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 χ2 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.

► Fitting the semi-prompt non-resolved photon spectrum after fission. ► Energy–time dependence can be factorized. ► Physical model, statistical model, sampling procedure. ► The best fit is: lognormal for energy and F for time.