New method for unfolding neutron source spectra

Abstract

For solving the Fredholm equation of the first kind, the domain can be discretized in M spheres and N energy bins using a Bonner multisphere spectrometer, in which the neutron flux is to be deduced from the response matrix Rij(E), and the count rate obtained for each sphere Ci. For this study we use an approach that introduces certain neutron energy indeterminations, which are difficult to account for if some absolute calculations are required to be performed. For M different from N, a problem arises after obtaining the deconvolution of this equation, because the extracted solution is not unique, even if a host neutron energy spectrum is used. We propose a different method for extracting neutron energy spectra from the count rate obtained using a Bonner spectrometer. The method consists of partitioning the response matrix into a number of matrices such that M is equal to N, and depends on the response matrix and the number of spheres under consideration. Thus, the overall solution of the Fredholm equation can be divided and applied to N/M segments with M equations, and M unknowns, which can be solved in every energy segment for the neutron energy spectra. With this, the neutron spectra can be recovered by combining successive energy intervals as will be thoroughly described in the paper.