Optimization of the Neutron Spectrum Unfolding Algorithm Using Shifted Legendre Polynomials Based on Weighted Tikhonov Regularization

A weight-based algorithm for unfolding neutron spectra from the results of measurements with the Bonner multi-sphere spectrometer is proposed. Measurements are related to the spectrum through a system of Fredholm integral equations of the 1st kind. The energy dependences of the response functions for moderator spheres of different diameters have different extended shapes with mutual overlaps, which makes it difficult to get an appropriate solution for the ill-posed inverse task of spectrum unfolding. To solve the system of Fredholm integral equations we use decomposition of the spectrum into shifted Legendre polynomials and apply the Tikhonov regularization with weighting factors which are based on the condition numbers of the matrix constructed by the spectrometer response functions. It is shown that including the weight factors in the stabilizing functional ensures statistical balancing of the contributions of measurements with moderator spheres of different diameters. This allows one to determine the optimal set of spheres for measurements, as well as to more accurately unfold spectra using a more subtle regularization procedure. The proposed algorithm is used to unfold neutron spectra at the IREN JINR facility.