氧-氖核中$^{24}$ Na和$^{27}$ Al的禁戒电子俘获
Forbidden electron capture on $^{24}$Na and $^{27}$Al in degenerate oxygen-neon cores
摘要：
初始质量为$\sim 7$-11太阳质量的恒星在碳燃烧后形成简并的氧-氖核心。在这样的核心中捕获的电子可以触发失控的氧气燃烧，导致坍塌或热核爆炸。我们提供了一个详细的描述，在以前的工作中使用的形式主义，并将其应用到两个进一步的禁戒跃迁，是相关的简并氧氖核心：$4^+_\text{g.s.}\rightarrow{}2^+_1$过渡在$^{24}\text{Na}(e^-,ν_e)^{24}\text{Ne}$和${5/2^+_{\text{g.s.}} \rightarrow{} 1/2^+_{\text{g.s.}}}$过渡在$^{27}\text{Al}(e^-,ν_e)^{27}\text{Mg}$。通过壳模型计算和CVC理论的约束，确定了相关的核矩阵元素。然后，我们调查的天体物理学的影响，使用恒星演化代码MESA和通过时间尺度参数。在相关的温度范围内，禁戒跃迁大大降低了$^{24}\text{Na}(e^-,ν_e)^{24}\text{Ne}$和$^{27}\text{Al}(e^-,ν_e)^{27}\text{Mg}$的阈值密度。在MESA模型中，$^{24}\text{Na}(e^-,ν_e)^{24}\text{Ne}$现在在$^{24}\text{Mg}(e^-,ν_e)^{24}\text{Na}$发作后立即发生。对整体演变的影响是不确定的：这是由于已知的困难，占对流不稳定性引发的$A=24$电子捕获。$^{27}\text{Al}$和$^{27}\text{Mg}$之间的转换可能对早期演变有轻微影响，但不太可能影响结局。在计算温度$\log_{10}(T[\text{K}])\lesssim8.5$下$^{24}$ Na和$^{24}$ Ne之间的弱相互作用速率以及$\log_{10}(T[\text{K}])\lesssim8.8$下$^{27}$ Al和$^{27}$ Mg之间的弱相互作用速率时，应包括所研究的跃迁。
英文摘要：
Stars with an initial mass of $\sim 7$-11 solar masses form degenerate oxygen-neon cores following carbon burning. Electron captures in such cores can trigger runaway oxygen burning, resulting in either a collapse or a thermonuclear explosion. We provide a detailed description of the formalism used in previous work and apply it to two further forbidden transitions that are relevant to degenerate oxygen-neon cores: the $4^+_\text{g.s.}\rightarrow{}2^+_1$ transition in $^{24}\text{Na}(e^-,ν_e)^{24}\text{Ne}$ and the ${5/2^+_{\text{g.s.}} \rightarrow{} 1/2^+_{\text{g.s.}}}$ transition in $^{27}\text{Al}(e^-,ν_e)^{27}\text{Mg}$. The relevant nuclear matrix elements are determined through shell model calculations and constraints from CVC theory. We then investigate the astrophysical impact using the stellar evolution code MESA and through timescale arguments. In the relevant temperature range, the forbidden transitions substantially reduce the threshold densities for $^{24}\text{Na}(e^-,ν_e)^{24}\text{Ne}$ and $^{27}\text{Al}(e^-,ν_e)^{27}\text{Mg}$. In the MESA models, $^{24}\text{Na}(e^-,ν_e)^{24}\text{Ne}$ now occurs immediately following the onset of $^{24}\text{Mg}(e^-,ν_e)^{24}\text{Na}$. The impact on the overall evolution is uncertain: this is due to known difficulties in accounting for convective instabilities triggered by the $A=24$ electron captures. The transition between $^{27}\text{Al}$ and $^{27}\text{Mg}$ may have a minor effect on the early evolution but is unlikely to affect the outcome. The studied transitions should be included when calculating weak interaction rates between $^{24}$Na and $^{24}$Ne for temperatures $\log_{10}(T[\text{K}])\lesssim8.5$ and between $^{27}$Al and $^{27}$Mg for $\log_{10}(T[\text{K}])\lesssim8.8$.
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