  We study an ultracold trapped Fermi gas of atoms in two hyperfine states with
unequal populations. In this situation the usual BCS pairing is suppressed and
non-standard pairing mechanisms become important. These are treated by solving
the Bogoliubov-de Gennes equations, which at the same time correctly take into
account the finite size of the trapped system. We find results which can be
viewed as generalization of the LOFF phase to finite systems.
