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Estimation of Spatial Distributions of Neutron Captures in Resonance Absorbers

Donald Bogart

Nuclear Science and Engineering

Volume 41 / Number 1 / July 1970 / Pages 37-46


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The problem of precise calculation of spatial distributions of capture in resonance absorbers is crucial to the design of layered shields. Errors in spatial distribution of capture occur in multigroup neutron-transport calculations because of the necessarily broad energy groups employed. The single average-capture cross section in each group results in large underestimates of the capture rates near surfaces of resonance absorbers. Consequently, the spatial-capture gamma-ray generation and escape fraction are also in error. A method is presented for computing spatial-resonance-capture rates in thick layers. It employs group-effective resonance integrals to precalculate group-effective resonance cross sections that are universal functions of distance into the absorptive layer. The method is illustrated for captures in 238U for the energy region 0.5 eV to 100 keV. The method is applied to a spherical reactor-shield configuration that contains alternate layers of depleted uranium and lithium hydride. Detailed comparison is made of the results of a discrete ordinates multigroup calculation with those of the present method. The comparison shows that the difference in spatial-capture distribution of the Sn broad treatment of resonance capture causes the capture gamma-ray dose to be always underestimated. For example, the difference in spatial-capture distribution in a 7-cm slab of 238U causes the leakage dose to be a factor of 2 smaller than that obtained with the present method. The apparent generality of the present method suggests that it may be applied directly to the results of layered shield calculations made by Sn broad-group methods. Application of the method to the experimental variation of epicadmium capture with depth from the surface of metallic-uranium rods up to 5 cm in diameter as measured by Hellstrand provided spatial capture rates that agreed with experiment very well.

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