  We consider the normal phase of a strongly interacting Fermi gas, which can
have either an equal or an unequal number of atoms in its two accessible spin
states. Due to the unitarity-limited attractive interaction between particles
with different spin, noncondensed Cooper pairs are formed. The starting point
in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory,
which approximates the pairs as being noninteracting. Here, we consider the
effects of the interactions between the Cooper pairs in a Wilsonian
renormalization-group scheme. Starting from the exact bosonic action for the
pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism
with the Wilsonian approach. We compare our findings with the recent
experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and
Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good
agreement. We also make predictions for the population-imbalanced case, that
can be tested in experiments.
