On the estimation of the higher-order terms in the Z-1 expansion perturbation theory for the two-electron systems

Convergence behavior of the coefficients epsilonsub(n) in the Z-1 expansion has been examined for the heliumlike atoms in the ground 1S state as well as for those in the 2p23p state. The results indicated that if the effect of epsilonsub(n) (n >= 22) is amended to the analysis given by Levy et al. on the discontinuity in electrostatic potential for the two electron system, the critical charge Zsub(c) becomes to be 0.911048, which is very close to Stillinger's estimate based upon a different approach. Interrelation of the present work and similar work done by Stillinger using a different approach is discussed. It is pointed out that the fact that the present analysis gives essentially the similar results to those given by Stillinger suggests that the results obtained may be regarded as very reliable. (J.P.N.)