The interelectronic angle in doubly excited states and the quality of approximate quantum numbers

Abstract

We present complex scaling calculations of the cosine of the interelectronic angle in doubly excited states of helium below the N = 4 threshold. Since it is directly connected to one of the approximate quantum numbers commonly used to classify doubly excited states, an analysis of this expectation value will give information about the quality of this quantum number. Deviations from the predicted value already occur in the lowest manifold of resonances and are interpreted as a mixture of different basis states. This assertion is tested by a direct doubly excited symmetry basis expansion. Two types of mixing are observed; mixing of basis states to form Rydberg series and mixing of Rydberg series converging to the same threshold. As a possible origin of the basis state mixing which affects the Rydberg series as a whole, avoided crossings in the variation of the resonance energies with respect to the nuclear charge Z are discussed. Mixing between Rydberg series is due to close degeneracies in the resonance energies and connected with avoided crossings in the quantum defect. Both types can easily be distinguished by regarding real and imaginary parts of the complex expectation value.