Deformation of hypernuclei studied with antisymmetrized molecular dynamics

An extended version of antisymmetrized molecular dynamics was developed to study the structure of $p$-$\mathit{sd}$ shell hypernuclei. By using an effective $\Lambda$N interaction, we investigated the energy curves of ${}_{\Lambda }^9$Be, ${}_{\Lambda }^{13}$C, and ${}^{20,}{}_{\hspace{0.5em}\Lambda }^{21}$Ne as a function of nuclear quadrupole deformation. The changes to nuclear deformation caused by $\Lambda$ particles are discussed. We found that $\Lambda$ in the $p$ wave enhances nuclear deformation, while that in the $s$ wave reduces it. This effect is most prominent in ${}_{\hspace{0.5em}\Lambda }^{13}$C. The possibility of parity inversion in ${}_{\hspace{0.5em}\Lambda }^{20}$Ne is also examined.

Figure 1

Energy curves as a function of the nuclear quadrupole deformation $\beta$ for (a) ${}_{\Lambda }^9$Be, (b) and (c) ${}_{\hspace{0.5em}\Lambda }^{13}$C, (d) and (e) ${}_{\hspace{0.5em}\Lambda }^{20}$Ne, and (f) and (g) ${}_{\hspace{0.5em}\Lambda }^{21}$Ne. Panels (a), (b), (d), and (f) compare the positive-parity states of normal nuclei (${\Psi }_N^{+}$) with the hypernuclear states of the ${\Psi }_N^{+}\otimes {\Lambda }_s$ and ${\Psi }_N^{+}\otimes {\Lambda }_p$ configurations. Panels (c), (e), and (g) compare the negative-parity states (${\Psi }_N^{-}$) with the hypernuclear states of the ${\Psi }_N^{-}\otimes {\Lambda }_s$ and ${\Psi }_N^{-}\otimes {\Lambda }_p$ configurations. Open circles show the energy minimum on each curve. Energies of hypernuclei are shifted in the figure for the sake of the presentation.

Figure 2

The single-particle energies of ${\Lambda }_s$ and ${\Lambda }_p$ of ${}_{\hspace{0.5em}\Lambda }^{13}$C as a function of quadrupole deformation of the core nucleus ${}^{12}\mathrm{C}$. The solid (dashed) line shows the energy of ${\Lambda }_s$ coupled to the positive (negative) parity state of ${}^{12}\mathrm{C}$. The dotted line shows the energy of ${\Lambda }_p$ coupled to the positive-paritystate of ${}^{12}\mathrm{C}$.

Figure 3

Density plots of the intrinsic wave function at each minimum on the energy curve. Contour lines show the density of the nuclear part ${\Psi }_N$, and the color plot shows the $\Lambda$ single-particle orbital ${\phi }_{\Lambda }$. Dots in the figure show the centroids of Gaussian wave packets on the nuclear part ${\Psi }_N$.