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Chin. Phys. B, 2021, Vol. 30(2): 023101    DOI: 10.1088/1674-1056/abc156

Complex coordinate rotation method based on gradient optimization

Zhi-Da Bai(白志达)1,2, Zhen-Xiang Zhong(钟振祥)1,†, Zong-Chao Yan(严宗朝)3,1,4, and Ting-Yun Shi(史庭云)1
1 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China; 2 University of Chinese Academy of Sciences, Beijing 100049, China; 3 Department of Physics, University of New Brunswick, Fredericton, New Brunswick E3B 5A3, Canada; 4 Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China
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.
Keywords:  complex coordinate rotation method      resonant state      metastable state      gradient optimization  
Received:  23 August 2020      Revised:  22 September 2020      Accepted manuscript online:  15 October 2020
PACS:  31.10.+z (Theory of electronic structure, electronic transitions, and chemical binding)  
  31.15.-p (Calculations and mathematical techniques in atomic and molecular physics)  
  34.80.-i (Electron and positron scattering)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 91636216, 11974382, and 11474316), the Chinese Academy of Sciences Strategic Priority Research Program (Grant No. XDB21020200), and by the YIPA Program. ZCY acknowledges the support of NSERC, SHARCnet, and ACEnet of Canada.
Corresponding Authors:  Corresponding author. E-mail:   

Cite this article: 

Zhi-Da Bai(白志达), Zhen-Xiang Zhong(钟振祥), Zong-Chao Yan(严宗朝), and Ting-Yun Shi(史庭云) Complex coordinate rotation method based on gradient optimization 2021 Chin. Phys. B 30 023101

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