An Activation Experiment to Determine the Coefficients in the Laguerre Expansion of Perturbed Thermal-Neutron Spectra

A method is presented for the experimental determination of Laguerre coefficients in a polynomial expansion of strongly perturbed neutron spectra. A response matrix is constructed from the associated Laguerre functions of order one and Breit-Wigner cross sections. The magnitude of the coefficients is obtained by applying this matrix to the activations induced in selected isotopes by simultaneous exposure to the spectrum. It is shown that the coefficients characterize the spectrum and can serve as a measure of concentration of the spectrum-perturbing absorber. The method is tested experimentally by applying it to four spectra in water perturbed by addition of varying amounts of CdSO₄. It is found that three to four Laguerre coefficients can be obtained and the spectrum reconstructed from measured activations by Dy, Eu, Lu, and Yb.