Several prospective materials (neutron filter/moderator, beam reflector, gamma ray shielding and beam collimator) were studied with a view to generating thermal and epithermal neutron beams suited for boron neutron capture therapy (BNCT). The beams are delivered from the thermal and thermalizing column exits situated on two opposite faces of a TRIGA-II type reactor. An investigation was performed with Monte Carlo calculations from a viewpoint of obtaining sufficiently intense thermal and epithermal neutron beams separately, and little adulterated both with neutrons of extraneous energy ranges and with gamma rays. High-density graphite (G) would be the most suitable material for thermal neutron beams as a neutron filter/moderator, and the combination of aluminum (Al) and aluminum fluoride (AlF
3) for epithermal neutron beams. The graphite would be also the most promising material for thermal neutron beams as a beam reflector while for epithermal neutron beams the choice would be lead fluoride (PbF
2). The PbF
2 would be also the most suitable material for epithermal neutron beams as a gamma ray shielding, and bismuth (Bi) for thermal neutron beam. The PbF
2 would be also the most useful material for epithermal neutron beam as a beam collimator while for thermal neutron beam the choice would be the graphite The epithermal neutron beam for BNCT could be optimized with the progressive use of PbF
2.
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