Accurate calculation of resonances for a central-field model potential

TL;DR

This paper introduces a highly accurate method for calculating resonance energies in the Schrödinger equation with central-field potentials, outperforming previous approaches and providing benchmark results.

Contribution

The paper presents a novel rational approximation method for resonance calculation that improves accuracy and convergence over existing spherical-box techniques.

Findings

The new method achieves higher accuracy in resonance energies.

It demonstrates faster convergence compared to previous methods.

Results serve as benchmarks for future research.

Abstract

We obtain accurate resonance energies for the Schr\"{o}dinger equation with a central--field potential by means of a method based on a rational approximation to the logarithmic derivative of the wavefunction. We discuss the rate of convergence of our approach and compare present results with those obtained earlier by other authors. We show that present method is superior to the spherical--box approach applied recently to the same problem. As far as we know present results are more accurate than those available in the literature and may be a suitable benchmark for testing future approaches.