Monte Carlo calculation of point detector sensitivities to cross sections

Hall's differential operator method for the Monte Carlo calculation of sensitivities was extended so as to apply to point-detector-type problems. By this method the evaluation of the sensitivities of the detector response (or, equivalently, those of the neutron flux at the detector) to the cross sections of interest is concurrent with that of the very response. In such a Monte Carlo game, the neutron histories, or paths, are sampled, collision by collision, and the calculated contributions of each collision to the response and to its partial derivatives with respect to the relevant cross sections are accumulated. For each path these sums are the estimates for the response and its sensitivities. The Monte Carlo evaluations are then the respective averages of the individual path estimates. This scheme was applied to the analysis of the time-of-flight spectra of the leakage from the Livermore aluminum and carbon pulsed spheres. Measured and calculated spectra and some of their sensitivities are depicted, as an illustration, and discussed.