Three-nucleon bound states using realistic potential models

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 $T=3/2\mathrm{}$ state have been included in the calculations as well as the $n-p$ mass difference. The ${}^3\mathrm{H}{-}^3\mathrm{He}$ 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.