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

TL;DR

This study investigates the potential existence of the $^3_{\Lambda_c}$H hypernucleus using the quark-delocalization color-screening model, finding that certain states could be bound under specific parameters.

Contribution

The paper develops effective $N\Lambda_c$ potentials from the QDCSM and predicts the possible bound states of $^3_{\Lambda_c}$H, a novel application of this model to charmed hypernuclei.

Findings

Both $J^P=1/2^+$ and $J^P=3/2^+$ states are predicted to be bound.

Binding energies range from 0.08 to 1.31 MeV depending on parameters.

Bound states are sensitive to the color screening parameter $$.

Abstract

We probe the existence of the $^3_{\Lambda_c}$H where the $N\Lambda_c$ potentials are derived from the quark-delocalization color-screening model (QDCSM). The $N\Lambda_c$ system is studied and the $N\Lambda_c$ scattering length so as the effective range are obtained in the QDCSM. We construct effective Gaussian-type $N\Lambda_c$ potentials which reproduce the $N\Lambda_c$ scattering data given by the QDCSM. By solving the $NN\Lambda_c$ three body Schr\"odinger equation with the Gaussian expansion method, we calculate the energies of the $^3_{\Lambda_c}$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 or 1.2, where the $J^P=1/2^+$ state is bound by $0.08\sim0.85$ MeV and the $J^P=3/2^+$ state is bound by $0.15\sim1.31$ MeV with respect to the deuteron-$\Lambda_c$ threshold.