|
|
High-order Hamiltonian obtained by Foldy-Wouthuysen transformation up to the order of mα8 |
Tong Chen(陈彤)1, Xuesong Mei(梅雪松)2, Wanping Zhou(周挽平)3,‡, and Haoxue Qiao(乔豪学)1,† |
1. School of Physics and Technology, Wuhan University, Wuhan 430072, China; 2. Wuhan Maritime Communication Research Institute, Wuhan 430072, China; 3. School of Physics and Telecommunications, Huanggang Normal University, Huanggang 438000, China |
|
|
Abstract Complete relativistic corrections of an effective Hamiltonian for a single-particle system in an external electromagnetic field and their unitary equivalent form up to the order of mα8 are obtained. The derivation is based on two approaches applying Foldy-Wouthuysen (FW) transformation to the Dirac Hamiltonian for a particle in an external electromagnetic field. The results are consistent with the previous work at the mα6 and mα8 order correction [Phys. Rev. A 71 012503 (2005); Phys. Rev. A 100 012513 (2019)]. We also further consider the effect of anomalous magnetic moments, namely, the Dirac-Pauli equation, and obtain FW-Hamiltonians at the same order. The results obtained can be used for the subsequent calculation of relativistic and radiation effects in simple atomic and molecular systems.
|
Received: 31 July 2022
Revised: 19 October 2022
Accepted manuscript online: 31 October 2022
|
PACS:
|
31.15.ac
|
(High-precision calculations for few-electron (or few-body) atomic systems)
|
|
31.15.aj
|
(Relativistic corrections, spin-orbit effects, fine structure; hyperfine structure)
|
|
31.30.jy
|
(Higher-order effective Hamiltonians)
|
|
Fund: This work was supported by the National Natural Science Foundation of China (Grant Nos.12074295 and 12104420). |
Corresponding Authors:
Haoxue Qiao, Wanping Zhou
E-mail: qhx@whu.edu.cn;zhouwp@whu.edu.cn
|
Cite this article:
Tong Chen(陈彤), Xuesong Mei(梅雪松), Wanping Zhou(周挽平), and Haoxue Qiao(乔豪学) High-order Hamiltonian obtained by Foldy-Wouthuysen transformation up to the order of mα8 2023 Chin. Phys. B 32 083101
|
[1] Schiller S, Bakalov D and Korobov V I 2014 Phys. Rev. Lett. 113 023004 [2] Zheng X, Sun Y R, Chen J J, Jiang W, Pachucki K and Hu S M 2017 Phys. Rev. Lett. 118 063001 [3] Hanneke D, Fogwell S and Gabrielse G 2008 Phys. Rev. Lett. 100 120801 [4] Sturm S, Köhler F, Zatorski J, Wagner A, Harman Z, Werth G, Quint W, Keitel C H and Blaum K 2014 Nature 506 467 [5] Pachucki K, Jentschura U D and Yerokhin V A 2004 Phys. Rev. Lett. 93 150401 [6] Pachucki K, Jentschura U D and Yerokhin V A 2005 Phys. Rev. Lett. 94 229902 [7] I Eides M, Grotch H and Shelyuto V A 2001 Physics Reports 342 63 [8] Patkóś V C V, Yerokhin V A and Pachucki K 2021 Phys. Rev. A 103 042809 [9] Mei X S, Zhao S M and Qiao H X 2014 Chin. Phys. Lett. 31 063102 [10] Zhou W, Mei X and Qiao H 2019 Phys. Rev. A 100 012513 [11] Zhou W, Mei X and Qiao H 2020 arXiv preprint arXiv:2003.10068 [12] Foldy L L and Wouthuysen S A 1950 Phys. Rev. 78 29 [13] Reiher M and Wolf A 2004 The Journal of Chemical Physics 121 2037 [14] Xiao Z 2018 Phys. Rev. D 98 035018 [15] Okamura K 2021 J. Phys.: Condens. Matter 33 285501 [16] Chen T W and Chiou D W 2014 Phys. Rev. A 90 012112 [17] Jentschura U and Pachucki K 1996 Phys. Rev. A 54 1853 [18] Pachucki K 1998 J. Phys. B: Atom. Mol. Opt. Phys. 31 2489 [19] Carbonell J, Lazauskas R and Korobov V I 2004 J. Phys. B: Atom. Mol. Opt. Phys. 37 2997 [20] Pachucki K and Yerokhin V A 2011 J. Phys.: Conf. Ser. 264 012007 [21] Greiner W 1994 Relativistic quantum mechanics [22] Pachucki K 2005 Phys. Rev. A 71 012503 |
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|