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. A71 012503 (2005); Phys. Rev. A100 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.
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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