Three body charmed nuclei .

We study the $\Lambda_{c}$\textit{NN }three-body system by using the $\Lambda _{c}N $effective potential [1] within the method of hyperspherical functions (HF) in momentum representation, using realistic \textit{NN} local potentials. We solve nonrelativistic three-body Schrodinger equation in the framework of the method of HF [2] to find a ground state binding energy and corresponding wave function for the bound states with $J =$ 1$/$2 and 3$/$2 . The bound states energies are obtained for I$=$0: -21.07 MeV ($\Lambda_{c}$\textit{np, J }$\pi =$1/2$^{\mathrm{+}})$ and -21.74 MeV ($\Lambda_{\mathrm{c}}$\textit{np}, $J_{\mathrm{\pi }} \quad =$3/2$+)$, for $I=$1: -9.80 MeV ($\Lambda_{c}$\textit{nn, J}$_{\pi } =$1/2$^{\mathrm{+}})$ , -8.74 MeV ($\Lambda_{\mathrm{c}}$\textit{np}, $J_{\pi } \quad =$1/2$+)$, -6.82 MeV ($\Lambda _{\mathrm{c}}$\textit{pp}, $J_{\pi } \quad =$1/2$+)$, which are in good agreement with previous results obtained for the same potentials using variational method. \begin{enumerate} \item S. Maeda, M. Oka, A. Yokota, E.Hiyama, and Y. Liu, Prog. Theor. Exp. Phys. \textbf{2}, 023D02, (2016) \item R. Ya. Kezerashvili, Sh. M. Tsiklauri, I. N. Filikhin, V. M. Suslov, and B. Vlahovic, J. Phys. G: Nucl. Part. Phys. 43 065104 (2016). \end{enumerate}