$^{12}$ C（$α, γ$）$^{16}$ O截面在伽莫夫窗附近的可计算微观理论
Calculable microscopic theory for $^{12}$C($α, γ$)$^{16}$O cross section near Gamow window
摘要：
$^{12}$ C $(α, γ)^{16}$ O辐射俘获过程是恒星中产生氧元素的关键反应。测量伽莫夫窗口附近的截面非常困难，因为它太小了。为了解决这个长期存在的问题，我提出了一个微观的配方，旨在提供计算截面所需的所有材料。分别用全微观3 $α$ -粒子和4 $α$ -粒子组态描述了与反应有关的$^{12}$ C和$^{16}$ O的态，其中$α$粒子间的相对运动用相关高斯基函数展开.组态空间的优点是能够很好地描述$^{16}$ O态的约化$α$宽度振幅.电偶极和电四极跃迁都是辐射俘获过程的原因。$α$粒子被描述为具有混合有少量的同位旋$T=1$杂质组分的$(0s)^4$构型，该杂质组分对于解释等矢量电偶极跃迁至关重要。等压线电偶极子运营商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，使纸张自成一体，并准备进行数值计算。
英文摘要：
$^{12}$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 $^{12}$C and $^{16}$O relevant to the reaction are respectively described with fully microscopic 3 $α$-particle and 4 $α$-particle configurations, in which the relative motion among the $α$ particles is expanded in terms of correlated Gaussian basis functions. The configuration space has the advantage of being able to well describe the reduced $α$-width amplitudes of the states of $^{16}$O. Both electric dipole and electric quadrupole transitions are responsible for the radiative-capture process. The $α$ particle is described with a $(0s)^4$ configuration admixed with a small amount of an isospin $T=1$ 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.
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