  Radicals serve as source in dynamic nuclear polarization, but may also act as
polarization sink. If the coupling between the electron spins and different
nuclear reservoirs is stronger than any of the reservoirs' couplings to the
lattice, radicals can mediate hetero-nuclear mixing. Here, we report
radical-enhanced $^{13}$C relaxation in pyruvic acid doped with trityl. We find
a linear dependence of the carbon $T_1$ on field between 5 mT and 2 T. We
extend a model, employed previously for protons, to carbon, and predict
efficient proton-carbon mixing via the radical Non-Zeeman reservoir, for fields
from 20 mT to beyond 1 T. Discrepancies between the observed carbon relaxation
and the model are attributed to enhanced direct hetero-nuclear mixing due to
trityl-induced linebroadening, and a field-dependent carbon diffusion from the
radical vicinity to the bulk. Measurements of hetero-nuclear polarization
transfer up to 600 mT confirm the predicted mixing as well as both effects
inferred from the relaxation analysis.
