Geometric properties of the ground state of H and He in dense quantum plasmas

Xue Nan Li; Yong Zhi Zhang; Li Guang Jiao; Yuan Cheng Wang; Henry E. Montgomery; Yew Kam Ho; Stephan Fritzsche

doi:10.1140/epjd/s10053-023-00683-9

2024 Impact factor 1.5

Atomic, Molecular, Optical and Plasma Physics

Eur. Phys. J. D (2023) 77: 96
https://doi.org/10.1140/epjd/s10053-023-00683-9

Regular Article – Atomic Physics

Geometric properties of the ground state of H $^{-}$ $^{-}$ and He in dense quantum plasmas

Xue Nan Li¹, Yong Zhi Zhang¹^b, Li Guang Jiao²^,3^,4^c, Yuan Cheng Wang³^,4^,5, Henry E. Montgomery Jr.⁶, Yew Kam Ho⁷ and Stephan Fritzsche³^,4^,8

¹ College of Physical Science and Technology, Heilongjiang University, 150080, Harbin, People’s Republic of China
² College of Physics, Jilin University, 130012, Changchun, People’s Republic of China
³ Helmholtz-Institut Jena, 07743, Jena, Germany
⁴ GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291, Darmstadt, Germany
⁵ College of Physical Science and Technology, Shenyang Normal University, 110034, Shenyang, People’s Republic of China
⁶ Chemistry Program, Centre College, 40422, Danville, KY, USA
⁷ Institute of Atomic and Molecular Sciences, Academia Sinica, 10617, Taipei, Taiwan
⁸ Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, 07743, Jena, Germany

^b bokor@163.com
^c lgjiao@jlu.edu.cn

Received: 18 March 2023
Accepted: 25 May 2023
Published online: 6 June 2023

Abstract

The expectation values of radial and angular geometric quantities $⟨ r ⟩$ $\langle r \rangle$ , $⟨ r^{- 1} ⟩$ $\langle r^{-1} \rangle$ , $⟨ r^{2} ⟩$ $\langle r^{2} \rangle$ , $⟨ r_{12} ⟩$ $\langle r_{12} \rangle$ , $⟨ r_{12}^{- 1} ⟩$ $\langle r_{12}^{-1} \rangle$ , $⟨ r_{12}^{2} ⟩$ $\langle r_{12}^{2} \rangle$ , $⟨ r_{<} ⟩$ $\langle r_{<} \rangle$ , $⟨ r_{>} ⟩$ $\langle r_{>} \rangle$ , $⟨ cos (θ_{12}) ⟩$ $\langle \cos (\theta _{12}) \rangle$ , and $⟨ θ_{12} ⟩$ $\langle \theta _{12} \rangle$ for the ground states of the hydrogen negative ion and helium atom embedded in dense quantum plasmas are calculated using the Hylleraas configuration-interaction wave functions. The exponential cosine screened Coulomb potential is employed to model the effective interaction between charged particles in the dense quantum plasmas. The present calculations for free atoms show good agreement with other state-of-the-art predictions. In the plasma screening environments, our results improve previous estimations especially at large screening parameters. The radial expectation values $⟨ r_{<} ⟩$ $\langle r_{<} \rangle$ and $⟨ r_{>} ⟩$ $\langle r_{>} \rangle$ and the interelectronic angle $⟨ θ_{12} ⟩$ $\langle \theta _{12} \rangle$ for the plasma-screened hydrogen negative ion and helium atom are reported for the first time, and we show that the combination of them provides a fairly good description of the geometric structure of two-electron atoms in different screening conditions. We finally analyze the asymptotic behavior of ground-state energies and radial quantities for two-electron systems nearing the bound-continuum limit, and provide strong evidence that the two-electron critical screening parameters are in coincidence with those for one-electron atoms.

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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.