Thermalization of Neutrons in Graphite: Status and Error Analysis

Calculations related to the temperature coefficient of reactivity of enriched gas-cooled reactors show the high sensitivity of this parameter to the proper description of thermalization effects in the moderator. Additionally, the calculation of the temperature dependence of the inelastic-scattering cross section with current ENDF/B formalisms correlates the errors of the cross sections as functions of the temperature. Neglecting this temperature correlation introduces unnecessary conservatism in the estimation of the error of the reactivity coefficient.These two facts drove our efforts to characterize the present status of the inelastic cross section of graphite and to calculate its covariance file. The ENDF/B evaluation of the scattering matrix S(α, β, T) is still based on the approximations (incoherent component only) andphonon spectra of the early 1960s. Subsequent measurements showed that the structure observed in S(α, β, T) cannot be described using the incoherent approximation, and soon after the availability of highly intense neutron beams and large specimens of pyrolitic graphite have allowed the direct measurement of elastic constants of relevance for a better calculation of the phonon spectra. Calculations of the probability distributions of the moment and energy transfer, a and  β, in a Maxwellian spectrum allow us to define a range of α and β for which comparison of experimental and theoretical data are of most interest for reactor analysis, and to point out regions of deficient resolution or excessive details in the present α, β mesh used in the ENDF/B files. Because the phonon spectrum defines S(α, β, T), mathematical formulas have been found that allow the calculation of the covariance matrix of S by propagating the errors of the phonon spectra.