Adiabatic approximation in atomic three-body systems

We investigate the reliability of the adiabatic approximation in the hyperspherical harmonics formalism. It has been applied to a number of two-electron systems, both compact and loosely bound, with the interaction between the constituent particles being purely Coulombic. The results are compared with the exact ones obtained by solving the set of coupled differential equations numerically. The accuracy of this approximation for two-electron systems is compared with that for systems with nuclear interactions, and we find that the former is better. An explanation has been provided for better agreement with Coulombic systems, particularly for noncompact ones.