Relativistic Mean-Field and Beyond Approaches for Deformed Hypernuclei

We report the recent progress in relativistic mean-field (RMF) and beyond approaches for the low-energy structure of deformed hypernuclei. We show that the $\Lambda$ hyperon with orbital angular momentum $\ell=0$ (or $\ell>1$) generally reduces (enhances) nuclear quadrupole collectivity. The beyond mean-field studies of hypernuclear low-lying states demonstrate that there is generally a large configuration mixing between the two components $[^{A-1}Z (I^+) \otimes \Lambda p_{1/2}]^J$ and $[^{A-1}Z (I\pm2 ^+) \otimes \Lambda p_{3/2}]^J$ in the hypernuclear $1/2^-_1, 3/2^-_1$ states. The mixing weight increases as the collective correlation of nuclear core becomes stronger. Finally, we show how the energies of hypernuclear low-lying states are sensitive to parameters in the effective $N \Lambda$ interaction, the uncertainty of which has a large impact on the predicted maximal mass of neutron stars.Comment: 12 pages, 7 figures. A plenary talk given at the 13th International Conference on Hypernuclear and Strange Particle Physics, June 24-29, 2018, Portsmouth, V

Disappearance of nuclear deformation in hypernuclei: a perspective from a beyond-mean-field study

The previous mean-field calculation [Myaing Thi Win and K. Hagino, Phys. Rev. C{\bf 78}, 054311 (2008)] has shown that the oblate deformation in $^{28,30,32}$Si disappears when a $\Lambda$ particle is added to these nuclei. We here investigate this phenomenon by taking into account the effects beyond the mean-field approximation. To this end, we employ the microscopic particle-rotor model based on the covariant density functional theory. We show that the deformation of $^{30}$Si does not completely disappear, even though it is somewhat reduced, after a $\Lambda$ particle is added if the beyond-mean-field effect is taken into account. We also discuss the impurity effect of $\Lambda$ particle on the electric quadrupole transition, and show that an addition of a $\Lambda$ particle leads to a reduction in the $B(E2)$ value, as a consequence of the reduction in the deformation parameter.Comment: 6 pages, 5 figures. The version to appear in Phys. Rev.