{"date_updated":"2023-09-19T10:09:40Z","date_published":"2018-03-01T00:00:00Z","abstract":[{"text":"We prove that in Thomas–Fermi–Dirac–von Weizsäcker theory, a nucleus of charge Z &gt; 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.","lang":"eng"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","department":[{"_id":"RoSe"}],"doi":"10.1002/cpa.21717","oa_version":"Preprint","article_processing_charge":"No","author":[{"last_name":"Frank","full_name":"Frank, Rupert","first_name":"Rupert"},{"id":"404092F4-F248-11E8-B48F-1D18A9856A87","full_name":"Phan Thanh, Nam","first_name":"Nam","last_name":"Phan Thanh"},{"first_name":"Hanne","full_name":"Van Den Bosch, Hanne","last_name":"Van Den Bosch"}],"intvolume":"        71","oa":1,"issue":"3","type":"journal_article","isi":1,"day":"01","article_type":"original","status":"public","volume":71,"external_id":{"isi":["000422675800004"],"arxiv":["1606.07355"]},"publication":"Communications on Pure and Applied Mathematics","_id":"446","date_created":"2018-12-11T11:46:31Z","page":"577 - 614","title":"The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory","quality_controlled":"1","acknowledgement":"We thank the referee for helpful suggestions that improved the presentation of the paper. We also acknowledge partial support by National Science Foundation Grant DMS-1363432 (R.L.F.), Austrian Science Fund (FWF) Project Nr. P 27533-N27 (P.T.N.), CONICYT (Chile) through CONICYT–PCHA/ Doctorado Nacional/2014, and Iniciativa Científica Milenio (Chile) through Millenium Nucleus RC–120002 “Física Matemática” (H.V.D.B.).\r\n","publication_status":"published","language":[{"iso":"eng"}],"month":"03","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1606.07355"}],"publist_id":"7377","publisher":"Wiley-Blackwell","citation":{"ieee":"R. Frank, P. Nam, and H. Van Den Bosch, “The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory,” <i>Communications on Pure and Applied Mathematics</i>, vol. 71, no. 3. Wiley-Blackwell, pp. 577–614, 2018.","apa":"Frank, R., Nam, P., &#38; Van Den Bosch, H. (2018). The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. <i>Communications on Pure and Applied Mathematics</i>. Wiley-Blackwell. <a href=\"https://doi.org/10.1002/cpa.21717\">https://doi.org/10.1002/cpa.21717</a>","ista":"Frank R, Nam P, Van Den Bosch H. 2018. The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. Communications on Pure and Applied Mathematics. 71(3), 577–614.","chicago":"Frank, Rupert, Phan Nam, and Hanne Van Den Bosch. “The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory.” <i>Communications on Pure and Applied Mathematics</i>. Wiley-Blackwell, 2018. <a href=\"https://doi.org/10.1002/cpa.21717\">https://doi.org/10.1002/cpa.21717</a>.","short":"R. Frank, P. Nam, H. Van Den Bosch, Communications on Pure and Applied Mathematics 71 (2018) 577–614.","ama":"Frank R, Nam P, Van Den Bosch H. The ionization conjecture in Thomas–Fermi–Dirac–von Weizsäcker theory. <i>Communications on Pure and Applied Mathematics</i>. 2018;71(3):577-614. doi:<a href=\"https://doi.org/10.1002/cpa.21717\">10.1002/cpa.21717</a>","mla":"Frank, Rupert, et al. “The Ionization Conjecture in Thomas–Fermi–Dirac–von Weizsäcker Theory.” <i>Communications on Pure and Applied Mathematics</i>, vol. 71, no. 3, Wiley-Blackwell, 2018, pp. 577–614, doi:<a href=\"https://doi.org/10.1002/cpa.21717\">10.1002/cpa.21717</a>."},"year":"2018"}