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Effective Hamiltonian for doubly excited Helium states based on four dimensional Harmonic Oscillator

Effective Hamiltonians for doubly excited Heliums states based on approximate O(4) symmetry are revised. New quantum numbers for a 4D Harmonic Oscillator are assigned to Helium states with both electrons in the n=2 shell. An effective Hamiltonian operator is constructed and optimzed by means of non-linear least-square fits to the energy levels of the Helium isoelectronic series. The results are interpreted in terms of electron correlation and a possible unified description of two-electron atom intrashell states.