3 research outputs found
Nonlinear collective nuclear motion
For each real number a Lie algebra of nonlinear vector fields on
three dimensional Euclidean space is reported. Although each algebra is
mathematically isomorphic to , only the vector
fields correspond to the usual generators of the general linear group. The
vector fields integrate to a nonstandard action of the general
linear group; the case integrates to a local Lie semigroup. For
each , a family of surfaces is identified that is invariant with
respect to the group or semigroup action. For positive the surfaces
describe fissioning nuclei with a neck, while negative surfaces
correspond to exotic bubble nuclei. Collective models for neck and bubble
nuclei are given by irreducible unitary representations of a fifteen
dimensional semidirect sum spectrum generating algebra spanned by its
nonlinear subalgebra plus an abelian nonlinear inertia tensor
subalgebra.Comment: 13 pages plus two figures(available by fax from authors by request