Theoretical interpretation of current-to-flux ratio in low-energy neutron transport

A physical value, current-to-flux ratio (CF ratio), is known in neutron transport theory. In boron neutron capture therapy (BNCT), it is recognized to be a very crucial design index. However, even now, the theoretical interpretation of the CF ratio is not yet clear. As detailed in the present paper, if considering the current (angular) distribution, in a low-energy slowing-down field of neutron in such as BNCT, in the exit region of the moderator assembly (beam shaping assembly (BSA)), it was found that the current distribution of neutrons shows a cosine distribution. In the present study, a new mathematical model was proposed and by numerical experiments the availability was thoroughly discussed. As a result, observation of the cosine distribution in the exit region of the moderator assembly was found to be caused by a rapid and linear change of the flux intensity at around the exit surface. In addition, the CF ratio was theoretically proved to be less than 2/3, meaning that in BNCT the regulation, CF ratio > 0.7, cannot be realized if employing a flat surface at the exit of the BSA.In conclusion, in the low‑energy neutron transport of such as BNCT, if the CF ratio is fixed, the current distribution in the exit region of an assembly like a BSA is fixed, and it becomes a cosine distribution. This result is quite crucial and valuable especially in the neutronics design of BNCT as well as in other neutron transport applications in nuclear engineering.