Exotic structure of medium-heavy hypernuclei in the Skyrme Hartree-Fock model

We study exotic structure of medium heavy hypernuclei with core nuclei of Ar isotopes and ${}^{40}\mathrm{Ca}$. Particulary, the superdeformed (SD) states and the corresponding hypernuclei are calculated in the frame of the Skyrme Hartree-Fock (SHF) + BCS model together with a microscopic $\mathrm{\Lambda }N$ interaction. We found that the $\mathrm{\Lambda }$ separation energy of the ground state is larger than that of the SD state. The result is consistent with the antisymmetrized molecular dynamics (AMD) calculation, but inconsistent with that of relativistic mean field (RMF). The similarity between SHF and AMD and the difference of $\mathrm{\Lambda }$ separation energy between SHF and RMF both come from the density distribution in the core nuclei and the corresponding hypernuclei.

Figure 1

The calculated energy surfaces of (a) ${}^{40}\mathrm{Ca}$ and ${}_{\mathrm{\Lambda }}{}^{41}\mathrm{Ca}$ (b) ${}^{36}\mathrm{Ar}$ and ${}_{\mathrm{\Lambda }}{}^{37}\mathrm{Ar}$, (c) ${}^{37}\mathrm{Ar}$ and ${}_{\mathrm{\Lambda }}{}^{38}\mathrm{Ar}$, and (d) ${}^{39}\mathrm{Ar}$ and ${}_{\mathrm{\Lambda }}{}^{40}\mathrm{Ar}$ as a function of the deformation parameter ${\beta }_2$. The Skyrme interaction SkI4 is used for nucleonic part, while the NSC89 potential is used for $\mathrm{\Lambda }N$ interaction. The energy surfaces of hypernuclei are shifted by 14 MeV upward for display purpose.

Figure 2

The same as Fig. 1, but for the calculated energy surfaces of ${}^{38}\mathrm{Ar}$ and ${}_{\mathrm{\Lambda }}{}^{39}\mathrm{Ar}$ without pairing interaction.

Figure 3

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

Figure 4

The $\mathrm{\Lambda }$-nucleon potentials of the ground state and the SD state in ${}_{\mathrm{\Lambda }}{}^{37}\mathrm{Ar}$ along (a) the $r$ direction and (b) the $z$ direction. The SHF potentials are calculated by using a Skyrme interaction SkI4 with the hyperon-nucleon interaction NSC89, while the RMF potentials are calculated by using an effective Lagrangian PK1-Y1.