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High-precision calculation of relativistic corrections for hydrogen-like atoms with screened Coulomb potentials
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  • Hui Xie,
  • Li Guang Jiao,
  • Ai Liu,
  • Y.K. Ho
Hui Xie
Jilin University
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Li Guang Jiao
Jilin University
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Ai Liu
Jilin University
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Y.K. Ho
Institute of Atomic and Molecular Sciences Academia Sinica
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Abstract

The first-order relativistic corrections to the non-relativistic energies of hydrogen-like atom embedded in plasma screening environments are calculated in the framework of direct perturbation theory by using the generalized pseudospectral method. The standard Debye-Hückel potential, exponential cosine screened Coulomb potential, and Hulthén potential are employed to model different screening conditions and their effects on the eigenenergies of hydrogen-like atoms are investigated. The relativistic corrections which include the relativistic mass correction, Darwin term, and the spin-orbit coupling term for both the ground and excited states are reported as functions of screening parameters. Comparison with previous theoretical predictions shows that both the relativistic mass correction and spin-orbit coupling obtained in this work are in good agreement with previous estimations, while significant discrepancy and even opposite trend is found for the Darwin term. The overall relativistic-corrected system energies predicted in this work, however, are in good agreement with the fully relativistic calculations available in the literature. We finally present the scaling law of the first-order relativistic corrections and discuss the validity of the direct perturbation theory with respect to both the nuclear charge and the screening parameter.

Peer review status:ACCEPTED

20 Jan 2021Submitted to International Journal of Quantum Chemistry
21 Jan 2021Submission Checks Completed
21 Jan 2021Assigned to Editor
27 Jan 2021Reviewer(s) Assigned
07 Feb 2021Review(s) Completed, Editorial Evaluation Pending
08 Feb 2021Editorial Decision: Revise Minor
11 Feb 20211st Revision Received
11 Feb 2021Submission Checks Completed
11 Feb 2021Assigned to Editor
17 Feb 2021Reviewer(s) Assigned
25 Feb 2021Review(s) Completed, Editorial Evaluation Pending
25 Feb 2021Editorial Decision: Accept