Conditional Variances Pertinent to Doppler Effect Studies

This paper discusses the statistical uncertainties of the self-shielded group cross section and its temperature derivative associated with the use of the biased selection technique where resonances are chosen to match the observed value of the unshielded cross section. Since the self-shielded group cross section can always be pictured as a superposition of an infinitely dilute term and a self-shielding term, the problem amounts to the estimation of the conditional variances of the self-shielding term and its temperature derivative for any given value of the infinitely dilute cross section. A semianalytical method based on the NR-approximation has been developed to estimate these conditional variances. Both qualitative and quantitative discussions are given for cases of ²³⁹Pu and ²³⁸U under various physical conditions.