Parameter Optimization and Uncertainty Analysis of FREYA for Spontaneous Fission

Background: The complete event fission simulation code FREYA is used to study correlations in fission. To make the best possible simulations, FREYA one must find the optimized values of the five physics-based parameters which characterize the events produced by FREYA. So far this has been done only empirically or by brute force computational techniques. Purpose: We seek to develop a method of parameter optimization for FREYA that would include uncertainty quantification and an analysis of the correlations between the parameters. Methods: We focus on spontaneous fission as a simpler test case of the method. We first check the results of previous optimizations for $^{252}$Cf(sf) and then go on to develop a simulated annealing approach to optimize the parameters. Although $^{252}$Cf(sf) has the most measured observables, we are able to apply the technique to all spontaneously fissioning isotopes in the current version of FREYA. Results: We find optimal values of the five FREYA parameters, with uncertainties, for all isotopes studied. Our results are compared with available data. The parameter values are physically reasonable and in accord with intuition, even in cases where the data for optimization are sparse to non-existent. Conclusions: The simulated annealing method provides a way to determine the best parameters for the phenomenologically-successful fission model FREYA. We have developed an algorithm that can be updated to include additional isotopes or more data sets for the current isotopes as they become available.