The structure of nuclear systems derived from low momentum nucleon–nucleon potentials

Abstract

Various nuclear structure observables are evaluated employing low-momentum nucleonnucleon (NN) potentials V low−k derived from the CD-Bonn and Nijmegen NN interactions V N N . By construction, the high momentum modes of the original V N N are integrated out in V low−k , with the requirement that the deuteron binding energy and low energy phase shifts of V N N are exactly reproduced. Using this interaction, we evaluate the bulk properties (binding energy and saturation density) of nuclear matter and finite nuclei, in particular their dependence on the cut-off parameter. We also study the pairing gap and the residual interaction in nuclear matter in terms of the Landau parametrization. At low and medium densities, the HF and BHF binding energies for nuclear matter calculated with the V low−k 's derived from the CD-Bonn and Nijmegen potentials are nearly identical. The pairing gaps and Landau parameters derived from V low−k are remarkably close to those given by the full-space V N N . The V low−k interactions, however, fail to reproduce the saturation property of nuclear matter at higher densities if the cut-off for the high momentum modes is assumed density independent.

Low-momentum nucleon-nucleon interaction and its application to few-nucleon systems

“…By solving the Yakubovsky equations we can calculate the binding energy of 4 He. A similar tendency of the Λ dependence for 3 H can be also seen in the results for 4 He. In Fig.…”

“…Kuckei et al [4] investigated the nuclear matter and the closed-shell nucleus 16 O by using the LMNN interaction obtained by Bogner et al They concluded that the LMNN interaction can be a very useful tool for low energy nuclear structure calculations, and one should be cautious if the observable of interest is sensitive to the single-particle spectrum at energies above the cutoff momentum.…”

Nuclear matter in the crust of neutron stars

“…Our special attention was focussed on isospin T = 1 pairing for nucleon pairs with total momentum equal to zero in the 1 S 0 partial wave like in an earlier approach in a spherical box [8]. Using the standard BCS approach the pairing gap ∆ k for pair of nucleons with momenta k and −k is obtained by solving the gap equation [27] …”

Is nuclear matter perturbative with low-momentum interactions?

“…This misconception still persists and has recently led to the conclusion that low-momentum two-nucleon interactions are "wrong" since they do not give saturation in nuclear matter and finite nuclei are overbound for lower cutoffs [17,18]. The missing physics that invalidates this conclusion is many-body forces, which were completely neglected in those studies.…”