Comprehensive analysis of electron correlations in three-electron atoms

Abstract

We study the electron correlations in singly, doubly, and triply excited states of a three-electron atom. While electron correlation in general is weak for singly excited states, correlation plays major roles in determining the characteristics of doubly and triply excited states. Using the adiabatic approximation in hyperspherical coordinates, we show that the distinction between singly, doubly, and triply excited states is determined by the radial correlations, while finer distinctions within doubly or triply excited states lie in the angular correlations. Partial projections of the body-fixed frame wave functions are used to demonstrate the characteristic nodal surfaces which provide clues to the energy ordering of the states. We show that doubly excited states of a three-electron atom exhibit correlations that are similar to the doubly excited states of a two-electron atom. For the triply excited states, we show that the motion of the three electrons resemble approximately that of a symmetric top.