The three-nucleon bound state using realistic potential models

The bound states of ${}^3$H and ${}^3$He have been calculated using the Argonne $v_{18}$ plus the Urbana three-nucleon potential. The isospin $T=3\mathrm{/}2$ state have been included in the calculations as well as the $n$-$p$ mass difference. The ${}^3$H-${}^3$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 CD-Bonn interaction are also presented. It is shown that the ${}^3$H and ${}^3$He binding energy difference can be predicted model independently.