Taming the Yukawa potential singularity: improved evaluation of bound states and resonance energies

TL;DR

This paper introduces an improved numerical approach for analyzing bound states and resonances in the Yukawa potential by analytically handling its singularity and employing complex scaling, enabling detailed spectral analysis.

Contribution

It presents a novel method combining analytical singularity treatment with numerical basis expansion and complex scaling to accurately evaluate Yukawa potential spectra.

Findings

Bound states cross into resonances as potential parameters vary

Efficient numerical scheme with Gauss quadrature improves spectral calculations

Trajectories of states in the complex energy plane are mapped

Abstract

Using the tools of the J-matrix method, we absorb the 1/r singularity of the Yukawa potential in the reference Hamiltonian, which is handled analytically. The remaining part, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. Analysis of resonance energies and bound states spectrum is performed using the complex scaling method, where we show their trajectories in the complex energy plane and demonstrate the remarkable fact that bound states cross over into resonance states by varying the potential parameters.