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

TL;DR

This paper proves that bosonic Coulomb systems with certain charge configurations lack a normalizable ground state, highlighting fundamental limitations in their stability.

Contribution

It establishes the absence of a ground state for bosonic Coulomb systems at critical charge conditions, advancing understanding of their spectral properties.

Findings

No normalizable ground state exists at critical charge

Ground state energy equality implies absence of bound state

Results apply to systems with N particles and K static nuclei

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 $E_{N}^{N-1} = E_{N-1}^{N-1}$.