  Radioactive isotopes produced through cosmic muon spallation are a background
for rare-event detection in $\nu$ detectors, double-$\beta$-decay experiments,
and dark-matter searches. Understanding the nature of cosmogenic backgrounds is
particularly important for future experiments aiming to determine the pep and
CNO solar neutrino fluxes, for which the background is dominated by the
spallation production of $^{11}$C. Data from the Kamioka liquid-scintillator
antineutrino detector (KamLAND) provides valuable information for better
understanding these backgrounds, especially in liquid scintillators, and for
checking estimates from current simulations based upon MUSIC, FLUKA, and
GEANT4. Using the time correlation between detected muons and neutron captures,
the neutron production yield in the KamLAND liquid scintillator is measured to
be $(2.8 \pm 0.3) \times 10^{-4} \mu^{-1} g^{-1} cm^{2}$. For other isotopes,
the production yield is determined from the observed time correlation related
to known isotope lifetimes. We find some yields are inconsistent with
extrapolations based on an accelerator muon beam experiment.
