Three-nucleon bound states using realistic potential models

Abstract

The bound states of ${}^{3}\mathrm{H}$ and ${}^{3}\mathrm{He}$ have been calculated by using the Argonne ${v}_{18}$ plus the Urbana IX three-nucleon potential. The isospin $T=3/2$ state have been included in the calculations as well as the $n\ensuremath{-}p$ mass difference. The ${}^{3}\mathrm{H}{\ensuremath{-}}^{3}\mathrm{He}$ mass difference has been evaluated through the charge-dependent terms explicitly included in the two-body potential. The calculations have been performed using two different methods: the solution of the Faddeev equations in momentum space and the expansion on the correlated hyperspherical harmonic basis. The results are in agreement within $0.1%$ and can be used as benchmark tests. Results for the charge-dependent--Bonn interaction in conjunction with the Tucson-Melbourne three-nucleon force are also presented. It is shown that the ${}^{3}\mathrm{H}$ and ${}^{3}\mathrm{He}$ binding energy difference can be predicted model independently.