$$^{12}\mathrm{C}(\alpha , \gamma )^{16}$$ 12 C ( α , γ ) 16 O radiative-capture process is a key reaction to produce the element of oxygen in stars. Measuring the cross section near the Gamow window is extremely hard because it is too small. To make a theoretical contribution towards resolving the long-standing problem, I present a microscopic formulation that aims at providing all materials needed to calculate the cross section. The states of $$^{12}\mathrm{C}$$ 12 C and $$^{16}\mathrm{O}$$ 16 O relevant to the reaction are respectively described with fully microscopic 3 $$\alpha $$ α -particle and 4 $$\alpha $$ α -particle configurations, in which the relative motion among the $$\alpha $$ α particles is expanded in terms of correlated Gaussian basis functions. The configuration space has the advantage of being able to well describe the reduced $$\alpha $$ α -width amplitudes of the states of $$^{16}$$ 16 O. Both electric dipole and electric quadrupole transitions are responsible for the radiative-capture process. The $$\alpha $$ α particle is described with a $$(0s)^4$$ ( 0 s ) 4 configuration admixed with a small amount of an isospin $$T=1$$ T = 1 impurity component, which is crucially important to account for the isovector electric dipole transition. The isoscalar electric dipole operators are also taken into account up to the first order beyond the long-wavelength approximation. All the necessary ingredients are provided to make the paper self-contained and ready for numerical computations.

中文翻译：

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$$^{12}$$C($$\alpha , \gamma $$)$$^{16}$$O Gamow Window 附近的横截面的可计算显微理论

$$^{12}\mathrm{C}(\alpha , \gamma )^{16}$$ 12 C ( α , γ ) 16 O 辐射捕获过程是在恒星中产生氧元素的关键反应。测量 Gamow 窗口附近的横截面非常困难，因为它太小了。为了对解决长期存在的问题做出理论贡献，我提出了一个微观公式，旨在提供计算横截面所需的所有材料。与反应相关的$$^{12}\mathrm{C}$$ 12 C和$$^{16}\mathrm{O}$$ 16 O的状态分别用完全微观的3 $$\alpha $来描述$α -particle 和 4 $$\alpha $$ α -粒子配置，其中 $$\alpha $$ α 粒子之间的相对运动根据相关的高斯基函数展开。配置空间的优点是能够很好地描述 $$^{16}$$$16 O 状态的减小的 $$\alpha $$ α 宽度幅度。电偶极子和电四极子跃迁都负责辐射捕获过程。$$\alpha $$ α 粒子被描述为 $$(0s)^4$$ ( 0 s ) 4 构型和少量同位旋 $$T=1$$ T = 1 杂质成分，其中对于解释等向量电偶极子跃迁至关重要。等标量电偶极子算子也被考虑到超过长波长近似的一阶。提供了所有必要的成分，使论文自成一体并准备好进行数值计算。电偶极子和电四极子跃迁都负责辐射捕获过程。$$\alpha $$ α 粒子被描述为 $$(0s)^4$$ ( 0 s ) 4 构型和少量同位旋 $$T=1$$ T = 1 杂质成分，其中对于解释等向量电偶极子跃迁至关重要。等标量电偶极子算子也被考虑到超过长波长近似的一阶。提供了所有必要的成分，使论文自成一体并准备好进行数值计算。电偶极子和电四极子跃迁都负责辐射捕获过程。$$\alpha $$ α 粒子被描述为 $$(0s)^4$$ ( 0 s ) 4 构型和少量同位旋 $$T=1$$ T = 1 杂质成分，其中对于解释等向量电偶极子跃迁至关重要。等标量电偶极子算子也被考虑到超过长波长近似的一阶。提供了所有必要的成分，使论文自成一体并准备好进行数值计算。这对于解释等向量电偶极子跃迁至关重要。等标量电偶极子算子也被考虑到超过长波长近似的一阶。提供了所有必要的成分，使论文自成一体并准备好进行数值计算。这对于解释等向量电偶极子跃迁至关重要。等标量电偶极子算子也被考虑到超过长波长近似的一阶。提供了所有必要的成分，使论文自成一体并准备好进行数值计算。