We probe the existence of the ${}_{{\mathrm{\Lambda }}_c}{}^3\mathrm{H}$ 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 as well so the effective ranges 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 ${}_{{\mathrm{\Lambda }}_c}{}^3\mathrm{H}$ with isospin $I=0$, $J^P=1/2^{+}$ and $I=0$, $J^P=3/2^{+}$ under different color screening parameter $\mu$. The $J^P=1/2^{+}$ and $J^P=3/2^{+}$ states are both bound when the color screening parameter $\mu$ is set to 1.0 ${\mathrm{fm}}^{-2}$ or 1.2 ${\mathrm{fm}}^{-2}$, where the $J^P=1/2^{+}$ state is bound by 0.08–0.85 MeV and the $J^P=3/2^{+}$ state is bound by 0.15–1.31 MeV with respect to the deuteron-${\mathrm{\Lambda }}_c$ threshold.

• Received 3 August 2023
• Accepted 6 December 2023

DOI:https://doi.org/10.1103/PhysRevC.109.014001