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}\textrm{H}\left(d,p\right) ^{3}\textrm{H}$ and $^{2} \textrm{H} \left(d,n\right) ^{3}\textrm{He}$ reactions. The corresponding Maxwellian-averaged thermonuclear reaction rates of relevance in astrophysical plasmas at temperatures in the range from $10^{6}$ K to $10^{10}\left(\textrm{or }1.3\times10^{8}\right)$ 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 +6.50\:{U_{e}}/{T_{9}}\right) $ for both $ ^{2}\textrm{H}\left(d,p\right) ^{3}\textrm{H}$ and $^{2} \textrm{H} \left(d,n\right) ^{3}\textrm{He}$ reactions. This series of values has been selected based on theoretical and experimental studies conducted so far.