SOME GENERAL CONSTRAINTS ON IDENTICAL BAND SYMMETRIES

We argue on general grounds that nearly identical bands observed for s uperdeformation and less frequently for normal deformation must be exp licable in terms of a symmetry having a microscopic basis. We assume t hat the unknown symmetry is associated with a Lie algebra generated by terms bilinear in fermion creation and annihilation operators. Observ ed features of these bands and the general properties of Lie groups ar e then used to place constraints on acceptable algebras. Additional co nstraints are placed by assuming that the collective spectrum is assoc iated with a dynamical symmetry, and examining the subgroup structure required by phenomenology. We observe that requisite symmetry cannot b e unitary, and that the simplest known group structures consistent wit h these minimal criteria are associated with the Ginocchio algebras em ployed in the fermion dynamical symmetry model. However, our arguments are general in nature, and we propose that they imply model-independe nt constraints on any candidate explanation for identical bands.