Abstract
The $n+^{3}\mathrm{H},$ $p+^{3}\mathrm{He},$ $p+^{3}\mathrm{H},$ and $n+^{3}\mathrm{He}$ elastic and charge exchange reactions at low energies are studied by means of the hyperspherical harmonic method. The considered nuclear Hamiltonians include modern two- and three-nucleon interactions, and in particular results are reported in case of chiral two-nucleon potentials, with and without the inclusion of chiral three-nucleon (3N) interactions. A detailed study of the convergence and numerical stability of the method is presented. We have found that the effect the 3N force is in general tiny except for $p+^{3}\mathrm{H}$ scattering below the opening of the $n+^{3}\mathrm{He}$ channel. In such a case, the effect of 3N forces is appreciable and a clear dependence on the cutoff used to regularize the high-momentum tail of the interactions is observed. Such a dependence is related to the presence of the poorly known sharp ${0}^{+}$ resonance, considered to be the first excited state of $^{4}\mathrm{He}$.
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