Possible modes of angular motion in4S degrees triply excited states

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Abstract
A model where the radial freedoms are frozen is used to simulate the 4S degrees triply excited states of lithium-like atoms with all electrons in the same shell. It is confirmed by direct observation of the wavefunction that the 4S degrees states prefer the equilateral triangle configuration. However, since the coplanar structure is prohibited by the 4S degrees symmetry, the plane of this triangle does not contain the nucleus. Besides, the sharp isosceles and the flattened isosceles shapes are found to appear in higher states. Different modes of motion are found around the equilateral triangle shape, and they are coupled in a specific manner. Accordingly, different types of collisions are found, namely the three-body head-on collision, planar two-body collision, and the quasi-three-body collision. Repeated occurrence of three-body head-on collisions is a basic mode and exists in all 4S degrees states. It was shown that this mode is associated with a periodic solution of the corresponding classical mechanisms system.