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

EdEdEdEd

C

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)

dEE 2*

wavelet coefficients

dE

EEEE

EEEC X

X

*1,

wavelet 0*

dEE

Discrete Wavelet Transform (DWT)

wavelet coefficients

dE

EEEE

EEEC X

X

*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

eEJ

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