标题： 分析捕获截面公式的改进 显示英文标题

标题： Refinement of an analytical capture cross section formula

摘要： 提出了一种高精度的解析公式，用于系统地描述从轻核到超重核反应体系的捕获截面。 基于经验势垒分布（EBD）方法，通过引入核表面修正来改进计算势垒高度的库仑参数$z$，对三个关键输入量进行了优化，将$Q$值和壳修正纳入势垒分布宽度的计算中，并考虑超重核体系的非弹性散射效应对势垒半径的影响。 通过这些改进，EBD 方法的模型精度不仅提高了计算势垒高度的准确性，也提高了预测捕获截面的准确性。 对于总共 426 个具有$ 35 < Z_1 Z_2 < 2600$的反应体系，预测截面与数据之间的平均偏差（以对数尺度计算）从 3.485 显著降低到 0.113。 显示英文摘要

摘要： An analytical formula with high accuracy is proposed for a systematic description of the capture cross sections from light to superheavy reaction systems. Based on the empirical barrier distribution (EBD) method, three key input quantities are refined by introducing nuclear surface correction to the Coulomb parameter $z$ for calculating the barrier height, incorporating the $Q$-value and shell correction into the barrier distribution width calculations, and considering the deep inelastic scattering effects of superheavy systems on the barrier radius. With these refinements, the model accuracy of the EBD method, not only the accuracy of the calculated barrier height but also the accuracy of the predicted capture cross sections, is substantially improved. The average deviation (in logarithmic scale) between the predicted cross sections and the data for a total of 426 reaction systems with $ 35 < Z_1 Z_2 < 2600$ is sharply reduced from 3.485 to 0.113.