Helium wave functions from distinguishable electron model

The property of solutions to a hypothetical distinguishable electron model (DEM) is discussed, which separates a two-electron atomic equation into a set of two one-electron equations, one for the fast (inner-orbital) electron and the other for the slow (outer-orbital) electron. The former equation includes the slow electron coordinate parametrically and its energy provides an effective potential for the motion of the slow electron. The DEM solutions are not acceptable directly for lower electronic states, but its concept can be used to construct simple correlated trial wave functions for two-electron atoms. Some numerical results are shown for the ground and low-lying excited states of the helium atom