Critical point,singularities and extrapolations in the helium iso-electronic sequence

The Z-expansion of two-electron systems is analyzed with the Padé technique with emphasis on establishing analytical properties of the function E(Z) formally associated with the power series expansion. The concept of critical point in this connection is stressed. For this sequence it occurs at Z_c = 0.911246 with E(Z_c) = ?0.415184. The structure of E(Z) for Z < Z_c is investigated. The use of Padé approximants to extrapolate values of electron affinities is emphasized.