Abstract
Recent studies [1] of the valence proton-neutron interaction through certain double differences of binding energies suggest that Nilsson orbitals with ΔK[ΔNΔn_zΔΛ] = 0[110] are responsible for large overlaps of wave functions in heavy deformed nuclei. We show that pairs of orbitals of this kind belong to neighboring irreducible representations of appropriate deformed U(3) algebras [2], being interconnected by deformed creation and annihilation operators. These deformed U(3) algebras correspond to oscillators with rational ratios of frequencies, which are examples of quantum superintegrable systems [3].
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