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) Questioned by recent experiments ( 45 Sc)

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 90 Nb Selective excitation of 1 + states Y. Kalmykov et al., Phys. Rev. Lett. 96 (2006)

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 level spacing  D   resolution  PT  W selectivity autocorrelation function 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) wavelet coefficients wavelet

Discrete Wavelet Transform (DWT) wavelet coefficients DWT:  E = 2 j and E x = k·  E with j, k = 1,2,3, … exact reconstruction vanishing moments this defines the shape and magnitude of the background

Decomposition of Spectra  (E) = A1 + D1 Background  (E) = A2 + D2 + D1

Application to the 90 Zr( 3 He,t) 90 Nb spectrum

Fluctuation analysis Background Statistics, local features Local fluctuations Autocorrelation function from wavelet 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) ; Phys. Rev. C73 (2006) (E) P. Demetriou and S. Goriely, Nucl. Phys. A695 (2001) 95 P. Leboeuf and J. Roccia, Phys. Rev. Lett. 97 (2006) 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/ (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)

Results and Model Predictions: 90 Nb, J  = 1 + Y. Kalmykov et al., Phys. Rev. Lett. 96 (2006)

Fine Structure of the ISGQR Selective excitation of 2 + states A. Shevchenko et al., Phys. Rev. Lett. 93 (2004)

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: 90 Zr

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

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)

Equilibration of Parity-Projected Level Densities Experiment: no parity dependence for E x > 8 MeV Core breaking - e.g. near shell closure 58 Ni  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. 68 Zn  pf-g9/2 is small Models: 90 Zr ρ - ≈ ρ + at E x ≈ 5 – 10 MeV but 58 Ni ρ - ≈ ρ + at E x ≈ 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 58 Ni and 90 Zr in contrast (for 58 Ni) 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) 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 208 Pb N. Ryezayeva et al., Phys. Rev. Lett. 89 (2002)

E1 Response in 208 Pb Excellent agreement of QPM with experiment ?

Transition Densities

ToroidalGDR E x > 10.5 MeVE x = 6.5 – 10.5 MeV Velocity Distributions

Spinflip M1 Resonance in 208 Pb 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 0 o intermediate energy (300 MeV optimal) high resolution angular distribution  E1 / M1 separation polarization observables  spinflip / non-spinflip separation

0 o 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 0 o as a tool to study E1 and spin-M1 strength distributions High-resolution study of 208 Pb 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: 90 Nb, J  = 1 +

Fine structure of Level Density: 58 Ni, J  = 2 +

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

Results and Model Predictions: 58 Ni, J  = 2 +

Wavelet analysis

Polarized Proton Scattering Experiment at RCNP HIPIS AVF Ring Cyclotron