Matching of experimental and statistical-model thermonuclear reaction rates at high temperatures

We address the problem of extrapolating experimental thermonuclear reaction rates toward high stellar temperatures (T>1 GK) by using statistical model (Hauser-Feshbach) results. Reliable reaction rates at such temperatures are required for studies of advanced stellar burning stages, supernovae, and x-ray bursts. Generally accepted methods are based on the concept of a Gamow peak. We follow recent ideas that emphasized the fundamental shortcomings of the Gamow peak concept for narrow resonances at high stellar temperatures. Our new method defines the effective thermonuclear energy range (ETER) by using the 8th, 50th, and 92nd percentiles of the cumulative distribution of fractional resonant reaction rate contributions. This definition is unambiguous and has a straightforward probability interpretation. The ETER is used to define a temperature at which Hauser-Feshbach rates can be matched to experimental rates. This matching temperature is usually much higher compared to previous estimates that employed the Gamow peak concept. We suggest that an increased matching temperature provides more reliable extrapolated reaction rates since Hauser-Feshbach results are more trustwhorthy the higher the temperature. Our ideas are applied to 21 (p,γ), (p,α), and (α,γ) reactions on A=20-40 target nuclei. For many of the cases studied here, our extrapolated reaction rates at high temperatures differ significantly from those obtained using the Gamow peak concept.