Shape of Lambda hypernuclei in (beta,gamma) deformation plane

Abstract

We study the shape of $\Lambda$ hypernuclei in the full ($\beta,\gamma$) deformation plane, including both axially symmetric and triaxial quadrupole deformations. To this end, we use the constrained Skyrme Hartree-Fock+BCS method on the three-dimensional Cartesian mesh. The potential energy surface is analyzed for carbon hypernuclei as well as for sd-shell hypernuclei such as $^{27,29}_{\Lambda}$Si and $^{25,27}_{\Lambda}$Mg. We show that the potential energy surface in the ($\beta,\gamma$) plane is similar to each other between the hypernuclei and the corresponding core nuclei, although the addition of $\Lambda$ hyperon makes the energy surface somewhat softer along the $\gamma$ direction. Our calculation implies that the energy of the $\gamma$ vibration for $^{25,27}_{\Lambda}$Mg nuclei is lowered by about 0.15 MeV with respect to that of $^{24,26}$Mg nuclei.