A model of charmed baryon-nucleon potential and 2- and 3-body bound states with charmed baryon
A potential model for the interaction between a charmed baryon ($Λ_c$, $Σ_c$, and $Σ_c^*$) and the nucleon ($N$) is constructed. The model contains a long-range meson ($π$ and $σ$) 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 $Λ_c N$ states with $J^π= 0^+$ and $1^+$ once the channel couplings among $Λ_c$, $Σ_c$ and $Σ_c^*$ are taken into account. One can also investigate many-body problems with the model. Here, we construct an effective $Λ_c N$ one-channel potential with the parameter set (d) and apply it to the 3-body $Λ_c NN$ system. The bound states with $J=1/2$ and $3/2$ are predicted.