TY - JOUR AB - 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. AU - Frank, Rupert AU - Phan Thanh, Nam AU - Van Den Bosch, Hanne ID - 446 IS - 3 JF - Communications on Pure and Applied Mathematics TI - The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory VL - 71 ER -