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Level Densities and Gamma Strength Functions from the Fine Structure of Giant Resonances
S-DALINAC
TU DARMSTADT
Spin- and parity-resolved level densities
* Supported by DFG under contracts SFB 634, 446-JAP-113/0/2, and NE 679/2-2
Polarized proton scattering as tool to extract complete E1/M1 strength functions
Peter von Neumann-Cosel
Institut für Kernphysik, Technische Universität Darmstadt
Monte-Carlo Shell Model Predictions
* 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
S.J. Lokitz, G.E.Mitchell, and J.F. Shriner, Jr., Phys. Rev. C71 (2005) 064315
Questioned by recent experiments (45Sc)
Requirements and Techniques
Selectivity - hadron scattering at extremely forward angles and intermediate energies
- electron scattering at 180° and low momentum transfers
High resolution - lateral and angular dispersion matching
- faint beam method
Discrete wavelet transform - background
Fluctuation analysis - level density
Example: Spinflip Gamow-Teller Resonance in 90Nb
Selective excitation of 1+ states
Y. Kalmykov et al., Phys. Rev. Lett. 96 (2006) 012502
Fluctuations and Level Densities
D / D Wigner
I / I Porter-Thomas
< D
< D < E
Fluctuation Analysis
Background
Statistics, local features
Local fluctuations
Autocorrelation function
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
Wavelets and Wavelet Transform
finite support (square integrable)
dEE2
*
wavelet coefficients
dE
EEE
EE
EEC XX
*1
,
wavelet 0*
dEE
Discrete Wavelet Transform (DWT)
wavelet coefficients
dE
EEE
EE
EEC XX
*1
,
DWT: E = 2j and Ex = k·E with j, k = 1,2,3, … exact reconstruction
vanishing moments
this defines the shape and magnitude of the background
11,0,0* mndEE
EEE Xn
Decomposition of Spectra
A1 D1
D2A2
Lowpass FilterL
Lowpass FilterL
Highpass FilterH
Highpass FilterH
(E)
(E) = A1 + D1
Background
(E) = A2 + D2 + D1
Application to the 90Zr(3He,t)90Nb spectrum
Fluctuation analysis
Background
Statistics, local features
Local fluctuations
Autocorrelation function
fromwavelet analysis
Level Density Models
Back-shifted Fermi gas model - semiempirical approach, shell and pairing effects - no distinction of parity
**** 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
HF-BCS - microscopic statistical model, MSk7 force, shell effects, pairing correlations, deformation effects, collective excitations - no distinction of parity
Many-body density of states (MBDOS) - two-component Fermi gas, shell effects, deformations, periodic orbits - no distinction of parity
Level Density Models
HFB - microscopic combinatorial model, MSk13 force, shell effects, pairing correlations, deformation effects, collective excitations - parity distinction - fluctuations with energy
Monte-Carlo shell model - microscopic model, large model space, pairing+quadrupole force - parity distinction
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 - parity distinction
D. Mocelj et al., Phys. Rev. C75 (2007) 045805
Results and Model Predictions: 90Nb, J = 1+
Y. Kalmykov et al., Phys. Rev. Lett. 96 (2006) 012502
Fine Structure of the ISGQR
Selective excitation of 2+ states
A. Shevchenko et al., Phys. Rev. Lett. 93 (2004) 122501
Fine Structure of the M2 Resonance
Selective excitation of 2- states
P. von Neumann-Cosel et al., Phys. Rev. Lett. 82 (1999) 1105
Level density of 2+ and 2- states: 90Zr
Level density of 2+ and 2- states: 58Ni
Test of Parity Dependence
Y. Kalmykov, C. Özen, K. Langanke, G. Martinez-Pinedo, P. von Neumann-Cosel, and A. Richter, Phys. Rev. Lett. 99 (2007) 202502
Equilibration of Parity-Projected Level Densities
Experiment: no parity dependence for Ex > 8 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
Models: 90Zr ρ- ≈ ρ+ at Ex ≈ 5 – 10 MeV
but 58Ni ρ- ≈ ρ+ at Ex ≈ 20 MeV
Summary and Outlook: Level Densities
Largely model-independent extraction from the spectra with the aid of a fluctuation analysis combined with a discrete wavelet analysis
Indication for fine structure of level densities at high excitation energies
Fine structure of giant resonances contains information on level densities of a given spin and parity
Further applications to GTR, IVGDR, ISGQR, M1, M2, … resonances in a wide range of nuclei
No experimental parity dependence for J = 2 states in 58Ni and 90Zr in contrast (for 58Ni) to current microscopic model calculations
Soft Dipole Modes and the Gamma Strength Function
Modeling requires knowledge of the salient features of these modes and an understanding of the underlying structure
Gamma strength function at low excitation energies is determined by soft dipole modes: PDR, M1 scissors mode, spin-M1 resonance …
PDR: current topic of research, many open questions
For the scissors mode this has been achieved in the last 25 years J. Enders, P. von Neumann-Cosel, C. Rangacharyulu, and A. Richter, Phys. Rev. C 71 (2005) 014306 K. Heyde, P. von Neumann-Cosel, and A. Richter, Rev. Mod. Phys., in preparation
Spin M1-resonance: few data in heavy nuclei, quenching?
New experimental approach: intermediate-energy polarized proton scattering
Reminder: The Pygmy Dipole Resonance in 208Pb
N. Ryezayeva et al., Phys. Rev. Lett. 89 (2002) 272502
E1 Response in 208Pb
Excellent agreement of QPM with experiment
?
Transition Densities
Toroidal GDR
Ex > 10.5 MeVEx = 6.5 – 10.5 MeV
Velocity Distributions
Spinflip M1 Resonance in 208Pb
R.M. Laszewski et al., Phys. Rev. Lett. 61 (1988) 1710
?Quenching ?
Low-Energy Dipole Modes
How can we elucidate the properties and structure of these low-energy dipole modes?
polarized proton scattering at 0o
intermediate energy (300 MeV optimal)
high resolution
angular distribution E1 / M1 separation
polarization observables spinflip / non-spinflip separation
0o Setup at RCNP
Background-Subtracted Spectrum
ΔE = 25 keV (FWHM)
Spectrum (Expanded)
Angular Distributions
Coulomb excitation dominant
B(E1) Strength
Status and Outlook
Intermediate-energy polarized proton scattering under 0o as a
tool to study E1 and spin-M1 strength distributions
High-resolution study of 208Pb as a reference case
E1/M1 decomposition under way
Complete measurement of spin-flip observables
Collaborations
Proton scattering
TU Darmstadt / RCNP Osaka / U Osaka / iThemba LABS / U Witwatersrand
T. Adachi, J. Carter, H. Fujita, Y. Fujita, K. Hatanaka, Y. Kalmykov, M. Kato, H. Matsubara, P. von Neumann-Cosel, H. Okamura, I. Poltoratska, V.Yu. Ponomarev, A. Richter, B. Rubio, H. Sakaguchi, Y. Sakemi, Y. Sasamoto, Y. Shimizu, F.D. Smit, Y. Tameshige, A. Tamii, J. Wambach, M. Yosoi, J. Zenihiro
Level Densities
TU Darmstadt / GSI
Y. Kalmykov, C. Özen, K. Langanke, G. Martínez-Pinedo, P. von Neumann-Cosel, A. Richter
Measured Spectrum
Signatures of Different E1 Modes in (p,p´)
Angular Distribution
Pronounced differences at small angles due to Coulomb-nuclear interference
Signatures of Different E1 Modes in (p,p´)
Asymmetry
Signature of toroidal mode in the asymmetry at small angles ?
Signatures of Low – Energy E1 modes in (e,e´)
Large difference in the momentum transfer dependence
Fine Structure of Level Density: 90Nb, J = 1+
Fine structure of Level Density: 58Ni, J = 2+
Angular Distribution: 90Zr(3He,t)90Nb
Constant level density as a constraint in the analysis
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
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
Results and Model Predictions: 58Ni, J = 2+
Wavelet analysis
Wavelet analysis
Wavelet analysis
Wavelet analysis
Polarized Proton Scattering Experiment at RCNP
HIPIS
AVF
Ring Cyclotron