AI 中文总结
研究$^{14}$Cβ衰变，用从头算核晶格有效场论，通过系统优化相互作用和跃迁算符，得到与实验相符结果，消除壳模型和从头算研究差距，解释$^{14}$C长寿命，让NLEFT成为核跃迁研究实用工具。
AI 中文摘要
放射性碳定年法的物理基础$^{14}$C半衰期为5730年，与典型核物理预期相比异常长，其起源数十年来一直是争论焦点。本文报告了$^{14}$Cβ衰变的从头算核晶格有效场论（NLEFT）计算。使用系统优化的相互作用和从手征有效场论一致导出的跃迁算符，得到与实验测量的Gamow-Teller矩阵元$M_\text{GT}^\text{exp}\simeq 2\times 10^{-3}$相符的结果。首先表明手征相互作用和高阶弱流对将GT矩阵元淬灭到物理值至关重要，其中三核子力的优化不可或缺。然后说明淬灭深深植根于核壳模型中$^{14}$N的基态结构，其中S波和D波成分存在竞争，对所用相互作用敏感。发现物理上的$^{14}$N基态由D波构型主导，这是淬灭的关键因素。探索了衰变矩阵元对低能常数微调的敏感性，揭示了$^3S_1$通道两核子接触力和单π介子交换三核子力的突出作用。这项工作消除了壳模型和从头算研究$^{14}$Cβ衰变之间的差距，为$^{14}$C异常长寿命提供了有效且直接的解释，并使NLEFT成为系统研究核跃迁的实用工具。
英文摘要
The 5730-year half-life of $^{14}$C, the physical basis of radiocarbon dating, is anomalously long compared to typical nuclear-physics expectations. Its origin has remained a subject of debate for many decades. Here we report an \textit{ab initio} nuclear lattice effective field theory (NLEFT) calculation of $^{14}$C $β$ decay. Using systematically optimized interactions and transition operators consistently derived from chiral effective field theory, We obtain a result consistent with the Gamow-Teller matrix element $M_\text{GT}^\text{exp}\simeq 2\times 10^{-3}$ measured with the current uncertainty of $O(10^{-2})$. We first show that chiral interactions and weak currents beyond leading-order are essential for quenching the GT matrix element to the physical value, among which the optimization of three-nucleon forces is indispensable. We then illustrate that the quenching is deeply rooted in the ground-state structure of $^{14}$N as found in the nuclear shell model, where the competition between $S$- and $D$-wave components exists, sensitive to the interaction employed. The physical $^{14}$N ground state is found to be dominated by $D$-wave configurations, which constitutes the key factor for the quenching. The sensitivity of the decay matrix element to the fine-tuning of low-energy-constants is explored, revealing the prominent role of the $^3S_1$-channel two-nucleon contact force and the one-pion-exchange three-nucleon force. This work eliminates the gap between shell-model and \textit{ab initio} studies of $^{14}$C $β$ decay, provides a valid and straightforward explanation for the anomalous long lifetime of $^{14}$C, and turns NLEFT into a practical tool for the systematic study of nuclear transitions.
