Hyperspherical angular adiabatic separation for three-electron atomic systems

The symmetry breaking introduced by the adiabatic approximation was shown to be quite smooth and the total invariance can be recovered when few couplings were introduced, which was reflected by the doublet potential curve degeneracy. Thus, the method can be pointed out as an alternative procedure to analyze the three-electron problem using two systems of ordinary differential equations instead of solving partial differential equations. Only few couplings need to be introduced to achieve good accuracy.