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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 |
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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.
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Received: 31 July 2022
Revised: 19 October 2022
Accepted manuscript online: 31 October 2022
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PACS:
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31.15.ac
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(High-precision calculations for few-electron (or few-body) atomic systems)
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31.15.aj
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(Relativistic corrections, spin-orbit effects, fine structure; hyperfine structure)
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31.30.jy
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(Higher-order effective Hamiltonians)
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| 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
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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
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