Monte Carlo uncertainty of theHe3(α,γ)Be7reaction rate

Abstract

Background: The $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ reaction is of critical importance in determining the flux of solar neutrinos through the $pp$-II and $pp$-III chains. For this reason and others, the description of the cross section and its extrapolation towards low-energy has always been a matter of intense debate. While large systematic differences have been present in the past, several recent measurements are all in excellent statistical agreement.Purpose: The convergence of the recent individual experimental measurements of the $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ reaction prompts a global analysis of the reaction data. From the combined data, a more precise estimate of the low-energy cross section can be determined.Results: A global $R$-matrix fit is used to describe the $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ data as well as scattering data over a similar energy range. The $R$-matrix fit is then subjected to a Monte Carlo analysis to extract the uncertainties on the cross section and corresponding reaction rate.Conclusion: By combining several recent measurements of the $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$ reaction, the combined data yield a zero energy $S$ factor of $S(0)=0.542\ifmmode\pm\else\textpm\fi{}0.011(\text{MC}\phantom{\rule{4.pt}{0ex}}\text{fit})\ifmmode\pm\else\textpm\fi{}0.006{(\text{model})}_{\ensuremath{-}0.011}^{+0.019}(\text{phase}\phantom{\rule{4.pt}{0ex}}\text{shifts})$ keV b. This gives a total uncertainty in $S(0)$ of $+0.023/\ensuremath{-}0.017$ keV b.