Source Nuclide Density First-Order and Second-Order Sensitivities in Monte Carlo Codes

Application of perturbation capabilities for density sensitivities in Monte Carlo radiation transport codes has been limited because changing source nuclide densities or source material densities changes the intrinsic source, and in most Monte Carlo codes, the user-input source is independent of the user-input materials. The perturbation capability then has no way of accounting for changes in the intrinsic source. This paper derives the sensitivity of a response with respect to a source nuclide density in terms of a portion due to the transport operator and a portion due to the source rate density. The Monte Carlo perturbation method computes the portion due to the transport operator, and the portion due to the source rate density is computed in postprocessing using parameters from the precomputed intrinsic source calculation. This paper derives first- and second-order sensitivities. The equations require the response to be separated by contribution from each of the sources modeled. A test problem containing several (α,n) and spontaneous fission neutron sources verifies the method.