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arXiv · 1707.07547

Helium-like and Lithium-like ions: Ground state energy

Alexander V. Turbiner·Juan C. Lopez Vieyra·Horacio Olivares Pilon
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Abstract

It is shown that the non-relativistic ground state energy of helium-like and lithium-like ions with static nuclei can be interpolated in full physics range of nuclear charges $Z$ with accuracy of not less than 6 decimal digits (d.d.) or 7-8 significant digits (s.d.) using a meromorphic function in appropriate variable with a few free parameters. It is demonstrated that finite nuclear mass effects do not change 4-5 s.d. for $Z \in [1,50]$ for 2-,3-electron systems and the leading relativistic and QED corrections leave unchanged 3-4 s.d. for $Z \in [1,12]$ in the ground state energy for 2-electron system, thus, the interpolation reproduces definitely those figures. A meaning of proposed interpolation is in a construction of unified, {\it two-point} Pade approximant (for both small and large $Z$ expansions) with fitting some parameters at intermediate $Z$.

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Alexander V. Turbiner, Juan C. Lopez Vieyra, Horacio Olivares Pilon. 2017-07-21. Helium-like and Lithium-like ions: Ground state energy. https://arxiv.org/abs/1707.07547

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