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

Abstract

Low-momentum nucleon-nucleon interactions are derived within the framework of a unitary-transformation theory, starting with realistic nucleon-nucleon interactions. A cutoff momentum $\ensuremath{\Lambda}$ is introduced to specify a border between the low- and high-momentum spaces. By Faddeev-Yakubovsky calculations the low-momentum interactions are investigated with respect to the dependence of ground-state energies of $^{3}\mathrm{H}$ and $^{4}\mathrm{He}$ on the parameter $\ensuremath{\Lambda}$. It is found that we need the momentum cutoff parameter $\ensuremath{\Lambda}\ensuremath{\geqslant}5\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ in order to reproduce satisfactorily the exact values of the binding energies for $^{3}\mathrm{H}$ and $^{4}\mathrm{He}$. The calculation with $\ensuremath{\Lambda}=2\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ recommended by Bogner et al. leads to considerable overbinding at least for few-nucleon systems.