An improved response matrix derivation model for fast calculation of neutron moderation spectra

The optimal design of the moderator for Boron Neutron Capture Therapy (BNCT) depends on the efficient acquisition of neutron beam energy spectra. Traditional approaches involve tedious procedures and substantial computational effort. This paper proposes a derivation method based on a recursive response matrix. Using the measured transmission and reflection matrices of the moderator as a benchmark, a block-diagonal interlayer correction matrix is introduced to compensate for nonlinear deviations, compressing the 300-dimensional correction matrix to 10 dimensions. By optimizing with the differential evolution algorithm and incorporating linear interpolation, rapid calculation of response matrices for arbitrary thicknesses in the range 1 to 25 cm is achieved. Experiments on AlF₃, MgF₂, and BiF₃ moderators show that the coefficient of determination R² is above 0.99 for thicknesses from 1 to 5 cm and remains above 0.93 at 25 cm for all three materials. The computation time is significantly reduced compared to direct Monte Carlo simulations. This method overcomes the bottlenecks of low efficiency and limited accuracy in traditional energy spectrum matrix acquisition, saving computational cost while enabling efficient neutron beam energy spectrum determination.