Complex coordinate rotation method based on gradient optimization

doi:10.1088/1674-1056/abc156

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: zxzhong@wipm.ac.cn

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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

1 Michishio K, Tachibana T, Terabe H, Igarashi A, Wada K, Kuga T, Yagishita A, Hyodo T and Nagashima Y 2011 Phys. Rev. Lett. 106 153401
2 Ceeh H, Hugenschmidt C, Schreckenbach K, G\"artner S A, Thirolf P G, Fleischer F and Schwalm D 2011 Phys. Rev. A 84 062508
3 Huang B, Sidorenkov L A, Grimm R and Hutson J M 2014 Phys. Rev. Lett. 112 190401
4 Zhao C Y, Han H L, Wu M S and Shi T Y 2019 Phys. Rev. A 100 052702
5 Ning Y, Yan Z C and Ho Y K 2015 Phys. Plasmas 22 013302
6 Yan Z C and Ho Y K 2008 Phys. Rev. A 78 012711
7 Yan Z C and Ho Y K 2018 Phys. Rev. A 98 062702
8 Sullivan J P, Gilbert S J, Buckman S J and Surko C M 2001 J. Phys. B 34 L467
9 Korobov V I, Bakalov D and Monkhorst H J 1999 Phys. Rev. A 59 R919(R)
10 Korobov V I 2003 Phys. Rev. A 67 062501
11 Korobov V I 2014 Phys. Rev. A 89 014501
12 Ponomarev L I 1990 Contemp. Phys. 31 219
13 Lu B N, Zhao E G and Zhou S G 2012 Phys. Rev. Lett. 109 072501
14 Wheeler J A 1937 Phys. Rev. 52 1107
15 Wigner E P and Eisenbud L 1947 Phys. Rev. 72 29
16 Simon B 1973 Ann. Math. 97 247
17 Raju S B and Doolen G 1974 Phys. Rev. A 9 1965
18 Ho Y K 1983 Phys. Rep. 99 1
19 Feshbach H 1962 Ann. Phys. 19 287
20 Lin C D 1984 Phys. Rev. A 29 1019
21 Igarashi A and Shimamura I 2004 Phys. Rev. A 70 012706
22 Han H, Zhong Z, Zhang X and Shi T 2008 Phys. Rev. A 78 044701
23 Hu M H, Yao S M, Wang Y, Li W, Gu Y Y and Zhong Z X 2016 Chem. Phys. Lett. 654 114
24 Doolen G D 1975 J. Phys. B 8 525
25 B\"urgers A and Lindroth E 2000 Eur. Phys. J. D 10 327
26 Li T and Shakeshaft R 2005 Phys. Rev. A 71 052505
27 Kar S and Ho Y K 2012 Phys. Rev. A 86 014501
28 Ho Y K 1979 Phys. Rev. A 19 2347
29 Ho Y K 1981 Phys. Rev. A 23 2137
30 Gning Y, Sow M, Traor\'e A, Dieng M, Diakhate B, Biaye M and Wagu\'e A 2015 Radiat. Phys. Chem. 106 1–6
31 B\"urgers A, Wintgen D and Rost J 1995 J. Phys. B 28 3163
32 Ho Y K and Bhatia A K 1991 Phys. Rev. A 44 2895
33 Drake G W F and Makowski A J 1988 J. Opt. Soc. Am. B 5 2207
34 Yan Z C, Zhang J Y and Li Y 2003 Phys. Rev. A 67 062504
35 Fletcher R 2000 Practical Methods of Optimization (Chichester: John Wiley and Sons)

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