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Comparison of Different Numerical Methods Used in Delayed Neutron Decay Parameters Estimation

Jinkai Wang, Warren D. Reece

Nuclear Science and Engineering

Volume 167 / Number 2 / February 2011 / Pages 154-164


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The relative yields of delayed neutrons and the half-lives of their precursor nuclei are usually determined indirectly by the least-squares method based on the differences between experimental and fitted data. It is noted that the recommended values from ENDF/B-VII, ENDF/B-VI.8, JENDL-3.3, JEF-2.2, and JEFF-3.1 are significantly different. To evaluate these parameters, the measured data sets used in this research were simulated by the Monte Carlo method, and they were strict Poisson distributed data generated from Keepin's six-group data. Three different numerical methods (matrix inverse with singular value decomposition, Levenberg-Marquardt, and quasi Newton) with different regularization techniques were applied to estimate the parameter values. The fitted results were proven to be very unstable, and their calculated results were very different even for the same data set. Further investigation found ill-conditioned problems to be the reason for this instability. A better numerical method was suggested in this research.

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