Data Covariances from R-Matrix Analyses of Light Nuclei

After first reviewing the parametric description of light-element reactions in multichannel systems using R-matrix theory and features of the general LANL R-matrix analysis code EDA, we describe how its chi-square minimization procedure gives parameter covariances. This information is used, together with analytically calculated sensitivity derivatives, to obtain cross section covariances for all reactions included in the analysis by first-order error propagation. Examples are given of the covariances obtained for systems with few resonances (He-5) and with many resonances (C-13). We discuss the prevalent problem of this method leading to cross section uncertainty estimates that are unreasonably small for large data sets. The answer to this problem appears to be using parameter confidence intervals in place of standard errors.