  We study atoms with N electrons, and nuclear charge Z. It is well known that
the cationic regime, Z > N is qualitatively described by Thomas-Fermi theory.
The anionic regime, Z < N, on the other hand, is characterized by an
instability threshold at Z_c <~ N-1, below which the atom spontaneously emits
an electron. We compute the slope of the energy curve at Z=N-1 by means of a
simple model that depends on the electron affinity and the covalent radius of
the neutral atom with N-1 electrons. This slope is used in order to estimate
Z_c, which is compared with previous numerical results. Extrapolation of the
linear behaviour in the opposite direction, up to Z=N, allows us to estimate
the ionization potential of the atom with N electrons. The fact that the
obtained ionization potentials are qualitatively correct is an indication that,
with regard to certain properties, neutral atoms are closer to the anionic
instability threshold than they are to the Thomas-Fermi, large Z, regime. A
regularized series is written for the ionization potential that fits both, the
large Z and Z\to Z_c regimes.
