  The onset of 1S0 proton spin-singlet pairing in neutron-star matter is
studied in the framework of the BCS theory including medium polarization
effects. The strong three-body coupling of the diproton pairs with the dense
neutron environment and the self-energy effects severely reduce the gap
magnitude, so to reshape the scenario of the proton superfluid phase inside the
star. The vertex corrections due to the medium polarization are attractive in
all isospin-asymmetry range at low density and tend to favor the pairing in
that channel. However quantitative estimates of their effect on the energy gap
do not give significant changes. Implications of the new scenario on the role
of pairing in neutron-star cooling is briefly discussed.
