Author:
Chen Tong,Mei Xuesong,Zhou Wanping,Qiao Haoxue
Abstract
Abstract
In this work, complete relativistic corrections of effective Hamiltonian for single particle system in external electromagnetic field and their unitary equivalent form up to the order of $m\alpha^8$ are obtained. The derivation is based on two approaches about Foldy-Wouthuysen(FW) transformation to the Dirac Hamiltonian in external electromagnetic field. The results are consistent with the previous work at the $m\alpha^6$ and $m\alpha^8$ order correction[K. Pachucki, Phys. Rev. A 71, 012503 (2005); W. Zhou, X. Mei, and H. Qiao, 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 obtained results can be used for the subsequent calculation of relativistic and radiation effects in simple atomic and molecular systems.
Subject
General Physics and Astronomy