An algorithm for automated extraction of resonance parameters from the stabilization method

The application of the stabilization method (Hazi and Taylor, 1970 [1]) to extract accurate energy and lifetimes of resonance states is challenging: The process requires labor-intensive numerical manipulation of a large number of eigenvalues of a parameter-dependent Hamiltonian matrix, followed by a fitting procedure. In this article, we present ReSMax, an efficient algorithm implemented as an open-access Python code, which offers full automation of the stabilization diagram analysis in a user-friendly environment while maintaining high numerical precision of the computed resonance characteristics. As a test case, we use ReSMax to analyze the natural parity doubly-excited resonance states (1Se, 3Se, 1Po, and 3Po) of helium, demonstrating the accuracy and efficiency of the developed methodology. The presented algorithm is applicable to a wide range of resonances in atomic, molecular, and nuclear systems.采用稳定化方法（stabilization method）（Hazi与Taylor，1970年[1]）提取共振态的精确能量与寿命颇具挑战：该流程需对大量参数依赖型哈密顿矩阵的本征值开展耗时耗力的数值处理，随后还需执行拟合步骤。本文提出ReSMax算法——一款以开源Python代码实现的高效工具，可在用户友好的环境中全自动完成稳定图分析，同时保证计算得到的共振特性具备极高数值精度。以氦原子的自然宇称双激发共振态（¹Sₑ、³Sₑ、¹Pₒ与³Pₒ）作为测试案例，采用ReSMax进行分析，验证了所提方法的准确性与高效性。本算法可应用于原子、分子及核物理系统中的各类共振现象。