its impact on future measurements; the application of a neutron
tagging technique using correlated triggers was found to improve this $^9$Li
measurement. The measured yields were generally found to be comparable with
theoretical calculations, except the cases of the isotopes $^8$Li/$^8$B and
$^9$Li.
