  The $^1S_0$ superfluidity of neutron matter is studied in the framework of
the generalized Gorkov equation. The vertex corrections to the pairing
interaction and the self-energy corrections are introduced and approximated on
the same footing in the gap equation. A suppression of the pairing gap by more
than 50% with respect to the BCS prediction is found, which deeply changes the
scenario for the dynamical and thermal evolution of neutron stars.
