  The influence of short-range correlations (SRC) on the spectral distribution
of neutrons is incorporated in the solution of the gap equation for the
${}^3P_2-{}^3F_2$ coupled channel in pure neutron matter at high density. This
effect is studied for three different realistic interactions. The gap in this
channel is strongly suppressed by these correlations but does not vanish. For a
consistent treatment we also include for the first time the effect of
long-range correlations (LRC) by incorporating polarization terms in addition
to the bare interaction. This allows the neutrons to exchange density and spin
fluctuations governed by the strength of Landau parameters with values that are
consistent with the available literature. While these LRC have an antiscreening
tendency, they only slightly increase the gap in the ${}^3P_2-{}^3F_2$ coupled
channel for all three realistic interactions as long as SRC are included. All
three interactions generate maximum gaps around 0.1 to 0.2 MeV at most with a
small dependence on the hardness of the interaction. These results are relevant
for the cooling scenarios of neutron stars, in particular the young neutron
star in Cassiopeia A.
