Accuracy of Analytical Treatments for Resonance Absorption in Doppler Resonance Regions

Abstract

Resonance shielding factors based on the assumption of constant collision density have been compared with those obtained by solving rigorously the slowing down equation. The results obtained by calculating numerically the flux for this assumption have been thoroughly examined for several compositions and temperatures. This detailed investigation has been based on consideration of the interaction effects between neighboring resonances in both the same and different nuclear species. The results obtained have permitted determination of the limits of accuracy obtained with conventional analytical methods. The accuracy of two typical methods of approximation based on the above basic assumption has also been investigated for important Doppler resonance regions in large fast reactor. The study has covered the resonance regions below 21.5 keV for 238U, and below lOkeV for 235U and 239Pu. It has been found that the results obtained numerically from the assumption of constant collision density are fairly good at higher energies, but the errors become large with decreasing neutron energy and the increasing concentration of fuel. Furthermore the shielding factor and the temperature coefficient of 239Pu are affected considerably by superposition of the resonances of 238U, and the errors are thereby accentuated by a factor of more than two. And the errors resulting from the analytical methods have been found larger than those incurred by the assumption of constant collision density.