  The low energy $n-\nuc{3}{H}$ elastic cross sections near the resonance peak
are calculated by solving the 4-nucleon problem with realistic NN interactions.
Three different methods -- Alt, Grassberger and Shandas (AGS), Hyperspherical
Harmonics and Faddeev-Yakubovsky -- have been used and their respective results
are compared. We conclude on a failure of the existing NN forces to reproduce
the $n-\nuc{3}{H}$ total cross section.
