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, accounting for electron screening effects, are calculated using S-factor functions derived from fits to low-energy D-D reaction data. For this purpose, a fitted S-factor model based on the NACRE compilation is employed, which constrains the energy range applicable to 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 Maxwellian-averaged thermonuclear reaction rates, relevant to astrophysical plasmas at temperatures ranging from $10^{6}$ K to $10^{10}$ K (or $1.3 \times 10^{8}$ K), are presented in tabular formats. The effects of electron screening are phenomenologically analyzed, with screening energy ($U_{e}$) values of 100, 400, 750, 1000, and 1250 eV being employed for this purpose. This selection of values is grounded in theoretical and experimental studies conducted to date. Ultimately, the numerical analysis reveals that the ratio of the screened reaction rate to the unscreened reaction rate can be expressed by the numerical formula $ \exp\left(4.70 +6.50{\times10^{-6}}U_{e}/{T_{9}}\right) $ for both the $^{2}\textrm{H}\left(d,p\right)^{3}\textrm{H}$ and $^{2}\textrm{H}\left(d,n\right)^{3}\textrm{He}$ reactions.