Abstract
We present a study of the effect of three-nucleon forces (3NFs) in \(p+{}^3\mathrm{He}\), \(p+{}^3\mathrm{H}\) and \(n+{}^3\mathrm{He}\) scattering at low energies. The used 3NF is derived from effective field theory at next-to-next-to-leading order. The four-nucleon scattering observables are calculated using the Kohn variational principle and the hyperspherical harmonics technique and the results are compared with available experimental data. We have found that the effect of introducing this particular 3NF 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 3NF is evident 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 a poorly known sharp \(0^+\) resonance, considered to be the first excited state of \({}^4\mathrm {He}\).
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