  We study pairing in low-density neutron matter including the screening
interaction due to the exchange of particle-hole and RPA excitations. As bare
force we employ the effective low-momentum interaction $V_{low\,k}$, while the
Fermi-liquid parameters are taken from a phenomenological energy density
functional (SLy4) which correctly reproduces the equation of state of neutron
matter. At low density, we find screening, i.e., pairing is reduced, while at
higher densities, we find anti-screening, i.e., pairing is enhanced. This
enhancement is mostly due to the strongly attractive Landau parameter $f_0$. We
discuss in detail the critical temperature $T_c$ in the limit of low densities
and show that the suppression of $T_c$ predicted by Gor'kov and
Melik-Barkhudarov can only be reproduced if the cutoff of the $V_{low\,k}$
interaction is scaled with the Fermi momentum. We also discuss the effect of
non-condensed pairs on the density dependence of $T_c$ in the framework of the
Nozi\`eres-Schmitt-Rink theory.
