Model-independent low momentum nucleon interaction from phase shift equivalence

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 similar to 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 similar to 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. (C) 2003 Elsevier B.V. All rights reserved.