The role of the screening potential in the deuteron-deuteron thermonuclear reaction rates

The deuteron-deuteron (D-D) thermonuclear reaction rates in metallic environments (considering the electron screening effects) is calculated using the S-factor functions which were obtained by fitting to low-energy data on D-D reactions. For this purpose, a fitted S-factor model based on the NACRE compilation is employed. This limited the energy range of Big Bang nucleosynthesis (BBN) for the ²H(d,p) ³H and ² H (d,n) ³He reactions. The corresponding Maxwellian-averaged thermonuclear reaction rates of relevance in astrophysical plasmas at temperatures in the range from 10⁶ K to 10¹⁰(or 1.3×10⁸) K are provided in tabular formats. In these evaluations, the screening energy (Uₑ) is assumed to be $100, 400, 750, 1000$ eV and $1250$ eV. This series of values has been selected based on theoretical and experimental studies conducted so far. % Eventually, our numerical analysis suggests that the ratio of the reaction rate with the screening potential to the reaction rate without the screening potential, can be described by the term exp(4.70 +6.50\:Uₑ/T₉) for both ²H(d,p) ³H and ² H (d,n) ³He reactions. This series of values has been selected based on theoretical and experimental studies conducted so far.