中国物理B ›› 2023, Vol. 32 ›› Issue (8): 83101-083101.doi: 10.1088/1674-1056/ac9e98

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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. 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
  • 收稿日期:2022-07-31 修回日期:2022-10-19 接受日期:2022-10-31 发布日期:2023-07-28
  • 通讯作者: Haoxue Qiao, Wanping Zhou E-mail:qhx@whu.edu.cn;zhouwp@whu.edu.cn
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China (Grant Nos.12074295 and 12104420).

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. 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
  • Received:2022-07-31 Revised:2022-10-19 Accepted:2022-10-31 Published:2023-07-28
  • Contact: Haoxue Qiao, Wanping Zhou E-mail:qhx@whu.edu.cn;zhouwp@whu.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (Grant Nos.12074295 and 12104420).

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摘要： 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.

关键词: high-order correction, relativistic corrections, Foldy-Wouthuysen (FW) transformation, effective Hamiltonians

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.

Key words: high-order correction, relativistic corrections, Foldy-Wouthuysen (FW) transformation, effective Hamiltonians

中图分类号:  (High-precision calculations for few-electron (or few-body) atomic systems)

  • 31.15.ac
31.15.aj (Relativistic corrections, spin-orbit effects, fine structure; hyperfine structure) 31.30.jy (Higher-order effective Hamiltonians)