Deterministic sampling approach for the propagation of uncertainties in nuclear reaction models

Abstract

Uncertainty propagation of model parameters through nuclear reaction models is critical for nuclear data evaluation and other applications. Nuclear reaction models generally contain nonlinear functions of the model parameters, making the process of uncertainty propagation difficult. Usually stochastic approaches like the Monte Carlo method are employed to propagate the uncertainties through nuclear reaction models. The Monte Carlo method does provide proper results, but it takes a lot of computational power and time, which makes the process of uncertainty propagation difficult. Deterministic sampling approaches may provide results with accuracy using less computational time making the process of uncertainty propagation fast. In this study we have explored the use of a deterministic sampling approach called the unscented transform method for the uncertainty propagation in the nuclear reaction models. As a test case we have propagated the uncertainties of correlated optical model parameters through the optical model calculations for total and reaction cross sections of the $n+^{56}\mathrm{Fe}$ reaction. The results obtained using the unscented transform method are then compared with the results of the Monte Carlo method. It has been observed that the unscented transform method provides results practically similar to the Monte Carlo method in less computational time. It is concluded in this study that the unscented transform method can propagate uncertainties effectively through optical model calculations and there should be further investigation of the use of this method for other nuclear reaction models.