### Abstract

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 Z_{c} is approached. Existence of a ground state at Z_{c} is shown under the condition Z_{c} < N-K, where K is the maximal number of electrons that can be removed at Z_{c} without changing the energy.

Original language | English (US) |
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Article number | 1350021 |

Journal | Reviews in Mathematical Physics |

Volume | 26 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2014 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Keywords

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

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## Cite this

Bellazzini, J., Frank, R. L., Lieb, E. H., & Seiringer, R. (2014). Existence of ground states for negative ions at the binding threshold.

*Reviews in Mathematical Physics*,*26*(1), [1350021]. https://doi.org/10.1142/S0129055X13500219