  We present detailed results for the model-independent low momentum
nucleon-nucleon interaction V_{low k}. By introducing a cutoff in momentum
space, we separate the Hilbert space into a low momentum and a high momentum
part. The renormalization group is used to construct the effective interaction
V_{low k} in the low momentum space, starting from various high precision
potential models commonly used in nuclear many-body calculations. With a cutoff
in the range of $\Lambda ~ 2.1 fm^{-1}$, the new potential V_{low k} is
independent of the input model, and reproduces the experimental phase shift
data for corresponding laboratory energies below $E_{lab} ~ 350 MeV$, as well
as the deuteron binding energy with similar accuracy as the realistic input
potentials. The model independence of V_{low k} demonstrates that the physics
of nucleons interacting at low momenta does not depend on details of the high
momentum dynamics assumed in conventional potential models. V_{low k} does not
have momentum components larger than the cutoff, and as a consequence is
considerably softer than the high precision potentials. Therefore, when V_{low
k} is used as microscopic input in the many-body problem, the high momentum
effects in the particle-particle channel do not have to be addressed by
performing a Brueckner ladder resummation or short-range correlation methods.
By varying the cutoff, we study how the model independence of V_{low k} is
reached in different partial waves. This provides numerical evidence for the
separation of scales in the nuclear problem, and physical insight into the
nature of the low momentum interaction.
