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

Abstract

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 ${}^2\text{H}{\left(d,p\right)}^3\text{H}$ and ${}^2\text{H}{\left(d,n\right)}^3\text{He}$ reactions. The corresponding Maxwellian-averaged thermonuclear reaction rates of relevance in astrophysical plasmas at temperatures in the range from $10^6$ K to $10^{10}\left(\text{or }1.3\times 10^8\right)$ K are provided in tabular formats. In these evaluations, the screening energy ($U_e$) 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 $\exp \left(4.70+6.50U_e/T_9\right)$ for both ${}^2\text{H}{\left(d,p\right)}^3\text{H}$ and ${}^2\text{H}{\left(d,n\right)}^3\text{He}$ reactions. This series of values has been selected based on theoretical and experimental studies conducted so far.

Comments: 23 Pages, 2 figure, 11 Tables