The present theory is concerned with the boundhyphen;state components of autoionizing states. The bound and quasibound states of a twohyphen;electron system of a given symmetry type were grouped into clusters, and a wavefunction's natural eigenvalues (NEV's) were defined. The theory was used to show that thenth NEV of every approximate wavefunction can be made to yield an upper bound to the energy of any state in thenth cluster. The arguments for a twohyphen;electron system are extendable to an arbitrary manyhyphen;electron system. Configurationhyphen;interaction (CI) results for several autoionizing states of anShyphen;function helium atom were presented, and upper bounds to several autoionizinghyphen;state energies were obtained. The rather complicated structure of autoionizinghyphen;state CI roots was shown to result from the intersection of rather simple curves for the autoionizing states with CI roots belonging to states of lower clusters. The intersections are nonphysical and occur because an incomplete set of basis functions was used in the CI calculation.
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