Increased Precision in Gamow Window Calculations for Thermonuclear Reaction Rates

The simulations of many astrophysical events require the input of thermonuclear reaction rates. These rate calculations involve a numerical integration over the Gamow window for each reaction. Standard codes to calculate rates, such as the tools at nucastrodata.org, utilize a Gaussian approximation\footnote{See, e.g., C. E. Rolfs and W. S. Rodney, ``Cauldrons in the Cosmos,'' The University of Chicago Press, Chicago (1988), p. 158.} to estimate the relative energy range (Gamow window) over which the calculation is performed numerically. This analytic method fails for low Z particles such as d($d,p$)t and d($d,n$)$^3$He reactions at low temperatures, which are important for Big Bang Nucleosynthesis (BBN). A new FORTRAN code was written and tested that numerically determines the lower energy limit whose contribution to the integration over the Gamow Window is less than 1.0\% at a given temperature. The code also determines the Gamow peak energy numerically, instead of using the formula for a constant S-factor. These developments will extend the rate calculation capabilities at nucastrodata.org to include BBN and enhance upcoming features at bigbangonline.org. This research is supported by the U. S. Department of Energy.