An effective field theory (EFT) for a nuclear reaction at low energies is studied. The astrophysical S-factor of radiative \(\alpha \) capture on \(^{12}\hbox {C}\) at the Gamow-peak energy, \(T_\mathrm{G} = 0.3\) MeV, is a fundamental quantity in nuclear astrophysics, and we construct an EFT for the reaction. To fix parameters appearing in the effective Lagrangian, the EFT is applied to the study for three reactions: elastic \(\alpha \)–\(^{12}\hbox {C}\) scattering at low energies, the E1 transition of radiative \(\alpha \) capture on \(^{12}\hbox {C}\), and \(\beta \) delayed \(\alpha \) emission from \(^{16}\hbox {N}\). We report an estimate of the \(S_{E1}\)-factor of the reaction through the E1 transition at \(T_\mathrm{G}\) by employing the EFT. We also discuss applications of EFTs to nuclear reactions at low energies.

研究了低能核反应的有效场论（EFT）。在Gamow峰能量\（T_ \ mathrm {G} = 0.3 \）  MeV下，在\（^ {12} \ hbox {C} \）上在\（^ {12} \ hbox {C} \）上捕获的辐射\（\ alpha \）的天体S因子为是核天体物理学中的一个基本量，我们为该反应构建了一个EFT。为了确定有效拉格朗日方程中出现的参数，将EFT应用于以下三个反应的研究：低能时的弹性\（\ alpha \） – \（^ {12} \ hbox {C} \）散射，E 1跃迁\（^ {12} \ hbox {C} \）上辐射\（\ alpha \）捕获的数量，并且\（\ beta \）延迟\（^ {16} \ hbox {N} \）的\（\ alpha \）发射。我们采用EFT报告了通过\（T_ \ mathrm {G} \）处E 1跃迁对反应的\（S_ {E1} \）-因子的估计。我们还讨论了EFT在低能核反应中的应用。