We study the effect of a $\Lambda$ hyperon immersed in the doubly magic nuclei, $^{ 16}$O, $^{ 40}$Ca, $^{ 48}$Ca, and $^{ 208}$Pb, as well as the neutron magic nucleus $^{ 90}$Zr. For a $\Lambda$ in the $1s$ and $1p$ states in $^{ 17}_{ \Lambda}$O, $^{ 41}_{ \Lambda}$Ca, $^{ 49}_{ \Lambda}$Ca, $^{ 91}_{ \Lambda}$Zr, and $^{ 209}_{ \Lambda}$Pb, we compare the single-particle energies and density distributions of the core nucleons with those of the nuclei without the $\Lambda$, as well as the point proton and neutron radii. A remarkable finding is that the bound $\Lambda$ induces a significant asymmetry in the proton-neutron density distributions in the core nucleus. This in turn gives rise to an appreciable, iso-vector mean field. As a consequence, the neutrons in the core are more attracted to the center of the nucleus, while the protons are pushed away, in comparison with those in the corresponding nucleus without the $\Lambda$.
Categories: nucl-th hep-ex hep-lat hep-ph nucl-ex