Regression analysis for a bottom-up approach to analyzing semi-prompt fission gamma yields

We present an empirical model that describes the yield of gamma rays emitted by fission in the time interval from 20 to 958 ns following a fission event. The analysis is based on experimental data from neutron-induced fission of ²³⁵U and ²³⁹Pu. The model is devised by first using regression analysis to identify likely patterns in the data and to choose plausible fitting functions. We provide statistical and physical arguments in support of time and energy independence. The intensity of the emitted gamma rays can be described as a bivariate distribution that is the product of independent variates for energy and time. We test several plausible distribution families for the energy and time variates and use maximum likelihood and minimum χ ² to estimate distribution parameters. Because of the uncertainty in the experimental data, multiple combinations of variate pairs give rise to a surface that plausibly well fits the observations well. The best-fit variate turns out to be lognormal in energy and F in time. The findings illustrated in this paper can be used to simulate gamma ray de-excitation from fission in Monte Carlo codes.