Absence of a Ground State for Bosonic Coulomb Systems with Critical Charge

Abstract

We consider bosonic Coulomb systems with $N$-particles and $K$ static nuclei. Let $E_N^Z$ denote the ground state energy of a bosonic molecule of the total nuclear charge $Z$. We prove that the system has no normalizable ground state when $E_N^{N-1}=E_{N-1}^{N-1}$.

7 pages. To appear in Reports on Mathematical Physics

References in corpus (4)

• Geometric methods for nonlinear many-body quantum systems
• Bound States at Threshold resulting from Coulomb Repulsion
• Existence of ground states for negative ions at the binding threshold
• Zero Energy Bound States and Resonances in Three--Particle Systems