The baryon-decuplet in the chiral dynamics of Lambda-hyperons in nuclear matter

We study the long range part of the $\Lambda$-hyperon optical potential in nuclei using Quantum Many Body techniques and flavor-SU(3) Chiral Lagrangians as starting point. More precisely, we study the contributions to the $\Lambda$-hyperon optical potential due to the long-range two-pion exchange, with $\Sigma$ and $\Sigma^*$ baryons in the internal baryonic lines and considering Nh and $\Delta$h excitations. We also consider the contribution to the spin-orbit potentials that comes out from these terms. Our results support a natural explanation of the smallness of the $\Lambda$-nuclear spin-orbit interaction and shows the importance of the $\Sigma^*$ and $\Delta$ degrees of freedom for the hyperon-nucleus interactions.