After the demonstration of the feasibility of hypernuclear spectroscopy with heavy-ion beams, the HypHI Collaboration will next focus on the study of proton- and neutron-rich hypernuclei. The use of a fragment separator for the production and separation of rare isotope beams is a crucial aspect to producing hypernuclei far from the stability line. Precise spectroscopy of exotic hypernuclei is planned to be carried out at the GSI and later at the FAIR facility with the FRS and Super-FRS fragment separators. A systematic study and an optimization analysis were performed in order to determine optimal experimental conditions for producing hypernuclei with high isospin. The optimal conditions are obtained based on theoretical models for the heavy-ion induced reaction and hypernuclei production. Experimental efficiencies for the production of exotic secondary beams were also taken into account via Monte Carlo simulations of the fragment separator. The developed methodology is presented to deduce the expected yields of $^8_Lambda$Be and subsequently other proton-rich and neutron-rich hypernuclei.
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