  We develop a simple, mean-field-like theory for the normal phase of a unitary
Fermi gas by deriving a self-consistent equation for its self-energy via a
momentum-dependent coupling constant for both attractive and repulsive
universal fermions. For attractive universal fermions in the lower branch of a
Feshbach resonance, we use zero-temperature Monte Carlo results as a starting
point for one-step iteration in order to derive an analytical expression for
the momentum-dependent self-energy. For repulsive universal fermions in the
upper branch of a Feshbach resonance, we iteratively calculate the
momentum-dependent self-energy via our self-consistent equation. Lastly, for
the case of population imbalance, we propose an ansatz for higher order virial
expansion coefficents. Overall, we find that our theory is in good agreement
with currently available, high temperature experimental data.
