Superdeformed $\Lambda$ hypernuclei within 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. 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 the SD state becomes larger than that of a 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 important information on the localization of the density profile of SD states.

Figure 1

The energies of (a) ${}^{36}\mathrm{Ar}$ and ${}_{\Lambda }^{37}\mathrm{Ar}$, (b) ${}^{38}\mathrm{Ar}$ and ${}_{\Lambda }^{39}\mathrm{Ar}$, and (c) ${}^{40}\mathrm{Ar}$ and ${}_{\Lambda }^{41}\mathrm{Ar}$ as a function of the deformation parameter ${\beta }_2$. The $\Lambda$ hyperon is injected into the lowest $s$ orbit and three $p$ orbits. The Nilsson quantum numbers ${\Omega }^{\pi }\left[N{n}_3{m}_l\right]$ of the corresponding $\Lambda$ orbits are marked.

Figure 2

Two-dimensional density distributions in the $r$-$z$ plane ($r=\sqrt{x^2+y^2}$ and the $z$ axis is the symmetric one) for (a) ${}^{36}$Ar and ${}_{\Lambda }^{37}$Ar, (b) ${}^{38}$Ar and ${}_{\Lambda }^{39}$Ar, and (c) ${}^{40}$Ar and ${}_{\Lambda }^{41}$Ar. The asterisks denote SD states.

Figure 3

Two-dimensional density distributions in the $r$-$z$ plane ($r=\sqrt{x^2+y^2}$ and the $z$ axis is the symmetric one) for the $\Lambda$ hyperon in the ground state ${}_{\Lambda }^{37}$Ar and the SD state ${}_{\Lambda }^{37}$Ar${}^{*}$.

Figure 4

Two-dimensional density distributions in the $r$-$z$ plane ($r=\sqrt{x^2+y^2}$ and the $z$ axis is the symmetric one) in the ground state and the SD state of ${}^{40}$Ca.