The triple alpha reaction is a key to $^{12}$C production and is expected to occur in weakly-coupled, thermal plasmas as encountered in normal stars. We investigate how Coulomb screening affects the structure of a system of three alpha particles in such a plasma environment by precise three-body calculations within the Debye-Huckel approximation. A three-alpha model that has the Coulomb interaction modified in the Yukawa form is employed. Precise three-body wave functions are obtained by a superposition of correlated Gaussian bases with the aid of the stochastic variational method. The energy shifts of the Hoyle state due to the Coulomb screening are obtained as a function of the Debye screening length. The results, which automatically incorporate the finite size effect of the Hoyle state, are consistent with the conventional result based on the Coulomb correction to the chemical potentials of ions that are regarded as point charges in a weakly-coupled, thermal plasma. We have given a theoretical basis to the conventional point-charge approach to the Coulomb screening problem relevant for nuclear reactions in normal stars by providing the first evaluation of the Coulomb corrections to the $Q$ value of the triple alpha process that produces a finite size Hoyle state.

中文翻译：

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对热等离子体中三重α过程的 Q 值进行库仑筛选校正

三重α反应是产生$^{12}$C的关键，预计会发生在普通恒星中遇到的弱耦合热等离子体中。我们通过 Debye-Huckel 近似中的精确三体计算来研究库仑筛选如何影响这种等离子体环境中三个 alpha 粒子系统的结构。采用了库仑相互作用以汤川形式修改的三阿尔法模型。借助随机变分方法，通过相关高斯基的叠加获得精确的三体波函数。由于库仑屏蔽导致的霍伊尔态的能量位移是作为德拜屏蔽长度的函数获得的。结果，自动结合了霍伊尔态的有限尺寸效应，与基于对离子的化学势进行库仑校正的传统结果一致，这些离子被视为弱耦合热等离子体中的点电荷。我们通过对产生有限大小的三重 alpha 过程的 $Q$ 值的库仑校正进行首次评估，为与正常恒星中的核反应相关的库仑筛选问题的常规点电荷方法提供了理论基础霍伊尔州。