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High‐precision calculation of relativistic corrections for hydrogen‐like atoms with screened Coulomb potentials
Author(s) -
Xie Hui Hui,
Jiao Li Guang,
Liu Aihua,
Ho Yew Kam
Publication year - 2021
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.26653
Subject(s) - physics , relativistic quantum chemistry , perturbation theory (quantum mechanics) , coulomb , excited state , atomic physics , effective nuclear charge , quantum electrodynamics , quantum mechanics , ion , electron
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.