Testing the Delayed Gamma Capability in MCNP6

The mission of the Domestic Nuclear Detection Office is to quickly and reliably detect unauthorized attempts to import or transport special nuclear material for use against the United States. Developing detection equipment to meet this objective requires accurate simulation of both the detectable signature and detection mechanism.

A delayed particle capability was initially added to MCNPX 2.6.A in 2005 to sample the radioactive fission product parents and emit decay particles resulting from the decay chain. To meet the objectives of detection scenario modeling, the capability was designed to sample a particular time for emitting particular multiplicity of a particular energy. Because the sampling process of selecting both time and energy is interdependent, to linearize the time and emission sampling, atom densities are computed at several discrete time steps, and the time-integrated production is computed by multiplying the atom density by the decay constant and time step size to produce a cumulative distribution function for sampling the emission time, energy, and multiplicity. The delayed particle capability was initially given a time-bin structure to help reasonably reproduce, from a qualitative sense, a fission benchmark by Beddingfield, which examined the delayed gamma emission. This original benchmark was only qualitative and did not contain the magnitudes of the actual measured data but did contain relative graphical representation of the spectra. A better benchmark with measured data was later provided by Hunt, Mozin, Reedy, Selpel, and Tobin at the Idaho Accelerator Center; however, because of the complexity of the benchmark setup, sizable systematic errors were expected in the modeling, and initial results compared to MCNPX 2.7.0 showed errors outside of statistical fluctuation.

Presented here is a more simplified approach to benchmarking, utilizing closed form analytic solutions to the granddaughter equations for particular sets of decay systems. We examine five different decay chains (two-stage decay to stable) and show the predictability of the MCNP6 delayed gamma feature. Results do show that while the default delayed gamma calculations available in the MCNP6 1.0 release can give accurate results for some isotopes (e.g., ¹³⁷Ba), the percent differences between the closed form analytic solutions and the MCNP6 calculations were often >40% (²⁸Mg, ²⁸Al, ⁴²K, ⁴⁷Ca, ⁴⁷Sc, ⁶⁰Co). With the MCNP6 1.1 Beta release, the tenth entry on the DBCN card allows improved calculation within <5% as compared to the closed form analytic solutions for immediate parent emissions and transient equilibrium systems. While the tenth entry on the DBCN card for MCNP6 1.1 gives much better results for transient equilibrium systems and parent emissions in general, it does little to improve daughter emissions of secular equilibrium systems. Hypotheses were presented as to why daughter emissions of secular equilibrium systems might be mispredicted in some cases and not in others.