The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory

2016/06/23 by Frank, Rupert L., Nam, Phan Thành, Bosch, Hanne Van Den · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1606.07355

Abstract

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.

Cited by

• Schrodinger-Poisson-Slater equations with nonlinearity subscaled near zero
• Dissociation limits in Density Functional Theory

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