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Triaxial Projected Configuration Mixing

Triaxial Projected Configuration Mixing. Collective wave functions? Old results on Zr Few results on 24 Mg Many questions. First triaxial calculations: P. Bonche , H. Flocard , J. Meyer J. Dobaczewski , J. Skalski New developments: M. Bender.

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Triaxial Projected Configuration Mixing

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  1. Triaxial Projected Configuration Mixing Collective wave functions? Old results on Zr Few results on 24Mg Many questions

  2. First triaxial calculations: P. Bonche, H. Flocard, J. Meyer J. Dobaczewski, J. Skalski New developments: M. Bender

  3. Configuration Mixing Starting point: set of Wawave functions |a >, non-orthogonal: New set of wave functions: The unknown fm(a) are solutions of the HW equation:

  4. The f’s are non orthogonal, ill-behaved, …. Change of basis, using the overlap matrix, defining its square root: Very nice but not used directly!

  5. First, diagonalisation of the overlap I: And then Last summation restricted to a limited number of eigenvalues It is this equation that is solved!

  6. The collective wave function is And the eigenstates of the Hamiltonian is: Neither g nor f are the overlap Meaning of oblate, prolate, triaxial …. after configuration mixing?

  7. Projection of triaxial map: Triaxial minimum? lost of the meaning of q after projection! no orthogonality of wave functions!

  8. z=symmetry axis the maps for the other orientations have no simple interpretations

  9. Spectra obtained after projection of the lowest configuration: three possible orientations z= longest intermediate smallest axis Q=125 fm2, g = 16° (mean-field configuration) Same results AFTER K-mixing

  10. Spectroscopic properties of the min configuration before and after K-mixing compared to the Davidoff rotor model

  11. Configuration mixing: • comparison between different bases: • purely prolate • axial • purely triaxial • triaxial + a few prolate configurations We are not using a hamiltonian but a density functional generalized for non-diagonal matrix elements One must avoid pathologies: possible problems determined by projecting on N and Z with 9 and 29 points Triaxial region close to the oblate axis. No oblate points mixed with triaxial points.

  12. Small eigenvalues of the norm kernel indicate redundancy in a basis small eigenvalues (10-2) = not much information

  13. Cut in the Q,g plane: and GCM calculations All the GCM calculations: axial (prolate+oblate) purely triaxial (35 keV lower than axial) triaxial + prolate (160 keV lower than triaxial) Triaxial correlations described by configuration mixing of axial configurations!

  14. Spectra in 3 bases No vectors in common! increase of energy for excited states due to the correlations in the ground state!

  15. Very careful about language: « the nucleus is triaxial after projection on J » ! Analysis of phenomenological models (clever but with the hands) Sign of triaxialityor K-bands?

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