Virtual states in the coupled-channel problems with an improved complex scaling method

TL;DR

This paper presents an improved complex scaling method that effectively identifies virtual states and resonances in multichannel quantum scattering problems, surpassing traditional techniques in efficiency and accuracy.

Contribution

The authors develop a flexible contour approach in momentum space to enhance the complex scaling method for detecting virtual states, extending its applicability and efficiency.

Findings

Successfully identifies virtual states across Riemann sheets

More efficient than Fredholm determinant zero-search methods

Accurately characterizes resonances and virtual states

Abstract

We improve the complex scaling method (CSM) to obtain virtual states, which were previously challenging in the conventional CSM. Our approach solves the Schr\"odinger equation in the momentum space as an eigenvalue problem by choosing the flexible contours. It proves to be highly effective in identifying the poles across the different Riemann sheets in the multichannel scatterings. It is more straightforward and efficient than searching for the zeros of the Fredholm determinant of the Lippmann-Schwinger equation using the root-finding algorithms. This advancement significantly extends the capabilities of the CSM in accurately characterizing the resonances and virtual states in quantum systems.