Estimation of Doppler Effect in Fast Reactors

The detailed variation with energy of that part of the neutron cross section of an element which shows resonance behavior is temperature dependent. This dependence, the Doppler effect, arises from the temperature variation of neutron-nuclear relative velocity distribution. An effective cross section (dependent on reactor composition) useful in reactor calculations in place of the rapidly fluctuating actual cross section is defined. Knowledge of the variation of this effective cross section with material temperature is needed for calculation of the temperature coefficient of reactivity. Unfortunately, resolution of present measuring equipment does not permit sufficiently accurate measurement of cross sections in the energy range of interest in fast reactors (100 kev to several Mev), for Doppler effect calculation nor are direct measurements in this energy range available at present. To estimate Doppler effect, it has been assumed that in any energy range containing many resonances the actual cross section is equivalent, as far as reactor behavior is concerned, to a cross section constructed by selecting spacings between neighboring resonances and other resonance parameters independently from probability distributions of these parameters. In this manner, temperature coefficients may be calculated in terms of measured cross sections and various statistical parameters of the probability distributions, the parameters being estimated from low-energy data on actual resonances. In applying the low-energy data to the energy ranges of interest, the predictions of the statistical model of the nucleus, as developed by Weisskopf and others, are employed.