The Doppler effect in thermal reactors

Experimental and theoretical work on the Doppler effect in thermal reactors is reviewed for uranium metal, UO₂, thorium metal, and ThO₂. The experimental values of a, the fractional increase in resonance capture per °C, have a spread many times the quoted errors. The use of different slowing-down spectra has contributed to the discrepancies. For uranium metal, approximate corrections are made to obtain the coefficient α₀ appropriate to a $\text{1}\text{E}$ spectrum. The spread in the corrected values α₀ is smaller than that for α, but remains unsatisfactory. Other experimental difficulties arise in reactivity normalizations, in obtaining the statistical weight of samples and from spurious temperature effects. Theory and experiment agree on an increase of α₀ with increasing surface-to-mass ratio and that this is caused by an increase in the contribution of lower-energy resonances to the Doppler effect. It is also in agreement with the theoretical interpretation of the radial dependence of the Doppler effect in a lump. However in the region of practical interest where the surface-to-mass ratio is small, α₀ is almost constant. Experimental evidence on the temperature behaviour of α₀ is unsatisfactory but indicates that α₀, decreases with increasing temperature. Theory predicts that α₀ will vary approximately as $\text{T}{}^{\mathrm{<mtext>-1</mtext><mtext>2</mtext>}}$ where T is the Kelvin temperature. In the case of non-uniform temperature distribution in a fuel element, both experimental and theoretical effort is needed.