Bound States at Threshold resulting from Coulomb Repulsion

Details Bound States at Threshold resulting from Coulomb Repulsion Bound States at Threshold resulting from Coulomb Repulsion

2011-12-06

arxiv.org/abs/1112.1234v1

Physics

Mathematical Physics

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

Scientific paper

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.

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