An Algorithm for Automated Extraction of Resonance Parameters from the Stabilization Method

TL;DR

The paper introduces exttt{dosmax}, an open-source Python algorithm that automates the extraction of resonance parameters from stabilization diagrams, improving efficiency and precision in analyzing resonance states across various physical systems.

Contribution

The authors developed exttt{dosmax}, a fully automated, high-precision Python tool for analyzing stabilization diagrams, simplifying and accelerating the extraction of resonance energies and lifetimes.

Findings

exttt{dosmax} accurately analyzed helium resonance states.

The algorithm demonstrated high efficiency and precision.

Applicable to atomic, molecular, and nuclear resonances.

Abstract

The application of the stabilization method [A.~U.\ Hazi and H.~S.\ Taylor, Phys.~Rev.~A {\bf 1}, 1109 (1970)]) 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 \dosmax, an efficient algorithm implemented as an open-access \texttt{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 \dosmax to analyze the natural parity doubly-excited resonance states (${}^{1}\textnormal{S}^{\textnormal{e}}$, ${}^{3}\textnormal{S}^{\textnormal{e}}$, ${}^{1}\textnormal{P}^{\textnormal{o}}$, and ${}^{3}\textnormal{P}^{\textnormal{o}}$) 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.