Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in $^{23}$Na

Vaibhav Katyal, B. K. Sahoo

physics.atom-phCross-listedarXiv:2607.05012Jul 7, 2026

理论物理通讯：英文版

Hyperfine Constants for Low-Lying States in ^137Ba^＋

Yu, Kai-Zhi

Published Jan 1, 2007• 0 citations

OpenAlex

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Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in $^{23}$ NaInvestigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in $^{23}$Na

Vaibhav Katyal, B. K. Sahoo

Accurate determination of hyperfine structure constants in atomic systems provides important insight into the interplay of electron correlation and relativistic effects in the nuclear region. Although sodium (Na) is a relatively light atom, previous all-order relativistic many-body calculations of the magnetic dipole hyperfine constants for the low-lying states of $^{23}$ Na show noticeable discrepancies with experiment. To address this, we calculate the ionization potentials and hyperfine structure constants of $^{23}$ Na using relativistic coupled-cluster theory with explicit inclusion of triple excitations. We further incorporate corrections from the Breit interaction, quantum electrodynamics, and the Bohr-Weisskopf (BW) effect. Results from lower-order methods are also presented to assess the importance of different physical contributions across states. Our calculations demonstrate that contributions from the lower-order relativistic and BW effects play almost similar roles with the electron correlation effects, including triple excitations, and are essential for reconciling theoretical predictions with experimental observations. This study can also serve as a useful guide for understanding the role of triples in heavier alkali systems.Accurate determination of hyperfine structure constants in atomic systems provides important insight into the interplay of electron correlation and relativistic effects in the nuclear region. Although sodium (Na) is a relatively light atom, previous all-order relativistic many-body calculations of the magnetic dipole hyperfine constants for the low-lying states of $^{23}$Na show noticeable discrepancies with experiment. To address this, we calculate the ionization potentials and hyperfine structure constants of $^{23}$Na using relativistic coupled-cluster theory with explicit inclusion of triple excitations. We further incorporate corrections from the Breit interaction, quantum electrodynamics, and the Bohr-Weisskopf (BW) effect. Results from lower-order methods are also presented to assess the importance of different physical contributions across states. Our calculations demonstrate that contributions from the lower-order relativistic and BW effects play almost similar roles with the electron correlation effects, including triple excitations, and are essential for reconciling theoretical predictions with experimental observations. This study can also serve as a useful guide for understanding the role of triples in heavier alkali systems.

physics.atom-phCross-listedarXiv:2607.05012Jul 7, 2026

We perform accurate calculations of energy levels as well as fine and hyperfine splittings of the lowest

^{1,3}P_{J}, ^{3}S_{1}, ^{3}P_{J}^{e}

, and

^{1,3}D_{J}

excited states of the

^{9}\mathrm{Be}

atom using explicitly correlated Gaussian functions, and we report on the breakdown of the standard hyperfine structure theory. Because of the strong hyperfine mixing, which prevents the use of common hyperfine constants, we formulate a description of the fine and hyperfine structure that is valid for an arbitrary coupling strength and may have wide applications in many other atomic systems.

Investigating Role of Electron Correlation Effects via Triple Excitations for Precise Evaluation of Energies and Hyperfine Structure Constants in

^{23}

^{23}

Na show noticeable discrepancies with experiment. To address this, we calculate the ionization potentials and hyperfine structure constants of

^{23}

Na using relativistic coupled-cluster theory with explicit inclusion of triple excitations. We further incorporate corrections from the Breit interaction, quantum electrodynamics, and the Bohr-Weisskopf (BW) effect. Results from lower-order methods are also presented to assess the importance of different physical contributions across states. Our calculations demonstrate that contributions from the lower-order relativistic and BW effects play almost similar roles with the electron correlation effects, including triple excitations, and are essential for reconciling theoretical predictions with experimental observations. This study can also serve as a useful guide for understanding the role of triples in heavier alkali systems.