ar X iv : n uc l - th / 9 80 10 40 v 1 2 0 Ja n 19 98 Nonlinear Collective Nuclear Motion
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چکیده
For each real number Λ a Lie algebra of nonlinear vector fields on three dimensional Euclidean space is reported. Although each algebra is mathematically isomorphic to gl(3, R), only the Λ = 0 vector fields correspond to the usual generators of the general linear group. The Λ < 0 vector fields integrate to a nonstandard action of the general linear group; the Λ > 0 case integrates to a local Lie semigroup. For each Λ, a family of surfaces is identified that is invariant with respect to the group or semigroup action. For positive Λ the surfaces describe fissioning nuclei with a neck, while negative Λ surfaces correspond to exotic bubble nuclei. Collective models for neck and bubble nu-clei are given by irreducible unitary representations of a fifteen dimensional semidirect sum spectrum generating algebra gcm(3) spanned by its nonlinear gl(3, R) subalgebra plus an abelian nonlinear inertia tensor subalgebra.
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تاریخ انتشار 1998