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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