THE INTERELECTRONIC ANGLE IN DOUBLY-EXCITED STATES AND THE QUALITY OFAPPROXIMATE QUANTUM NUMBERS

We present complex scaling calculations of the cosine of the interelec tronic angle in doubly excited S-1(e) states of helium below the N = 4 threshold. Since it is directly connected to one of the approximate q uantum numbers commonly used to classify doubly excited states, an ana lysis of this expectation value will give information about the qualit y of this quantum number. Deviations from the predicted value already occur in the lowest manifold of resonances and are interpreted as a mi xture of different basis states. This assertion is tested by a direct doubly excited symmetry basis expansion. Two types of mixing are obser ved; mixing of basis states to form Rydberg series and mixing of Rydbe rg series converging to the same threshold. As a possible origin of th e basis state mixing which affects the Rydberg series as a whole, avoi ded crossings in the variation of the resonance energies with respect to the nuclear charge Z are discussed. Mixing between Rydberg series i s due to close degeneracies in the resonance energies and connected wi th avoided crossings in the quantum defect. Both types can easily be d istinguished by regarding real and imaginary parts of the complex expe ctation value.