Correct Interpretations of ENDF-102 Definitions for Resonance Effects

Abstract

My Uncle Willie circa 1600 wrote “What’s in a name; a rose by any other name would smell as sweet.” I fear in this case we have a somewhat similar problem in that we may be using the same word but are not using the same definition; specifically, the word Unresolved. The simplest physics definition as it applies to neutron resonances, is the energy point where we can no longer see/measure ALL – let me repeat that – ALL - of the individual resonances. That seems simple and clear, but the question is: how to represent resonances beyond this point in order to accurately reproduce the effects we have seen in measurements and expect/need to reproduce in our applications. We know there are more, unseen resonances, otherwise we wouldn’t say Unresolved. The ENDF approach is well defined in ENDF-102 and simple: for ENDF data the only way to represent Unresolved data is by using a theoretical model to define the distribution of resonances, including those that are too narrow to measure (i.e., are unresolved). It is important to note that in ENDF this is the one and only Unresolved model, e.g., there is no provision in ENDF to accurately define individually ALL resonances above the Resolved energy range – by ALL here I mean both those that we can measure and those that we cannot individually measure, but that theory and integral measurements tells us are present. An alternative approach, which would appear to be equally valid, would be to include the latest measured data as tabulated energy expendent data extending upwards in energy above the Resolved energy range. In this approach the evaluation would not include an ENDF style Unresolved energy range; it would only include a Resolved resonance region, followed by tabulated higher energy points, representing the resonances that could be measured beyond the Resolved range. But an important point to note: By listing these resonances above the resolved energy one admits that at least some resonances in this energy range are missing as Unresolved; i.e., they are too narrow or overlapping to measure. The purpose of this paper is to illustrate that the later approach, while done with good intentions, and appearing to be valid/adequate in plots, does not meet the need of our engineering applications. Why? As we will see below, of these two possible approaches, only the ENDF use of a model to statistically include the missing, i.e., unresolved, resonances, can meet our engineering needs to reproduce the integral effects we have measured and understand. Only with this statistical model can we predict and include in our calculated results the important effects of temperature (Doppler broadening), and energy integrals (self-shielding). Below I will first present results using two ENDF/B-VIII.1 evaluations, U235 and U238, that use the correct ENDF-102 definition of an Unresolved resonance region, using a statistical model to include the effects of resonances that theory predicts are present, but are too narrow to measure. These two evaluations reproduce the expected temperature (Doppler) and energy integral (self-shielding) effects that we expect. Next I will present results using one ENDF/B-VIII.1 evaluation, 26-Fe-56, that does not use an ENDF-102 Unresolved resonance region; instead above its Resolved energy range it lists many tabulated energy points, that look like measured data, but by definition, since they are included above the ENDF Resolved energy range there are missing Unresolved resonances, i.e., there are missing the resonances that are too narrow to resolve, i.e., are unresolved. My conclusion, and I hope yours, is that the below figures illustrate that this approach does not reproduce the temperature and energy integrals that we expect and need to accurately calculate results for our fission reactor calculations. As such this approach should not be used in ENDF formatted evaluations.