BRIKEN is a complex detection system to be installed at the RIB-facility of the RIKEN Nishina Center. It is aimed at the detection of heavy-ion implants, $beta$-particles, $gamma$-rays and $beta$-delayed neutrons. The whole detection setup involves the Advanced Implantation Detection Array (AIDA), two HPGe Clover detectors and a large set of 166 counters of 3He embedded in a high-density polyethylene matrix. This article reports on a novel methodology developed for the conceptual design and optimisation of the 3He-tubes array, aiming at the best possible performance in terms of neutron detection. The algorithm is based on a geometric representation of two selected parameters of merit, namely, average neutron detection efficiency and efficiency flatness, as a function of a reduced number of geometric variables. The response of the detection system itself, for each configuration, is obtained from a systematic MC-simulation implemented realistically in Geant4. This approach has been found to be particularly useful. On the one hand, due to the different types and large number of 3He-tubes involved and, on the other hand, due to the additional constraints introduced by the ancillary detectors for charged particles and gamma-rays. Empowered by the robustness of the algorithm, we have been able to design a versatile detection system, which can be easily re-arranged into a compact mode in order to maximize the neutron detection performance, at the cost of the gamma-ray sensitivity. In summary, we have designed a system which shows, for neutron energies up to 1(5) MeV, a rather flat and high average efficiency of 68.6%(64%) and 75.7%(71%) for the hybrid and compact modes, respectively. The performance of the BRIKEN system has been also quantified realistically by means of MC-simulations made with different neutron energy distributions.
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