Analysis of hyperspherical channels of three-electron atomic systems

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Abstract
Hyperspherical coordinates are used to study three-electron atomic systems. Within the adiabatic approximation, the Schrödinger equation for the three-electron systems is reduced to a set of partial differential equations of two hyperangles at each fixed hyper-radius. We restrict ourselves in the present paper to the configurations where the orbital angular momentum of each electron is zero. The adiabatic potential curves and the associated wave functions are obtained. We identify potential curves associated with singly, doubly, and triply excited states and analyze the nodal structure of the associated wave functions with respect to the two hyperangles.