AI 中文总结
该研究提出基于吸收马尔可夫链的框架计算核γ射线布居概率，应用于²⁵Mg(p,γ)²⁶Al反应关键共振，获基态布居概率并识别主导衰变跃迁，可传播核不确定性至天体反应速率。
AI 中文摘要
本文提出一种基于吸收马尔可夫链计算核衰变方案中γ射线布居概率的框架。该方法将激发态核态视为瞬态，长寿命能级视为吸收态，可通过转移矩阵精确获取布居分数。实验不确定性通过狄利克雷分布的蒙特卡洛采样传播，自然保持分支比向量的单位归一化物理约束。该框架应用于²⁵Mg(p,γ)²⁶Al反应中关键的Eᵣ=92 keV共振（Eₓ=6398 keV），该共振控制氢燃烧环境中²⁶Al的产生。结合分层贝叶斯框架内的多个实验数据集，得到基态布居概率f₀=0.68±0.06（1σ）±0.13（2σ），并首次识别出导致其不确定性的主导γ衰变跃迁。该形式主义重现了传统级联计算，同时提供解析灵敏度信息和透明的不确定性分解。该方法为将核结构不确定性传播至天体物理反应速率提供了通用且计算高效的工具，可轻松扩展至其他核。
英文摘要
A framework for computing $γ$-ray feeding probabilities in nuclear decay schemes based on absorbing Markov chains is presented. In this approach, excited nuclear states are treated as transient states and long-lived levels as absorbing states, allowing feeding fractions to be obtained exactly from the transition matrix. Experimental uncertainties are propagated via Monte Carlo sampling from Dirichlet distributions, which naturally maintains the physical constraint of unit normalization for branching-ratio vectors. This framework is applied to the key $E_r= 92$ keV resonance in the $^{25}$Mg(p,$γ$)$^{26}$Al reaction ($E_x = 6398$ keV), which governs the production of $^{26}$Al in hydrogen-burning environments. Combining multiple experimental datasets within a Hierarchical Bayesian framework, a ground-state feeding probability of $f_0 = 0.68 \pm 0.06~(1σ) \pm 0.13~(2σ)$ is found, and for the first time the dominant $γ$-decay transitions contributing to its uncertainty are identified. The formalism reproduces traditional cascade calculations while providing analytic sensitivity information and a transparent uncertainty decomposition. This approach offers a general and computationally efficient tool for propagating nuclear-structure uncertainties to astrophysical reaction rates and can be readily extended to other nuclei.
Comments8 pages, 6 figures. Accepted for publication in Phys. Rev. C
