Theoretical study of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>+</mml:mo><mml:mi>d</mml:mi><mml:mo>→</mml:mo><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts/><mml:none/><mml:mn>6</mml:mn></mml:mmultiscripts></mml:mrow><mml:mo>+</mml:mo><mml:mi>γ</mml:mi></mml:math> astrophysical capture process in a three-body model. II. Reaction rates and primordial abundance
Аннотация
The astrophysical $S$ factor and reaction rate of the direct capture process $\ensuremath{\alpha}+d\phantom{\rule{4pt}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{4pt}{0ex}}^{6}\mathrm{Li}+\ensuremath{\gamma}$, as well as the abundance of the $^{6}\mathrm{Li}$ element, are estimated in a three-body model. The initial state is factorized into the deuteron bound state and the $\ensuremath{\alpha}+d$ scattering state. The final nucleus $^{6}\mathrm{Li}$(${1}^{+}$) is described as a three-body bound state $\ensuremath{\alpha}+n+p$ in the hyperspherical Lagrange-mesh method. Corrections to the asymptotics of the overlap integral in the $S$ and $D$ waves have been done for the $E2 S$ factor. The isospin forbidden $E1 S$ factor is calculated from the initial isosinglet states to the small isotriplet components of the final $^{6}\mathrm{Li}$(${1}^{+}$) bound state. It is shown that the three-body model is able to reproduce the newest experimental data of the LUNA Collaboration for the astrophysical $S$ factor and the reaction rates within the experimental error bars. The estimated $^{6}\mathrm{Li}/\mathrm{H}$ abundance ratio of $(0.67\ifmmode\pm\else\textpm\fi{}0.01)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ is in a very good agreement with the recent measurement $(0.80\ifmmode\pm\else\textpm\fi{}0.18)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ of the LUNA Collaboration.