  We study pure neutron matter in the BEC-BCS crossover regime using
renormalization group based low-momentum interactions within the
Nozi\`eres-Schmitt-Rink framework. This is an attempt to go beyond the mean
field description for low-density matter. We work in the basis of so-called
Weinberg eigenvectors where the operator $G_0V$ is diagonal, which proves to be
an excellent choice that allows one to use non-local interactions in a very
convenient way. We study the importance of correlations as a function of
density. We notice that there is a significant reduction of the BCS critical
temperature at low-densities as the neutron matter approaches the unitary
limit.
