dorsal/arxiv
View SchemaNonlinear collective nuclear motion
| Authors | G. Rosensteel, J. Troupe |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9801040 |
| URL | https://arxiv.org/abs/nucl-th/9801040 |
| DOI | 10.1088/0954-3899/25/3/007 |
Abstract
For each real number $\Lambda$ a Lie algebra of nonlinear vector fields on three dimensional Euclidean space is reported. Although each algebra is mathematically isomorphic to $gl(3,{\bf R})$, only the $\Lambda=0$ vector fields correspond to the usual generators of the general linear group. The $\Lambda < 0$ vector fields integrate to a nonstandard action of the general linear group; the $\Lambda >0$ case integrates to a local Lie semigroup. For each $\Lambda$, a family of surfaces is identified that is invariant with respect to the group or semigroup action. For positive $\Lambda$ the surfaces describe fissioning nuclei with a neck, while negative $\Lambda$ 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 $gcm(3)$ spanned by its nonlinear $gl(3,{\bf R})$ subalgebra plus an abelian nonlinear inertia tensor subalgebra.
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"abstract": "For each real number $\\Lambda$ a Lie algebra of nonlinear vector fields on\nthree dimensional Euclidean space is reported. Although each algebra is\nmathematically isomorphic to $gl(3,{\\bf R})$, only the $\\Lambda=0$ vector\nfields correspond to the usual generators of the general linear group. The\n$\\Lambda \u003c 0$ vector fields integrate to a nonstandard action of the general\nlinear group; the $\\Lambda \u003e0$ case integrates to a local Lie semigroup. For\neach $\\Lambda$, a family of surfaces is identified that is invariant with\nrespect to the group or semigroup action. For positive $\\Lambda$ the surfaces\ndescribe fissioning nuclei with a neck, while negative $\\Lambda$ surfaces\ncorrespond to exotic bubble nuclei. Collective models for neck and bubble\nnuclei are given by irreducible unitary representations of a fifteen\ndimensional semidirect sum spectrum generating algebra $gcm(3)$ spanned by its\nnonlinear $gl(3,{\\bf R})$ subalgebra plus an abelian nonlinear inertia tensor\nsubalgebra.",
"arxiv_id": "nucl-th/9801040",
"authors": [
"G. Rosensteel",
"J. Troupe"
],
"categories": [
"nucl-th"
],
"doi": "10.1088/0954-3899/25/3/007",
"title": "Nonlinear collective nuclear motion",
"url": "https://arxiv.org/abs/nucl-th/9801040"
},
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