Equal-factors method for solutions of the extended Schroedinger equation for (Zns)2 states of heliumlike ions

An approximate method using iterative techniques developed for solving the extended Schroedinger equation is applied to principles of the first and second kind of balance theory and an example for (Zns)2 heliumlike ions is presented. The implementation of the equal-factors method presented here, which leads to a series of self-consistent equations, has advantages that provide the results for an entire series of energy levels and an entire isoelectronic sequence in a single calculation. Results for all two-electron ions for the ground-state energies for Z=1 to 10 are tabulated and compared with other results for these systems. Theoretical predictions of energy levels for (Z2s)2 to (Z11s)2, excited autoionizing states of heliumlike ions with Z=1,10, are tabulated as well. copyright 1996 The American Physical Society