Properties of electron density in weak binding conditions

When electrons are bounded by a weak external potential, the electronic density becomes smaller and smaller. In this regime, electron correlation becomes increasingly important. We analyze in details few relatively simple systems for which analytical or accurate numerical calculation can be performed. In particular we consider model atoms in which electrons are confined by a positive fractional charge [2, 4, 5, 6] or by a harmonic potential [1, 3]. In the first case we study the limit of the critical nuclear charge at which spontaneous ionization occurs and in the second case the limit of the so-called Wigner regime.