Analytical inequalities satisfied by the cross-section self-shielding factors

Recently, questions have arisen concerning the limits of the range of values within which a cross-section self-shielding factor (f-factor is restricted. Best upper and lower bounds for the range of values of an arbitrary f-factor are derived analytically from the definitions which form the basis for the computer codes currently employing the self-shielding method. A fundamental assumption used in the present derivation is that the fluxes and cross-sections be elements of a Hilbert Space. The strict upper and lower bounds for the f-factors are obtained by applying well-known inequalities from the theory of functions. In particular, it is shown that total and partial reaction f-factors can exceed unity. The conditions leading to such a situation are discussed from both a mathematical and a physical point of view. Due to its ease of application, it is planned to implement the results of this study in a routine checking procedure in codes employing the self-shielding method. 3 tables