Radial dependence of the doppler effect in bars of uranium and thorium

Abstract

If a lump containing uranium or thorium is heated in a reactor spectrum, the rate of neutron capture changes. This is called the ‘Doppler effect’. An experimental investigation shows that uniform heating of a sample of thorium or uranium causes a constant fractional increase in activation per atom throughout the main volume of the sample, upon which is superposed a peak close to, but inside, the surface of the samples. The peak rises above the volume effect by factors of 8 and 3 for uranium and thorium respectively and extends to a depth of 0·2 mm and 1·5 mm in the two cases. It is shown theoretically that this peak in the Doppler effect is due to activation in the resonances below 100 eV from impinging neutrons which have not suffered a potential scattering event. However, the theory predicts that at large penetrations the Doppler effect in the uncollided flux results in a decrease in activation with increasing temperature i.e. the opposite sign from the peak. Thus when averaged through a thick rod the net contribution of the resonances below 100 eV to the Doppler effect is small. It is predicted that the Doppler effect will be a maximum for uranium lumps 0·2 mm in size, the resonances below 100 eV being responsible for the maximum. An attempt is made to take account of the resonance scattering of the impinging flux. The volume Doppler effect arises mainly from the presence of potential scattering and the unresolved resonances make the larger contribution. Predictions made by L. DRESNER for the temperature dependence of the volume term of the effective resonance integral are consistent with the experimental results at the centre of the sample. For 1 in. bars of uranium and thorium, the experimental values of the Doppler coefficient ( 1 I +) ( d I +/dT ) are found to be (0·90 ± 0·17) × 10 −4 per °C and (2·7 ± 0·1) × 10 −4 per °C, where I + is the average effective resonance integral including the 1 v- contribution above the cadmium cut-off.