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.