Shell and cluster states of ${}_{\Lambda }^{21}$Ne studied with antisymmetrized molecular dynamics

The low-lying states of ${}_{\hspace{0.5em}\Lambda }^{21}$Ne are studied with antisymmetrized molecular dynamics for hypernuclei. We have obtained ten rotational bands where the number of bands are increased compared to ${}^{20}\mathrm{Ne}$ by adding a $\Lambda$ hyperon. Among them, we focus on the $K^{\pi }=0_1^{+}\otimes {\Lambda }_s$ and $K^{\pi }=0_1^{-}\otimes {\Lambda }_s$ bands. The former has a shell-model-like structure that has $\Lambda$ in an $s$ wave coupled to the ground band of ${}^{20}\mathrm{Ne}$. The latter is a cluster state that has a $\alpha +{}_{\hspace{0.5em}\Lambda }^{17}$O dicluster structure. The difference between their structures leads to the binding energy of $\Lambda$ particle $B_{\Lambda }$ and reduction of the $E2$ transition probabilities $B(E2)$.

Figure 1

Low-lying energy spectra of ${}^{20}\mathrm{Ne}$ obtained with AMD. For comparison, corresponding experimental data are also presented.

Figure 2

(a)–(c) Density distributions of the band head states of the $K^{\pi }=0_1^{+},K^{\pi }=0_1^{-}$ and $K^{\pi }=2_1^{-}$ bands in ${}^{20}\mathrm{Ne}$. (d)–(f) Corresponding states with ${\Lambda }_s$ in ${}_{\hspace{0.5em}\Lambda }^{21}$Ne. The solid lines show the nucleon density, while the color plot shows the density distribution of the $\Lambda$ hyperon. The closed circles show the centroids of nucleon wave packets.

Figure 3

Calculated low-lying energy spectra of ${}_{\hspace{0.5em}\Lambda }^{21}$Ne with a ${\Lambda }_s$ are presented with that of ${}^{20}\mathrm{Ne}$.

Figure 4

Calculated low-lying energy spectra of ${}_{\hspace{0.5em}\Lambda }^{21}$Ne with a ${\Lambda }_p$ are presented with that of ${}^{20}\mathrm{Ne}$.

Figure 5

GCM amplitude for the band head state $(1/2){}^{-}$ of the $0_1^{-}\otimes {\Lambda }_s$ band. The definition of a GCM amplitude is given in Eq. (23). The solid line represents the contribution from the $0_1^{-}\otimes {\Lambda }_s$ band as a function of nuclear deformation parameter $\beta$. The dashed line shows that from the $0_1^{+}\otimes {\Lambda }_p$ band.

Figure 6

Energy surface as function of nuclear deformation parameter $\beta$ for the $0_1^{+}$ (solid line) and the $8^{+}$ (dashed line) states of the ${}^{20}\mathrm{Ne}$ ground band and the corresponding states with ${\Lambda }_s,(1/2){}^{+}$ and $(15/2){}^{+}$, of ${}_{\hspace{0.5em}\Lambda }^{21}$Ne ground band are presented. The squares on each surface represent its minimum points. Note that the energy surfaces of the $(1/2){}^{+}$ and the $(15/2){}^{+}$ states are shifted by 14 and 17 $\mathrm{MeV}$, respectively.