## On the energy of a large atom.(English)Zbl 0722.35072

We announce a proof of an asymptotic formula for the groundstate energy of a large atom. The early work of Thomas-Fermi, Hartree-Fock, Dirac, and Scott predicted that for an atomic number Z, the energy is $$E(Z)\approx - c_ 0Z^{7/3}+c_ 1Z^ 2-c_ 2Z^{5/3}$$ for known $$c_ 0,c_ 1$$, and $$c_ 2$$ [see E. H. Lieb, Rev. Mod. Phys 53, 603-641 (1981)]. J. Schwinger [Phys. Rev. A 24, 2353-2361 (1981)] observed an additional effect and set down the modified formula $$E(Z)\approx -c_ 0Z^{7/3}+c_ 1Z^ 2-(10/9)c_ 2Z^{5/3}$$. Our proof shows that Schwinger’s formula is correct.

### MSC:

 35Q40 PDEs in connection with quantum mechanics 81V45 Atomic physics 81Q15 Perturbation theories for operators and differential equations in quantum theory

### Keywords:

asymptotic formula; groundstate energy; large atom
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### References:

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