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Derivation and Implementation of the Three-Region Problem in the SOURCES Code System

The SOURCES code system was designed to calculate neutron production rates and spectra in materials due to the decay of radionuclides [specifically from (α,n) reactions, spontaneous fission, and delayed neutron emission]. The current version (SOURCES-3 A) is capable of calculating (α,n) source rates and spectra for three types of problems: homogeneous materials, interface problems, and beam problems. Recent interest in (α,n) sources has prompted the development of a fourth scenario: the three-region problem. To allow SOURCES to confront this problem, the relevant equations defining the α-particle source rates and spectra at each interface and the neutron source rates and spectra per unit area of interface were derived. These equations (in discretized form) were added as a new subroutine to the SOURCES code system (dubbed SOURCES-4A). The new code system was tested by analyzing the results for a simple three-region problem in two limits: with an optically thin ‘intermediate region’ and with an optically thick ‘intermediate region.’ To further validate the code system, SOURCES-4A will be experimentally benchmarked as measured data becomes available.