  Momentum space entanglement entropy probes quantum correlations in
interacting fermionic phases. It is very sensitive to interactions, obeying
volume-law scaling in general, while vanishing in the Fermi gas. We show that
the R\'enyi entropy in momentum space has a systematic expansion in terms of
the phase space volume of the partition, which holds at all orders in
perturbation theory. This permits, for example, the controlled computation of
the entropy of thin shells near the Fermi wavevector in isotropic Fermi liquids
and BCS superconductors. In the Fermi liquid, the thin shell entropy is a
universal function of the quasiparticle residue. In the superconductor, it
reflects the formation of Cooper pairs. Momentum space R\'enyi entropies are
accessible in cold atomic and molecular gas experiments through a
time-of-flight generalization of previously implemented measurement protocols.
