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A New Calculation of Resonance Integrals

L. W. Nordheim

Nuclear Science and Engineering

Volume 12 / Number 4 / April 1962 / Pages 457-463


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A new method for the calculation of resonance integrals for both homogeneous and heterogeneous assemblies has been developed and programmed for the IBM-7090. It consists in a direct numerical solution of the integral equation for the average flux in the absorber, and obviates the necessity of choosing between the narrow and wide resonance approximations. Cross sections are calculated, inclusive of Doppler broadening, interference scattering, and the E−1/2 factor in the absorption cross section. The unresolved resonances are calculated in the narrow resonance approximation under consideration of the Porter-Thomas distribution of neutron widths. Available options include (1) choice of geometry—spherical, cylindrical, slab, and homogeneous; (2) Dancoff correction for absorbers of arbitrary transparency; and (3) integral treatment of admixed scatterers. The only input data required are the resonance parameters and specifications of temperature, composition, and geometry. Everything else is handled automatically. The program calculates directly the cases of interest without requiring any additional data handling. Resonance integrals have been computed for uranium and thorium metal and UO2 and ThO2 rods of various diameters and different temperatures. Quantitative agreement with the best available measurements is reached for U238, with respect to the absolute values of the resonance integrals, as well as with respect to their temperature dependence. An interesting new result is that the intergral treatment of the oxygen in UO2 gives a noticeable correction to the resonance integral for thick absorber rods. For Th232, the agreement is not quite as perfect. The differences can, however, be traced to inconsistencies in the available cross section data.

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