Nuclear Engineering ETDs

Publication Date



In the solution of the neutron transport equation, the k-effective eigenvalue is related to the average number of neutrons emitted in fission of the system. It can be shown that if the average number of neutrons emitted in fission and the average neutron energy spectrum is conserved, the criticality of a system remains the same without regard to the actual physical fission process. However, the fissioning of a nucleus leads to the emission of any number of neutrons with some probability with correlated emission energies that is a function of the incident neutron energy. In general, Monte Carlo codes used for criticality calculations do not use explicit fission multiplicity sampling instead opting for the expected-value outcome approach. As computational methods and resources advance, there is growing interest in high fidelity modeling, including nuclear fission physics modeling. Extensive criticality benchmarks have been established to verify and validate Monte Carlo calculations versus analytic solutions and benchmarked experiments using the expected-value outcome method and no verification-validation work has been done to date on using explicit fission neutron multiplicity models in MCNP6. To determine the effect of sampling fission multiplicity probability distributions during criticality (KCODE) calculations, it was necessary to modify MCNP6 to allow for the use of neutron fission multiplicity models during criticality calculations along with correlation of neutron emission energies. Previously, MCNP6 did not allow for the use of these models during criticality calculations and only allowed their use in fixed-source problems. It was found that explicit fission multiplicity sampling agreed within two standard deviations of expected-value outcome sampling calculated k-effective values. Various benchmark suites used to test MCNP6 k-effective criticality calculations demonstrated good agreement using explicit fission multiplicity sampling and confirmed the validity of using explicit fission multiplicity sampling in Monte Carlo criticality calculations.


Monte Carlo, criticality, fission multiplicity, fission neutron energy correlation, nuclear data uncertainty

Document Type




Degree Name

Nuclear Engineering

Level of Degree


Department Name

Nuclear Engineering

First Committee Member (Chair)

Busch, Robert

Second Committee Member

Brown, Forrest