Fission of heavy $\Lambda$ hypernuclei with the Skyrme-Hartree-Fock approach

It has been shown that the shape of a few deformed nuclei change toward spherical when a $\Lambda$ particle is added to them. This is caused because the interaction between a $\Lambda$ particle and a nucleon is attractive. This fact has motivated us to investigate the influence of $\Lambda$ particle on the fission of heavy nuclei. In this talk, we will discuss the fission-related phenomena of heavy $\Lambda$ hypernuclei with the constraint Skyrme-Hartree-Fock+BCS (SHF+BCS) method. We employ a Skyrme-type interaction for the $\Lambda N$ interaction and assume adiabaticity, that is, the $\Lambda$ particle is assumed to be in the lowest state at all deformations. We will show that the fission barrier heights increase by about 200 keV by adding a $\Lambda$ particle. Our result confirms that the $\Lambda$ particle is stuck to the heavier fission fragment, which is consistent with the experimental result of CERN. We will also discuss the deformation of heavy $\Lambda$ hypernuclei and the $\Lambda$ particle motion inside the core nuclei.