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

Alexander V. Turbiner, Juan C. Lopez Vieyra, Horacio Olivares Pilon
(Submitted on 21 Jul 2017 (v1), last revised 31 Oct 2017 (this version, v2))

It is shown that the non-relativistic ground state energy of helium-like and lithium-like ions with static nuclei can be easily interpolated in full physics range of nuclear charge
Z
with accuracy of not less than 6 decimal digits or 7-8 significant digits using a meromorphic function in appropriate variable with a few free parameters. It is demonstrated that finite nuclear mass effects do not changed 4-5 significant digits in energy (and assuming the same is true for relativistic and QED effects), thus, the interpolation reproduces them. A meaning of interpolation is in a construction of unified Pade approximant for both small and large
Z
expansions with fitting some parameters at intermediate
Z
.
Comments:
12 pages, 3 Tables, paper extended dramatically with finite-mass calculations in Lagrange mesh, and leading relativistic and QED corrections, one extra author added, 8 new references added
Subjects:
Atomic Physics (physics.atom-ph); Quantum Physics (quant-ph)
Cite as:
arXiv:1707.07547 [physics.atom-ph]
 
(or arXiv:1707.07547v2 [physics.atom-ph] for this version)

https://arxiv.org/abs/1707.07547

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