The hyperon mean free paths in the relativistic mean field

The $\Lambda$- and $\Xi^-$-hyperon mean free paths in nuclei are firstly calculated in the relativistic mean field (RMF) theory. The real parts of the optical potential are derived from the RMF approach, while the imaginary parts are obtained from those of nucleons with the relations: $U^{\mathrm{IY}}_{\mathrm{S}} = \alpha_{\sigma \mathrm{Y}}\cdot U_{\mathrm{S}}^{\mathrm{IN}}$ and $U^{\mathrm{IY}}_{\mathrm{V}} = \alpha_{\omega \mathrm{Y}}\cdot U_{\mathrm{V}}^{\mathrm{IN}}$ . With the assumption, the depth of the imaginary potential for $\Xi^-$ is $W_{\Xi}\simeq-$ 3.5 MeV, and for $\Lambda$ is $W_{\Lambda}\simeq-$ 7 MeV at low incident energy. We find that, the hyperon mean free path decreases with the increase of the hyperon incident energies, from 200 MeV to 800 MeV; and in the interior of the nuclei, the mean free path is about $2\sim 3$ fm for $\Lambda$, and about $4\sim 8$ fm for $\Xi^-$, depending on the hyperon incident energy.