1. Triaxial Projected Configuration Mixing 1.Collective wave functions? 2.Old results on Zr 3.Few results on 24 Mg 4.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    wave functions |  >, non-orthogonal: New set of wave functions: The unknown f   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?

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

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

13. Q=125 fm 2,   mean-field configuration) z= longest intermediate smallest axis Spectra obtained after projection of the lowest configuration: three possible orientations Same results AFTER K-mixing

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

15. Configuration mixing: comparison between different bases: 1.purely prolate 2.axial 3.purely triaxial 4.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.

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

17. 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! Cut in the Q,  plane: and GCM calculations

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

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