Complex coordinate rotation method based on gradient optimization

TL;DR

The paper introduces CCR-GO, a novel complex coordinate rotation method based on gradient optimization, which automatically finds resonant states and improves accuracy in atomic systems without manual parameter tuning.

Contribution

It presents a new implementation of complex coordinate rotation using gradient optimization, eliminating manual parameter adjustments and enhancing efficiency and accuracy.

Findings

Efficiently searches for resonant positions and widths.

Significantly improves accuracy over traditional methods.

Capable of accurately handling bound-state problems.

Abstract

In atomic, molecular, and nuclear physics, the method of complex coordinate rotation is a widely used theoretical tool for studying resonant states. Here, we propose a novel implementation of this method based on the gradient optimization (CCR-GO). The main strength of the CCR-GO method is that it does not require manual adjustment of optimization parameters in the wave function; instead, a mathematically well-defined optimization path can be followed. Our method is proven to be very efficient in searching resonant positions and widths over a variety of few-body atomic systems, and can significantly improve the accuracy of the results. As a special case, the CCR-GO method is equally capable of dealing with bound-state problems with high accuracy, which is traditionally achieved through the usual extreme conditions of energy itself.