Effective Surface of a Tubular Absorber in the Calculation of Resonance Integrals

The analytical expression for the effective resonance integral of a tubular absorber filled with moderator is obtained for the non-Doppler-broadened situation using the first collision probabilities for tubular geometry and is compared with the simpler expression by Carlvik and Pershagen. The effect of neutron transparency of the fuel on the resonance integral is shown to be important for a thin fuel region, and the correction factor in the calculation of the effective surface is given for the non-Doppler-broadened situation. The effect of Doppler broadening is examined in a simple manner. A correction factor lower than 0.8 is plausible for uranium oxide and metal tubes in the practical problems.