The influence of relativistic, Breit interaction, and QED effects on the and energy levels of Be-like () isoelectronic sequence

Cunqiang Wu; Runxia Zhao; Denghong Zhang; Mingwu Zhang; Yingli Xue; Deyang Yu; Chenzhong Dong; Xiaobin Ding

doi:10.1140/epjd/s10053-023-00709-2

2023 Impact factor 1.5

Atomic, Molecular, Optical and Plasma Physics

Eur. Phys. J. D (2023) 77: 129
https://doi.org/10.1140/epjd/s10053-023-00709-2

Regular Article – Atomic Physics

The influence of relativistic, Breit interaction, and QED effects on the $1 s^{2} 2 p^{2}$ $1s^{2}2p^{2}$ and $2 s 2 p^{3}$ $2s2p^{3}$ energy levels of Be-like ( $4 \leq Z \leq 74$ $4\!\le \!Z\!\le \!74$ ) isoelectronic sequence

Cunqiang Wu¹, Runxia Zhao¹, Denghong Zhang¹^,2, Mingwu Zhang³, Yingli Xue³, Deyang Yu³, Chenzhong Dong¹^,2 and Xiaobin Ding¹^,2^h

¹ Key Laboratory of Atomic and Molecular Physics and Functional Materials of Gansu Province, College of Physics and Electronic Engineering, Northwest Normal University, 730070, Lanzhou, China
² Gansu International Scientific and Technological Cooperation Base of Laser Plasma Spectroscopy, 730070, Lanzhou, China
³ Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, China

^h dingxb@nwnu.edu.cn

Received: 11 October 2022
Accepted: 20 June 2023
Published online: 6 July 2023

Abstract

The excitation energies of the Be-like ions (4 $\leq Z \leq$ $\le \! Z\!\le \!$ 74) doubly excited state $1 s^{2} 2 p^{2}$ $1\,s^{2}2p^{2}$ and doubly core-excited state $2 s 2 p^{3}$ $2s2p^{3}$ are calculated using the multi-configuration Dirac–Hartree–Fock method. The contributions of relativistic effects, Breit interaction, and QED effects to the excitation energies are analyzed and discussed in detail. A reasonable electron correlation model has been constructed using the active set method. The electron correlation and the finite size of the atomic nucleus correction have also been appropriately considered. The calculated results agree with the available theoretical and experimental data. It is found that the contribution of relativistic effects, Breit interaction, and QED effects to the excitation energy becomes significant with increasing Z. The contribution of the relativistic effects reaches about 8.5% at Z=74. The $^{3}$ $^{3}$ P $_{0}$ $_{0}$ level of the doubly excited state $1 s^{2} 2 p^{2}$ $1\,s^{2}2p^{2}$ is sensitive to the Breit interaction and the QED effects, but these two contributions cancel each other out. For the doubly core-excited state $2 s 2 p^{3}$ $2s2p^{3}$ , the Breit interaction and the QED effects are almost equally important, and their maximum contribution is about 0.5%. These results are expected to help future experimental and theoretical work.

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