Improving R-matrix estimates of astrophysical S-factors

We consider processes, such as the critically important α capture by 12C, which involve many nuclear resonance levels and reaction channels and also large energy extrapolations to obtain S-factors. The R-matrix is commonly used to analyze the data and make the extrapolations. We liberate the analysis from significant unreliability by showing that, contrary to general belief, the R-matrix has unique matching radii determined by the physics of the nuclear mean-field. The mean-field also reduces the S-factors slightly.