  We consider two nonperturbative methods originally used to derive shell model
effective interactions in nuclei. These methods have been applied to the two
nucleon sector to obtain an energy independent effective interaction V_{low k},
which preserves the low momentum half-on-shell T matrix and the deuteron pole,
with a sharp cutoff imposed on all intermediate state momenta. We show that
V_{low k} scales with the cutoff precisely as one expects from renormalization
group arguments. This result is a step towards reformulating traditional model
space many-body calculations in the language of effective field theories and
the renormalization group. The numerical scaling properties of V_{low k} are
observed to be in excellent agreement with our exact renormalization group
equation.
