University of Minnesota
School of Physics & Astronomy

Physics and Astronomy Calendar

Friday, March 20th 2020
12:30 pm:
Speaker: Alexander Turbiner (ICN-UNAM, Mexico and Stony Brook)
Subject: Phenomenology in atomic physics: Helium (Lithium) atomic case

With contemporary computational efforts the non-relativistic spectra of Helium (Lithium) atomic sequence He,Li + ,Be + + etc can be calculated with practically any accuracy. Today's physics ``limits" the accuracy to 4 figures in non-relativistic QM treatment and to 12-13 figures (when mass, rel and QED effects are included) then {\it terra incognita}: non-QED effects begin to contribute. Does exist a phenomenological description of these two domains?

Take one-, two-, three-electron atomic ions with infinitely-heavy charge Z and focus to the ground state energy. For Z≤20 , 4 figures are described by the Schroedinger equation, then (mass+rel + QED) corrections start to give
contributions. For all three systems,

{\it Observation 1:} the first 4 figures are described by a 2nd degree polynomial in Z in domain Z≤50(20) (for (1e) case this polynomial is known exactly: - Z2 ).

[surprisingly, Ettore Majorana was the first c.1930 who thought in this direction (excerpts from his recently found unpublished notes)]

{\it Observation 2:} Pade approximant (9,5): P9 / Q5 in variable \sqrt{Z-Z_B}, where ZB is the so-called 2nd critical charge, describes ground state energy in domain Z≤50 (for Helium-like) and Z≤20 (for Lithium like) with 13 figures!

{\it Observation 3:} (mass+rel+QED) corrections contribute in ground state energy to the figures 5,6,7 etc. First 3 figures {\it vs} Z are described by 4th degree polynomial in Z (!) for Z≤20 .

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