$β$-Oslo 与 Shape 分析在未分辨母态混合中的应用

中文摘要 AI 辅助

未分辨的β衰变基态与同核异能态混合物通过不同的激发能和自旋-宇称分布布居共同的子核。开发了一个框架来确定此类数据何时适用于传统的$β$-Oslo和Shape分析，以及哪些量保持可辨识性。物理初级-γ分布是分别归一化的分支核的平均；全局母态分数通常不等于激发能区间或接受的初级-γ样本中的分数。群体不变性、Oslo因子分解和总核能级密度的恢复被区分开来。精确的对数线性兼容性检验和低层瀑布替换恒等式分离了因子分解和第一代减除效应。对于Shape分析，匹配的末态自旋和宇称消除了共同的角动量因子，但可能保留激发依赖的E1/M1权重。图表示给出了一致性条件，并揭示了仅测量一个固定末态分离时丢失的信息。确定性的自旋-宇称分辨瀑布基准再现了群体不变极限，并表现出精确因子分解（使用有效而非总的能级密度）以及小的矩阵残差伴随显著的形状误差。评估的$\rb\rightarrow\sr$性质指定了一个相关应用，包括两个$2^+$候选末态和随时间变化的母态混合。数值示例是受控的合成测试，而非从$^{90}$Rb数据中提取。结果为解释未分辨母态测量和识别群体感知推断所需的额外观测提供了标准。

英文摘要

An unresolved mixture of beta-decaying ground and isomeric states populates a common daughter nucleus through different excitation-energy and spin-parity distributions. A framework is developed to determine when such data admit conventional $β$-Oslo and Shape analyses and which quantities remain identifiable. The physical primary-$γ$ distribution is an average of separately normalized branching kernels; the global parent fraction does not, in general, equal the fraction in an excitation-energy bin or an accepted primary-$γ$ sample. Population invariance, Oslo factorization, and recovery of the total nuclear level density are separated. An exact log-linear compatibility test and a lower-cascade replacement identity isolate factorization and first-generation-subtraction effects. For Shape analysis, matched final-state spins and parities remove common angular-momentum factors but can retain excitation-dependent E1/M1 weights. A graph representation gives consistency conditions and exposes the information lost when only one fixed final-state separation is measured. Deterministic spin-parity-resolved cascade benchmarks reproduce the population-invariant limit and exhibit both exact factorization with an effective, rather than total, level density and small matrix residuals accompanied by appreciable shape errors. Evaluated $\rb\rightarrow\sr$ properties specify a relevant application, including two $2^+$ candidate final states and time-dependent parent mixing. The numerical examples are controlled synthetic tests, not an extraction from $^{90}$Rb data. The results provide criteria for interpreting unresolved-parent measurements and for identifying the additional observations required for population-aware inference.

发表机构

• Department of Nuclear Physics, China Institute of Atomic Energy（中国原子能科学研究院核物理系）

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