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.

中文翻译：

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基于梯度优化的复坐标旋转方法

在原子、分子和核物理中，复坐标旋转方法是研究共振态的广泛使用的理论工具。在这里，我们提出了一种基于梯度优化（CCR-GO）的方法的新实现。CCR-GO方法的主要优点是不需要手动调整波函数中的优化参数；相反，可以遵循数学上明确定义的优化路径。我们的方法被证明在搜索各种少体原子系统的共振位置和宽度方面非常有效，并且可以显着提高结果的准确性。作为一种特殊情况，CCR-GO 方法同样能够以高精度处理边界状态问题，这在传统上是通过能量本身的通常极端条件来实现的。