  We discuss how the renormalization group can be used to derive effective
nuclear interactions. Starting from the model-independent low-momentum
interaction V_{low k}, we successively integrate out high-lying particle and
hole states from momentum shells around the Fermi surface as proposed by
Shankar. The renormalization group approach allows for a systematic calculation
of induced interactions and yields similar contributions to the scattering
amplitude as the two-body parquet equations. We review results for the 1S0 and
3P2 superfluid pairing gaps as well as the spin dependence of effective
interactions in neutron matter. Implications for the cooling of neutron stars
are discussed.
