Bound States at Threshold resulting from Coulomb Repulsion

Abstract

The eigenvalue absorption for a many-particle Hamiltonian depending on a parameter is analyzed in the framework of non-relativistic quantum mechanics. The long-range part of pair potentials is assumed to be pure Coulomb and no restriction on the particle statistics is imposed. It is proved that if the lowest dissociation threshold corresponds to the decay into two likewise non-zero charged clusters then the bound state, which approaches the threshold, does not spread and eventually becomes the bound state at threshold. The obtained results have applications in atomic and nuclear physics. In particular, we prove that atomic ion with atomic critical charge $Z_{cr}$ and $N_e$ electrons has a bound state at threshold given that $Z_{cr}\in (N_e-2,N_e-1)$, whereby the electrons are treated as fermions and the mass of the nucleus is finite.

This is a combined and updated version of the manuscripts arXiv:math-ph/0611075v2 and arXiv:math-ph/0610058v2

References in corpus (3)

• Rigorous conditions for the existence of bound states at the threshold in the two-particle case
• Zero Energy Bound States and Resonances in Three--Particle Systems
• Zero Energy Bound States in Many--Particle Systems

Cited by in corpus (7)

• Existence of ground states for negative ions at the binding threshold
• Tosio Kato's Work on Non--Relativistic Quantum Mechanics
• Why there is no Efimov effect for four bosons and related results on the finiteness of the discrete spectrum
• Atoms in the anionic domain, Z < N
• Regularized perturbative series for the ionization potential of atomic ions
• Universal Angular Probability Distribution of Three Particles near Zero Energy Threshold
• Absence of a Ground State for Bosonic Coulomb Systems with Critical Charge