近阈单中子共振的普适性质
Universal Properties of Near-Threshold Single-Neutron Resonances
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中文总结 AI 辅助
研究近阈单中子共振的普适宽度预测，利用有限方阱势的离散标度不变性推导出解析基线，应用于\(p\)波和\(d\)波共振，结果为识别中子共振受普适阈物理或结构相关效应影响提供几何基准。
中文摘要 AI 辅助
我们建立了对于\(L > 0\)分波中近阈单中子共振的普适宽度预测。我们的结果超越了维格纳关于阈附近截面的著名标度行为。我们表明有限方阱势在零能量处呈现离散标度不变性。由此，我们推导出一个仅依赖于几何、角动量和共振能量，而不依赖于内部短程核细节或径向激发的共振宽度解析基线。这是有限方阱势独有的非平凡性质。应用于观测到的\(p\)波和\(d\)波共振表明方阱结果提供了一个可靠基线。我们表明离散标度不变性在尖锐边界极限中消除了径向节点信息，但实际的伍德 - 萨克斯扩散打破了这种不变性，通过一个对内部径向激发敏感的因子抑制了约化宽度。这些结果为识别观测到的中子共振何时由普适阈物理控制以及何时表现出由结构相关效应驱动的系统偏差提供了一个简单的几何基准。
英文摘要
We establish universal width predictions for near-threshold single-neutron resonances in $L > 0$ partial waves. Our results go beyond Wigner's well-known scaling behavior of cross sections near threshold. We show that the finite square-well potential exhibits discrete scale invariance at zero energy. From this fact, we derive an analytic baseline for the resonance width that depends only on geometry, angular momentum, and resonance energy, and not on internal short-distance nuclear details or radial excitation. This is a nontrivial property that is unique to the finite square-well potential and does not occur for other potentials. Application to observed p-wave and d-wave resonances demonstrates that the square-well result provides a robust baseline. We show that discrete scale invariance erases radial-node information in the sharp-boundary limit, but realistic Woods-Saxon diffuseness breaks this invariance, suppressing the reduced width by a factor sensitive to the internal radial excitation. These results provide a simple geometric benchmark for identifying when observed neutron resonances are controlled by universal threshold physics and when they exhibit systematic deviations driven by structure-dependent effects.
