Derivation of modified approximate analytical formulae for calculating the direct and adjoint flux weighted resonance integrals using a variable neutron spectrum

In this work, modified approximate analytical formulae are derived for calculating the direct and adjointflux weighted resonance integrals using a variable neutron spectrum. These formulae are applied for both the solid and annular absorber lattice cells of di€erent mod- erator to fuel volume ratios. They are applied for the resonances of U-238 in the range from 4 to 1000 ev. According to these formulae, the percentage correction in the resonance integral weighted on the directflux is temperature independent and decreases with the moderator to fuel volume ratio, while for the adjointflux weighted resonance integral it increased with both the moderator to fuel volume ratio and temperature