Existence of ground states for negative ions at the binding threshold

Jacopo Bellazzini, Rupert L. Frank, Elliott H. Lieb, Robert Seiringer

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition. We investigate whether the electrons remain bound and whether the radius of the system stays finite as the critical value Zc is approached. Existence of a ground state at Zc is shown under the condition Zc < N-K, where K is the maximal number of electrons that can be removed at Zc without changing the energy.

Original languageEnglish (US)
Article number1350021
JournalReviews in Mathematical Physics
Issue number1
StatePublished - Feb 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Coulomb system
  • Many-body Schrödinger operator
  • threshold eigenvalue


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