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

Reliable reaction rates at high stellar temperatures are necessary for the study of advanced stellar burning stages, supernovae and x-ray bursts. We suggest a new procedure for extrapolating experimental thermonuclear reaction rates to these higher temperatures (T $>$ 1 GK) using statistical model (Hauser-Feshbach) results. Current, generally accepted, procedures involve the use of the Gamow peak, which has been shown to be unreliable for narrow resonances at high stellar temperatures [1]. Our new approach defines the effective thermonuclear energy range (ETER) by using the 8$^{th}$, 50$^{th}$ and 92$^{nd}$ percentiles of the cumulative distribution of fractional resonant reaction contributions. The ETER is then used to define a reliable temperature for matching experimental rates to Hauser-Feshbach rates. The resulting matching temperature is often well above the previous result using the Gamow peak concept. Our new method should provide more accurate extrapolated rates since Hauser-Feshbach rates are more reliable at higher temperatures. These ideas are applied to 21 (p,$\gamma$), (p,$\alpha$) and ($\alpha$,$\gamma$) reactions on a range of A = 20-40 target nuclei and results will be presented. \\[0pt] [1] J.~R.~Newton, C.~Iliadis, A.~E.~Champagne, A.~Coc, Y.~Parpottas and R.~Ugalde, Phys.~Rev.~C 75, 045801 (2007).