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Journal of Physics B Atomic Molecular and Optical Physics

Ab initio studies of electron correlation effects in magnetic dipolar hyperfine interaction of Cs

Yong-Bo Tang, Bing-Qiong Lou, Ting-Yun Shi

Published Jan 23, 2019• 16 citations
Publisher

Abstract

Abstract The hyperfine-structure constant A of the S , P , and D states in Cs atom with the principal quantum number n ≤ 12 are calculated using the Dirac–Fock approximation, the low-order many-body perturbation theory, and relativistic coupled-cluster method in single and double approximations with and without the inclusion of nonlinear terms. The importance of electron correlation effects, especially the nonlinear corrections of the cluster operators, is demonstrated by comparing the results of various approximations with available experimental values. Moreover, the correlation trends for individual electron correlation effects involving direct, core-polarization, and pair-correlation ones in members of Rydberg series are also investigated in the framework of the coupled-cluster theory. Some interesting features are observed.

DOI
10.1088/1361-6455/ab013c

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Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in 23^{23}23Na
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To enhance the current understanding of mechanisms contributing to magnetic hyperfine interactions in excited states of atomic systems, in particular, alkali-metal atom systems, the hyperfine fields in the excited 52S1/2−−82S1/25{}^{2}{S}_{1/2}--8{}^{2}{S}_{1/2}52S1/2​−−82S1/2​ states of potassium and 82S1/2−−122S1/28{}^{2}{S}_{1/2}--12{}^{2}{S}_{1/2}82S1/2​−−122S1/2​ states of francium atoms have been studied using the relativistic linked-cluster many-body perturbation procedure. The net theoretical values of the hyperfine fields for the excited states studied are in excellent agreement with available experimental data for both atoms. There is a significant decrease in importance of the correlation contribution in going from the ground state to the excited states, the correlation contributions as ratios of the direct contribution decreasing rapidly as one moves to the higher excited states. However, the contribution from the exchange core polarization (ECP) effect is nearly a constant fraction of the direct effect for all the excited states considered. Physical explanations are offered for the observed trends in the contributions from the different mechanisms. A comparison is made of the different contributing effects to the hyperfine fields in potassium and francium to those in the related system, rubidium, studied earlier. Extrapolating from our results to the highly excited states of alkali-metal atoms, referred to as the Rydberg states, it is concluded that in addition to the direct contribution from the excited valence electron to the hyperfine fields, a significant contribution is expected from the ECP effect arising from the influence of exchange interactions between electrons in the valence and core states.
The ZZZ-vector method in the relativistic coupled-cluster framework is used to calculate the magnetic hyperfine structure constant (AJ{A}_{J}AJ​) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The ZZZ-vector results are in very good agreement with the experiment. The AJ{A}_{J}AJ​ values of Li, Na, K, Rb, Cs, Be+{\mathrm{Be}}^{+}Be+, Mg+{\mathrm{Mg}}^{+}Mg+, Ca+{\mathrm{Ca}}^{+}Ca+, and Sr+{\mathrm{Sr}}^{+}Sr+ obtained in the ZZZ-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that the ZZZ-vector method with the single and double approximation can produce a more precise wave function in the nuclear region than the ECC method.
We demonstrate an iterative scheme for coupled-cluster property calculations without truncating the dressed properties operator. For validation, magnetic dipole hyperfine constants of alkaline-earth-metal ions are calculated using relativistic coupled-cluster theory and the role of electron correlation is examined. Then a detailed analysis of the higher-order terms is carried out. Based on the results, we arrive at an optimal form of the dressed operator, which we recommend for properties calculations with relativistic coupled-cluster theory.