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

Fission-related phenomena of heavy $Lambda$ hypernuclei are discussed with the constraint Skyrme-Hartree-Fock+BCS (SHF+BCS) method, in which a similar Skyrme-type interaction is employed also for the interaction between a $Lambda$ particle and a nucleon. Assuming that the $Lambda$ particle adiabatically follows the fission motion, we discuss the fission barrier height of $^{239}_{Lambda}$U. We find that the fission barrier height increases slightly when the $Lambda$ particle occupies the lowest level. In this case, the $Lambda$ particle is always attached to the heavier fission fragment. This indicates that one may produce heavy neutron-rich $Lambda$ hypernuclei through fission, whose weak decay is helpful for the nuclear transmutation of long-lived fission products. We also discuss cases where the $Lambda$ particle occupies a higher single-particle level.