Superdeformed $\Lambda$ hypernuclei from relativistic mean field models

We study the superdeformed (SD) states and corresponding SD hypernuclei of Ar isotopes with the multidimensionally-constrained relativistic mean field (MDC-RMF) models which can accommodate various shape degree of freedom. %The hyperon-nucleon $\sigma$-$\Lambda$ and $\omega$-$\Lambda$ interactions are introduced %in the same covariant framework. We found that the density profiles of SD states in Ar isotopes show a strong localization with a ring structure near the surface, while the central part of the density is dilute showing a hole structure. This localization of SD density induces an appreciable deformation in the hyperon wave function and results in a large overlap between the core and the hyperon in the SD hypernuclei of Ar isotopes. Then the $\Lambda$ separation energy of SD state becomes larger than that of normally deformed or spherical ground state. This feature is different from that found in other nuclei such as $^{32}$S, $^{56}$Ni, and $^{60}$Zn in which the $\Lambda$ separation energy of larger deformed state is smaller. In this context, the measurement of the $\Lambda$ separation energy may provide an important information on the localization of the density profile of SD states.