A model of charmed baryon–nucleon potential and two- and three-body bound states with charmed baryon
A potential model for the interaction between a charmed baryon ($\Lambda_c$, $\Sigma_c$, and $\Sigma_c^*$) and the nucleon ($N$) is constructed. The model contains a long-range meson ($\pi$ and $\sigma$) exchange part and a short-distance quark exchange part. The quark cluster model is used to evaluate the short-range repulsion and a monopole type form factor is introduced to the long-range potential to reflect the extended structure of hadrons. We determine the cutoff parameters in the form factors by fitting the $NN$ scattering data with the same approach and we obtain four sets of parameters (a -- d). The most attractive potential (d) leads to bound $\Lambda_c N$ states with $J^\pi= 0^+$ and $1^+$ once the channel couplings among $\Lambda_c$, $\Sigma_c$ and $\Sigma_c^*$ are taken into account. One can also investigate many-body problems with the model. Here, we construct an effective $\Lambda_c N$ one-channel potential with the parameter set (d) and apply it to the 3-body $\Lambda_c NN$ system. The bound states with $J=1/2$ and $3/2$ are predicted.