Resonance Capture and Doppler Coefficient in Cylindrical Uranium Fuel Elements

Double P/₀ diffusion theory is shown to be a sufficiently accurate representation for calculating resonance absorption and its temperature coefficient. The theory is formulated to allow for non-uniform temperature distributions and spatial variation of neutron cross sections. It is applied to uranium rods in graphite-moderated reactors, assuming a parabolic fuel-temperature distribution. Volume and surface temperature coefficients for absorption are defined. The energy distributions of these coefficients in strongly absorbing resonances are shown to differ Significantly. It is found that the total volume coefficient exceeds the total surface coefficient by 15% at normal operating temperatures. At higher temperatures the total volume coefficient is larger by 5%. Rowlands' formula for the effective uniform temperature is shown to be reliable for calculating the resonance integral and the volume temperature coefficient, but not for the surface coefficient.