Triaxial PowerPoint Presentation

Triaxial PowerPoint Presentation

2016-05-09 32K 32 0 0

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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. ID: 311950

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Presentations text content in Triaxial

Slide1

Triaxial Projected Configuration Mixing

Collective wave functions?

Old results on

Zr

Few results on

24

Mg

Many

questions

Slide2

First

triaxial

calculations:

P.

Bonche

, H.

Flocard

, J. Meyer

J.

Dobaczewski

, J.

Skalski

New developments:

M. Bender

Slide3

Configuration MixingStarting point: set of Wa wave functions |a >, non-orthogonal:

New set of wave functions:

The

u

nknown

f

m

(a)

are solutions of the HW equation:

Slide4

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!

Slide5

First,

diagonalisation of the overlap I:

And then

Last summation restricted to a limited number of eigenvalues

It is this equation that is solved!

Slide6

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?

Slide7

Slide8

Slide9

Slide10

Slide11

Projection of triaxial map:

Triaxial minimum?

lost of the meaning of

q

after projection!

no orthogonality of

wave functions!

Slide12

z=symmetry axis

the maps for the other

orientations have no

simple

interpretations

Slide13

Q=125 fm

2, g = 16°(mean-field configuration)

z= longest intermediate smallest axis

Spectra obtained after projection of the lowest configuration:

three possible orientations

Same results AFTER K-mixing

Slide14

Spectroscopic properties of the min configuration

before and after K-mixing

compared to the Davidoff rotor model

Slide15

Configuration mixing:comparison between different bases:purely prolateaxialpurely 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.

Slide16

Small eigenvalues of the norm kernel indicate redundancy in a basis

small eigenvalues (10

-2

) = not much information

Slide17

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,

g

plane: and GCM calculations

Slide18

increase of energy for excited states

due to the correlations in the ground state!

Spectra in 3 bases

No vectors in common!

Slide19

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?

Slide20

Slide21

Slide22


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