A feasibility study was performed to design thermal and epithermal neutron sources for radioisotope production and boron neutron capture therapy (BNCT) by moderating fast neutrons. The neutrons were emitted from the reaction between (9)Be, (181)Ta, and (184)W targets and 30 MeV protons accelerated by a small cyclotron at 300 μA. In this study, the adiabatic resonance crossing (ARC) method was investigated by means of (207)Pb and (208)Pb moderators, graphite reflector, and boron absorber around the moderator region. Thermal/epithermal flux, energy, and cross section of accumulated neutrons in the activator were examined through diverse thicknesses of the specified regions. Simulation results revealed that the (181)Ta target had the highest neutron yield, and also tungsten was found to have the highest values in both surface and volumetric flux ratio. Transmutation in the (98)Mo sample through radiative capture was investigated for the natural lead moderator. When the sample radial distance from the target was increased inside the graphite region, the production yield had the greatest value of activity. The potential of the ARC method is a replacement or complements the current reactor-based supply sources of BNCT purposes.