Abstract
We calculate the $^{3}\mathrm{He}+\mathit{p}$ scattering phase shifts for the $S$ and $P$ waves in a microscopic cluster model, in which the description of the $^{3}\mathrm{He}$ wave function is extended from a simple $(0s){}^{3}$ model to a three-body model. We employ two different nucleon-nucleon interactions, the Minnesota (MN) and AV${8}^{'}$ potentials, to investigate the role of the $d+2\mathit{p}$ channel in the low-energy phase shifts. The role of the $d+2\mathit{p}$ channel in the $P$-wave phase shifts is very sensitive to the choice of the potential. The $d+2\mathit{p}$ channel is indispensable in reproducing the resonant phase shifts in the AV${8}^{'}$ potential while it plays a minor role in the MN potential. On the contrary, the role of this channel in the $S$-wave nonresonant phase shifts is negligible in both potentials.
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