Model-independent low momentum nucleon interaction from phase shift equivalence

Abstract

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 Λ∼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.