The Effects on Reactivity Coefficients of Spectral Shifts Induced by Doppler Broadening

It is commonly accepted that the resonance reaction rate of any material increases when the temperature is raised. Using an exact Doppler-broadening kernel based on the Maxwellian distribution of nuclear velocities and an accurate integral transport method, we have shown that in a nuclear reactor the increase in resonance reaction rates with temperature at relatively high energy shifts the fine structure neutron spectrum in such a way that a net decrease in the neutron flux results at lower energies. In fast reactors, the decrease in the neutron flux at lower energy becomes more than the decrease in the self-shielding due to Doppler broadening and the net effect is a decrease in the resonance reaction rates. The quantification of the various components of the Doppler coefficient, T(dk/dT), in the liquid-metal fast breeder reactor benchmark (zero power reactor-6 Assembly 7) reveals that the spectral shift induced primarily by the broadening of ²³⁸U resonances causes the fissile material, ²³⁹Pu, to have a large negative (not positive) Doppler effect, which is 38% of the total. This prompt negative feedback indicates that prorating the Doppler signal by summing the Doppler contribution from each isotope based on first-order perturbation can lead to an error in the transient analysis. Calculation of the natural UO₂ sample Doppler worth in this assembly, in which the spectral shift effects are included, gives good agreement with the measured value.