1 / 4

Geometric model

Geometric model. A Bohr, 1952, ..................... G Gneuss, W Greiner 1971,. quadrupole tensor of collective coordinates (2 shape param’s, 3 Euler angles ). …corresponding tensor of momenta. neglect higher-order terms. neglect …. Potential energy :. Shape “phases”. B. oblate.

adam-williamson
Download Presentation

Geometric model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometric model A Bohr, 1952, ..................... G Gneuss, W Greiner 1971, .... quadrupole tensor of collective coordinates (2 shape param’s, 3 Euler angles ) …corresponding tensor of momenta neglect higher-order terms neglect … Potential energy: Shape “phases” B oblate spherical depends on 2 internal shape variables y prolate Cartesian polar A x Motion in the xy-plane represents evolution of nuclear shape in the principal axis system (PAS). See e.g.: JM Eisenberg, W Greiner: Nuclear Theory, vol.1 (North Holland, Amsterdam, 1970).

  2. Scaling properties 3 independent scales Energy Time Coordinates 4 external parameters => only 1 essential parameter arbitrary choice: (a) A=variable, B,C,K=1 (b) B=variable, A= –1, C,K=1 A=+1, C,K=1 (c) C=variable, A= –1, B,K=1 A=+1, B,K=1 (a) Dynamically equivalent classes determined by the dimensionless parameter (b+) (b–) In the quantum case, energy & time scales connected by the Planck constant =>2 essential parameters

  3. Angular momentum 5D system Principal Axes System Special case: 2D system Dynamics is fully determined by 2 coordinates and the associated 2 momenta

  4. Quantum dynamics Now only the restricted case: J=0 2 physically important quantization options (b) 5D system restricted to 2D (true geometric model of nuclei) (a) 2D system with an additional ansatz on the angular wave function (to avoid quasi-degeneracies due to the three-fold symmetry of V ) Although both options have the same classical limit, they yield different quantum spectra...

More Related