Clusterization and deformation of multi-$\mathrm{\Lambda }$ hypernuclei within a relativistic mean-field model

Deformed multi-$\mathrm{\Lambda }$ hypernuclei are studied within a relativistic mean-field model. In this paper, I take some $N=Z$ “hyper-isotope” chains, i.e., ${}_{n\mathrm{\Lambda }}{}^{8+n}\mathrm{Be},{}_{n\mathrm{\Lambda }}{}^{20+n}\mathrm{Ne}$, and ${}_{n\mathrm{\Lambda }}{}^{28+n}\mathrm{Si}$ systems where $n=2,4$ for Be and $n=2,8$ for Ne and Si. A sign of two-${}_{2\mathrm{\Lambda }}{}^6\mathrm{He}$ cluster structure is observed in the two-body correlation in ${}_{4\mathrm{\Lambda }}{}^{12}\mathrm{Be}$. In the Ne hyper-isotopes, the deformation is slightly reduced by addition of $\mathrm{\Lambda }$ hyperons, whereas it is significantly reduced or even disappears in the Si hyper-isotopes.

Figure 1

Neutron and $\mathrm{\Lambda }$ hyperon density distributions of (a) ${}^8\mathrm{Be}$, (b) ${}_{2\mathrm{\Lambda }}{}^{10}\mathrm{Be}$ with $\mathrm{\Lambda }$'s in $s$ orbital $\left({}_{2\mathrm{\Lambda }s}{}^{10}\mathrm{Be}\right)$, (c) ${}_{2\mathrm{\Lambda }}{}^{10}\mathrm{Be}$ with $\mathrm{\Lambda }$'s in $p\text{orbital}\left({}_{2\mathrm{\Lambda }p}{}^{10}\mathrm{Be}\right)$, and (d) ${}_{4\mathrm{\Lambda }}{}^{12}\mathrm{Be}$. The neutron densities ${\rho }_n$ are shown by contour map, which starts from 0.$1{\mathrm{fm}}^{-3}$ with the increments by 0.$1{\mathrm{fm}}^{-3}$. The $\mathrm{\Lambda }$-hyperon densities ${\rho }_{\mathrm{\Lambda }}$ are shown by color (grayscale) map. The densities at $y=0$ as a function of $z$ and $x$ are plotted. $z$ (vertical) is the symmetry axis.

Figure 2

Central potentials of (a) neutron and (b) $\mathrm{\Lambda }$ hyperon of Be hyper-isotopes, ${}^8\mathrm{Be},{}_{2\mathrm{\Lambda }s}{}^{10}\mathrm{Be},{}_{2\mathrm{\Lambda }p}{}^{10}\mathrm{Be}$, and ${}_{4\mathrm{\Lambda }}{}^{12}\mathrm{Be}$ along the symmetry axis. In ${}_{2\mathrm{\Lambda }s}{}^{10}\mathrm{Be}$ and ${}_{2\mathrm{\Lambda }p}{}^{10}\mathrm{Be}$, the two $\mathrm{\Lambda }$ hyperons occupy the $s$ and the $p$ orbital, respectively.

Figure 3

Comparison between the neutron (solid curve) and $\mathrm{\Lambda }$ hyperon (dashed curve) densities in ${}_{4\mathrm{\Lambda }}{}^{12}\mathrm{Be}$ along the symmetry axis.

Figure 4

Localization functions ${\overline{\mathcal{C}}}_{q\sigma }={\mathcal{C}}_{q\sigma }\frac{{\rho }_{q\sigma }}{\max {\rho }_{q\sigma }}$ on $zx$ plane in ${}_{4\mathrm{\Lambda }}{}^{12}\mathrm{Be}$ for (a) $\left(q\sigma \right)=(\mathrm{neutron}\uparrow )$ and (b) $\left(q\sigma \right)=(\mathrm{\Lambda }\uparrow )$. In panels (c) and (d) are plotted ${\overline{\mathcal{C}}}_{n\uparrow }$ and ${\overline{\mathcal{C}}}_{\mathrm{\Lambda }\uparrow }$, respectively, along the symmetry axis.

Figure 5

The density distributions on $zx$ plane in the Ne hyper-isotopes, (a) neutron in ${}^{20}\mathrm{Ne}$, (b) neutron in ${}_{2\mathrm{\Lambda }}{}^{22}\mathrm{Ne}$, (c) $\mathrm{\Lambda }$ hyperon in ${}_{2\mathrm{\Lambda }}{}^{22}\mathrm{Ne}$, (d) neutron in ${}_{8\mathrm{\Lambda }}{}^{28}\mathrm{Ne}$, and (e) $\mathrm{\Lambda }$ hyperon in ${}_{8\mathrm{\Lambda }}{}^{28}\mathrm{Ne}$. Panels (f) and (g) show the comparisons of neutron and $\mathrm{\Lambda }$ densities along the symmetry axis, respectively, among the hyper-isotopes. The $z$ axis (horizontal) is the symmetry axis.

Figure 6

Central potentials of (a) neutron and (b) $\mathrm{\Lambda }$ hyperon of Ne hyper-isotopes, ${}^{20}\mathrm{Ne},{}_{2\mathrm{\Lambda }}{}^{22}\mathrm{Ne}$, and ${}_{8\mathrm{\Lambda }}{}^{28}\mathrm{Ne}$.

Figure 7

Neutron and $\mathrm{\Lambda }$ hyperon density distributions of Si hyper-isotopes, ${}^{28}\mathrm{Si},{}_{2\mathrm{\Lambda }}{}^{30}\mathrm{Si}$, and ${}_{8\mathrm{\Lambda }}{}^{36}\mathrm{Si}$. The $z$ axis (horizontal) is the symmetry axis.