giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

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Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities S-DALINAC TU DARMSTADT Motivation Experimental data Fluctuation analysis Discrete wavelet transform and determination of background Results and test of models Summary and outlook Y. Kalmykov, K. Langanke, G. Martínez-Pinedo, P. von Neumann-Cosel, C. Özen, A. R. S-DALINAC / iThemba LABS / RCNP / KVI Supported by the SFB 634 of the Deutsche Forschungsgemeinschaft 2007

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2007. TU DARMSTADT. S-DALINAC. Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities. Motivation. Experimental data. Fluctuation analysis. Discrete wavelet transform and determination of background. Results and test of models. Summary and outlook. - PowerPoint PPT Presentation

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Page 1: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Giant resonances, fine structure, waveletsand

spin- and parity-resolved level densities

S-DALINAC

TU DARMSTADT

Motivation

Experimental data

Fluctuation analysis

Discrete wavelet transform and determination of background

Results and test of models

Summary and outlook

Y. Kalmykov, K. Langanke, G. Martínez-Pinedo, P. von Neumann-Cosel, C. Özen, A. R.

S-DALINAC / iThemba LABS / RCNP / KVI Supported by the SFB 634 of the Deutsche Forschungsgemeinschaft

2007

Page 2: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Level densities: Recent results

Back-shifted Fermi gas model* semiempirical approach, shell and pairing effects

***** T. Rauscher, F.-K. Thielemann, and K.-L. Kratz, Phys. Rev. C56 (1997) 1613

***** T. von Egidy and D. Bucurescu, Phys. Rev. C72 (2005) 044311; Phys. Rev. C73 (2006) 049901(E)

***** P. Demetriou and S. Goriely, Nucl. Phys. A695 (2001) 95

***** P. Leboeuf and J. Roccia, Phys. Rev. Lett. 97 (2006) 010401

Many-body density of states** two-component Fermi gas, shell effects, deformations, periodic orbits

HF-BCS*** microscopic statistical model, MSk7 force, shell effects, pairing correlations,

deformation effects, collective excitations

Page 3: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Level densities: Recent results

HFB* microscopic combinatorial model, MSk13 force, shell effects,

pairing correlations, deformation effects, collective excitations

Monte-Carlo shell model*** microscopic model, large model space, pairing+quadrupole force

***** C. Özen, K. Langanke, G. Martinez-Pinedo, and D.J. Dean, nucl-th/0703084 (2007)

***** S. Hilaire and S. Goriely, Nucl. Phys. A779 (2006) 63

Large-scale prediction of the parity distribution in the level density** macroscopic-microscopic approach, deformed Wood-Saxon potential, BCS occupation numbers, back-shifted Fermi Gas model

***** D. Mocelj et al., Phys. Rev. C75 (2007) 045805

Page 4: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Monte-Carlo shell model predictions: pf + g9/2 shell

** Y. Alhassid, G.F. Bertsch, S. Liu, and H. Nakada, Phys. Rev. Lett. 84 (2000) 4313

Total level density (not spin projected) shows strong parity dependence*

small

- important at low energies

29gpf

** S.J. Lokitz, G.E.Mitchell, and J.F. Shriner, Jr., Phys. Rev. C71 (2005) 064315

Questioned by recent experiments (45Sc)**

Page 5: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Fine structure of the spin-flip GTR: A = 90

Selective excitation of 1+ states

Y. Kalmykov et al., Phys. Rev. Lett. 96 (2006) 012502

Page 6: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Fine structure of the ISGQR: A = 90

Selective excitation of 2+ states

A. Shevchenko et al., Phys. Rev. Lett. 93 (2004) 122501

Page 7: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Fine structure of the M2 resonance: A = 90

Selective excitation of 2- states

P. von Neumann-Cosel et al., Phys. Rev. Lett. 82 (1999) 1105

Page 8: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Summary of experiments

58Ni(3He,t)58Cu

J = 1+

58Ni(e,e´)

J = 2-

58Ni(p,p´)

J = 2+

A = 58

90Zr(3He,t)90Nb

J = 1+

90Zr(e,e´)

J = 2-

90Zr(p,p´)

J = 2+

A = 90

Page 9: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Experimental techniques

Selectivityhadron scattering at extremely forward angles and intermediate energieselectron scattering at 180° and low momentum transfers

High resolution lateral and angular dispersion matching faint beam method*

Background discrete wavelet transform***

Level density fluctuation analysis**

*** H. Fujita et al., Nucl. Instr. and Meth. A484 (2002) 17

**** Y. Kalmykov et al., Phys. Rev. Lett. 96 (2006) 012502

**** P.G. Hansen, B. Jonson, and A. Richter, Nucl. Phys. A518 (1990) 13

Page 10: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Fluctuations and level densities

D / D Wigner

I / I Porter-Thomas

< D

< D < E

Page 11: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Fluctuation analysis

Background

Statistics, local features

Local fluctuations

Autocorrelation function

Page 12: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Autocorrelation function and mean level spacing

variance

2

22

10X

XX

Ed

EdEdC

level spacing D

,

21 f

DC

resolution

PTW selectivity

autocorrelation function

XX

XX

EdEd

EdEdC

S. Müller, F. Beck, D. Meuer, and A. Richter, Phys. Lett. 113B (1982) 362

P.G. Hansen, B. Jonson, and A. Richter, Nucl. Phys. A518 (1990) 13

Page 13: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

How to determine the background in the spectra?

Page 14: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Wavelets and wavelet transform

finite support (square integrable)

dEE2

*

wavelet coefficients

dE

EEE

EE

EEC XX

*1

,

wavelet 0*

dEE

Page 15: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Wavelet analysis

Page 16: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Wavelet analysis

Page 17: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Wavelet analysis

Page 18: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Wavelet analysis

Page 19: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Discrete wavelet transform

wavelet coefficients

dE

EEE

EE

EEC XX

*1

,

Discrete wavelet transform* E = 2j and EX = k·E with j, k = 1,2,3, …

exact reconstruction is possible is fast

http://www.mathworks.com/products/wavelet/

vanishing moments

this defines the shape and magnitude of the background

11,0,0* mndEE

EEE Xn

Page 20: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Decomposition of spectra

A1 D1

D2A2

Lowpass FilterL

Lowpass FilterL

Highpass FilterH

Highpass FilterH

(E)

(E) = A1 + D1

Background

(E) = A2 + D2 + D1

Page 21: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Application: Decomposition of 90Zr(3He,t)90Nb spectrum

Page 22: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Fluctuation analysis

Background

Statistics, local features

Local fluctuations

Autocorrelation function

fromwavelet analysis

Page 23: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Angular distribution: 90Zr(3He,t)90Nb

The requirement of a constant level density in all spectra is a constraint in the analysis

Page 24: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Results and model predictions: A = 90, J = 1+

Y. Kalmykov et al., Phys. Rev. Lett. 96 (2006) 012502

Page 25: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Results and model predictions: A = 58, J = 2+

Page 26: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Phenomenological and microscopic models

BSFG, MB DOS parameters fitted to experimental data no distinction of parity

Different quality of model predictions

HF-BCS microscopic no distinction of parity

HFB, SMMC fully microscopic calculation of levels with spin and parity

HFB fine structure of level densities

Page 27: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Ingredients of HFB

Nuclear structure: HFB calculation with a conventional Skyrme force single particle energies pairing strength for each level quadrupole deformation parameter deformation energy

Collective effects rotational enhancement vibrational enhancement disappearance of deformation at high energies

Page 28: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Ingredients of SMMC

Partition function of many-body states with good J

Expectation values at inverse temperature = 1/kT

Level density from inverse Laplace transform in the saddle-point approximation

J

JE

J Z

EEeEdE

ddE

eE

J

ZE

J

JJ

2

ln

HJJ eZ

,Tr

Page 29: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Fine structure of level density: A = 90, J = 1+

Page 30: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Fine structure of level density: A = 58, J = 2+

Both for A = 90 and A = 58 level densities at this Ex seem not to be a smooth function

Page 31: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Level density of 2+ and 2- states: 90Zr

Page 32: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Level density of 2+ and 2- states: 58Ni

Page 33: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Problem

58Ni: strong parity dependence: - << +

HFB and SMMC

90Zr: weak parity dependence: - ≈ +

Test of parity dependence of level densities

Experiments: no parity dependence

Page 34: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Equilibration of parity-projected level densities

58Ni

- ≈ + at Ex ≈ 20 MeV

90Zr

- ≈ + at Ex ≈ 5 – 10 MeV

Core breaking e.g. near shell closure 58Ni sd-pf transitions are important

- would be enlarged

Two energy scales which determine -/+ pair-breaking

5 – 6 MeV for intermediate mass nuclei shell gap between opposite-parity states near the Fermi level

depends strongly on the shell structure, e.g. 68Zn pf-g9/2 is small

Page 35: Giant resonances, fine structure, wavelets and spin- and parity-resolved level densities

Summary and outlook

Wavelet analysis for a nearly model-independent background determination

Fluctuation analysis

Indication for fine structure of level densities at high excitation energies

Spin- and parity-resolved level densities in 58Ni, 90Zr, 90Nb

Fine structure of giant resonances

Further applications to GTR, IVGDR, ISGQR … in a wide range of nuclei

Comparison with current nuclear structure model predictions

No parity dependence for J = 2 in 58Ni and 90Zr