The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory - Frank, Rupert; Phan Thanh, Nam; Van Den Bosch, Hanne (Communications on Pure and Applied Mathematics, 2018)
We prove that in Thomas–Fermi–Dirac–von Weizsäcker theory, a nucleus of charge Z > 0 can bind at most Z + C electrons, where C is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential.
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