# Critical nuclear charges for *N*-electron atoms

## A. V. Sergeev and Sabre Kais

One-particle model with a spherically-symmetric screened Coulomb
potential is proposed to describe the motion of a loosely bound electron
in a multi-electron atom when the nuclear charge,
which is treated as a continuous parameter, approaches its
critical value. The critical nuclear charge, Z_c, is the minimum charge
necessary to bind N electrons.
Parameters of the model are chosen to meet known binding energies
of the neutral atom and the isoelectronic negative ion.
This model correctly describes the asymptotic behavior of the binding energy
in the vicinity of the critical charge, gives accurate
estimation of the critical charges in comparison with ab initio calculations
for small atoms and is in full agreement with the prediction of the
statistical theory of large atoms. Our results rule out the stability of
doubly charged atomic negative ions in the gas phase. Moreover, the critical
charge obeys the proposed inequality, N-2 <= Z_c <= N-1.
We show that in the
presence of a strong magnetic field many atomic dianions
become stable.

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