Existence of ground states for negative ions at the binding threshold

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

doi:10.1142/S0129055X13500219

Existence of ground states for negative ions at the binding threshold

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

Mathematics

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10 Scopus citations

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)
Article number	1350021
Journal	Reviews in Mathematical Physics
Volume	26
Issue number	1
DOIs	https://doi.org/10.1142/S0129055X13500219
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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10.1142/S0129055X13500219

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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 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.",

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AU - Bellazzini, Jacopo

AU - Frank, Rupert L.

AU - Lieb, Elliott H.

AU - Seiringer, Robert

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N2 - 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.

AB - 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.

KW - Coulomb system

KW - Many-body Schrödinger operator

KW - threshold eigenvalue

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ER -

Existence of ground states for negative ions at the binding threshold

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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