Formation of double-$\Lambda$ hypernuclei at PANDA

We study the formation of single- and double-$\Lambda$ hypernuclei in antiproton-induced reactions relevant for the forthcoming PANDA experiment at FAIR. We use the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) transport model with relativistic mean-fields for the description of non-equilibrium dynamics and the statistical multifragmentation model (SMM) for fragment formation. This combined approach describes the dynamical properties of strangeness and fragments in low energy $\bar{p}$-induced reactions fairly well. We then focus on the formation of double-$\Lambda$ hypernuclei in high energy $\bar{p}$-nucleus collisions on a primary target including the complementary $\Xi$-induced reactions to a secondary one, as proposed by the PANDA collaboration. Our results show that a copious production of double-$\Lambda$ hyperfragments is possible at PANDA. In particular, we provide first theoretical estimations on the double-$\Lambda$ production cross section, which strongly rises with decreasing energy of the secondary $\Xi$-beam.