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Asymptotics for Bosonic atoms

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It was proved by Benguria and Lieb that for an atom where the ‘electrons’ do not satisfy the exclusion principle, the critical electron number N c, i.e., the maximal number of electrons the atom can bind, satisfies lim infz→∞Nc/Z ⩾ 1 + γ, where Z is the nuclear charge. Here γ is a positive constant derived from the Hartree model. We complete this result by proving that the correct asymptotics for N c(Z) is indeed z→∞Nc/Z = 1 + γ.

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This work was done while the author was a graduate student at Princeton University supported by a Danish Research Academy fellowship and U.S. National Science Foundation grant PHY-85-15288-A03.

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Solovej, J.P. Asymptotics for Bosonic atoms. Lett Math Phys 20, 165–172 (1990). https://doi.org/10.1007/BF00398282

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