Possibility of generating the ${}_{{\mathrm{\Lambda }}_c}^3$H in the quark-delocalization color-screening model

We probe the existence of the ${}_{{\mathrm{\Lambda }}_c}^3$H where the $N{\mathrm{\Lambda }}_c$ potentials are derived from the quark-delocalization color-screening model (QDCSM). The $N{\mathrm{\Lambda }}_c$ system is studied and the $N{\mathrm{\Lambda }}_c$ scattering length so as the effective range are obtained in the QDCSM. We construct effective Gaussian-type $N{\mathrm{\Lambda }}_c$ potentials which reproduce the $N{\mathrm{\Lambda }}_c$ scattering data given by the QDCSM. By solving the $NN{\mathrm{\Lambda }}_c$ three body Schrödinger equation with the Gaussian expansion method, we calculate the energies of the ${}_{{\mathrm{\Lambda }}_c}^3$H with isospin $I=0$, $J^P=1\mathrm{/}{2}^{+}$ and $I=0$, $J^P=3\mathrm{/}{2}^{+}$ under different color screening parameter $\mu$. The $J^P=1\mathrm{/}{2}^{+}$ and $J^P=3\mathrm{/}{2}^{+}$ states are both bound when the color screening parameter $\mu$ is set to 1.0 or 1.2, where the $J^P=1\mathrm{/}{2}^{+}$ state is bound by $0.08\sim 0.85$ MeV and the $J^P=3\mathrm{/}{2}^{+}$ state is bound by $0.15\sim 1.31$ MeV with respect to the deuteron-${\mathrm{\Lambda }}_c$ threshold.