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Level Densities and Gamma Strength Functions from the Fine Structure of Giant Resonances

TU DARMSTADT. S-DALINAC. Level Densities and Gamma Strength Functions from the Fine Structure of Giant Resonances. Peter von Neumann-Cosel Institut für Kernphysik, Technische Universität Darmstadt. Spin- and parity-resolved level densities. Polarized proton scattering as tool to extract

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Level Densities and Gamma Strength Functions from the Fine Structure of Giant Resonances

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  1. TU DARMSTADT S-DALINAC Level Densities and Gamma Strength Functions from the Fine Structure of Giant Resonances Peter von Neumann-Cosel Institut für Kernphysik, Technische Universität Darmstadt • Spin- and parity-resolved level densities • Polarized proton scattering as tool to extract • complete E1/M1 strength functions * Supported by DFG under contracts SFB 634, 446-JAP-113/0/2, and NE 679/2-2

  2. Monte-Carlo Shell Model Predictions • Total level density (not spin projected) shows strong parity dependence * Y. Alhassid, G.F. Bertsch, S. Liu, and H. Nakada, Phys. Rev. Lett. 84 (2000) 4313 • Questioned by recent experiments (45Sc) S.J. Lokitz, G.E.Mitchell, and J.F. Shriner, Jr., Phys. Rev. C71 (2005) 064315

  3. 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 • Fluctuation analysis • - level density • Discrete wavelet transform • - background

  4. Example: Spinflip Gamow-Teller Resonance in 90Nb • Selective excitation of 1+ states Y. Kalmykov et al., Phys. Rev. Lett. 96 (2006) 012502

  5. Fluctuations and Level Densities • D/D Wigner • I/I Porter-Thomas • G < D • G < D < DE

  6. Fluctuation Analysis • Background • Statistics, • local features • Local • fluctuations • Autocorrelation • function

  7. Autocorrelation Function and Mean Level Spacing • autocorrelation function • variance • level spacing D • a = aPT + aW selectivity • s resolution 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

  8. Wavelets and Wavelet Transform • wavelet • finite support (square integrable) • wavelet coefficients

  9. Discrete Wavelet Transform (DWT) • wavelet coefficients • DWT: dE= 2jandEx = k·dE with j, k = 1,2,3, … exact reconstruction • vanishing moments • this defines the shape and magnitude of the background

  10. Decomposition of Spectra s(E) = A1 + D1 s(E) = A2 + D2+ D1 Background

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

  12. Fluctuation analysis • Background from wavelet analysis • Statistics, • local features • Local • fluctuations • Autocorrelation • function

  13. 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) • Many-body density of states (MBDOS) • - two-component Fermi gas, shell effects, deformations, periodic orbits • - no distinction of parity 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 P. Demetriou and S. Goriely, Nucl. Phys. A695 (2001) 95

  14. Level Density Models • HFB • - microscopic combinatorial model, MSk13 force, shell effects, pairing correlations, • deformation effects, collective excitations • - parity distinction • - fluctuations with energy 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 • 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)

  15. Results and Model Predictions: 90Nb, Jp = 1+ Y. Kalmykov et al., Phys. Rev. Lett. 96 (2006) 012502

  16. Fine Structure of the ISGQR • Selective excitation of 2+ states A. Shevchenko et al., Phys. Rev. Lett. 93 (2004) 122501

  17. Fine Structure of the M2 Resonance • Selective excitation of 2- states P. von Neumann-Cosel et al., Phys. Rev. Lett. 82 (1999) 1105

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

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

  20. 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

  21. Equilibration of Parity-Projected Level Densities • Experiment: no parity dependence for Ex > 8 MeV • Models: 90Zr ρ-≈ ρ+at Ex ≈ 5 – 10 MeV • but 58Ni ρ- ≈ ρ+ at Ex ≈ 20 MeV • Two energy scales which determine r-/r+ • - 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 Dpf-g9/2 is small • Core breaking • - e.g. near shell closure 58Ni Dsd-pf transitions are important r- would be enlarged

  22. Summary and Outlook: Level Densities • Fine structure of giant resonances contains information on level densities of • a given spin and parity • Largely model-independent extraction from the spectra with the aid of a • fluctuation analysis combined with a discrete wavelet analysis • No experimental parity dependence for J = 2 states in 58Ni and 90Zr in • contrast (for 58Ni) to current microscopic model calculations • Indication for fine structure of level densities at high excitation energies • Further applications to GTR, IVGDR, ISGQR, M1, M2, … resonances in a • wide range of nuclei

  23. Soft Dipole Modes and the Gamma Strength Function • Gamma strength function at low excitation energies is determined by soft • dipole modes: PDR, M1 scissors mode, spin-M1 resonance … • Modeling requires knowledge of the salient features of these modes and an • understanding of the underlying structure • 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 • PDR: current topic of research, many open questions • Spin M1-resonance: few data in heavy nuclei, quenching? • New experimental approach: intermediate-energy polarized proton scattering

  24. Reminder: The Pygmy Dipole Resonance in 208Pb N. Ryezayeva et al., Phys. Rev. Lett. 89 (2002) 272502

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

  26. Transition Densities

  27. Velocity Distributions Toroidal GDR Ex = 6.5 – 10.5 MeV Ex > 10.5 MeV

  28. Spinflip M1 Resonance in 208Pb Quenching ? ? R.M. Laszewski et al., Phys. Rev. Lett. 61 (1988) 1710

  29. 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

  30. 0o Setup at RCNP

  31. Background-Subtracted Spectrum ΔE = 25 keV (FWHM)

  32. Spectrum (Expanded)

  33. Angular Distributions • Coulomb excitation dominant

  34. B(E1) Strength

  35. Status and Outlook • Intermediate-energy polarized proton scattering under 0oas 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

  36. Collaborations • Level Densities • TU Darmstadt / GSI • Y. Kalmykov, C. Özen, K. Langanke, G. Martínez-Pinedo, P. von Neumann-Cosel,A. Richter • 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

  37. Measured Spectrum

  38. Signatures of Different E1 Modes in (p,p´) Angular Distribution • Pronounced differences at small angles due to Coulomb-nuclear interference

  39. Signatures of Different E1 Modes in (p,p´) Asymmetry • Signature of toroidal mode in the asymmetry at small angles ?

  40. Signatures of Low – Energy E1 modes in (e,e´) • Large difference in the momentum transfer dependence

  41. Fine Structure of Level Density: 90Nb, Jp = 1+

  42. Fine structure of Level Density: 58Ni, Jp = 2+

  43. Angular Distribution: 90Zr(3He,t)90Nb • Constant level density as a constraint in the analysis

  44. 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

  45. Ingredients of SMMC • Partition function of many-body states with good Jp • Expectation values at inverse temperature b = 1/kT • Level density from inverse Laplace transform in the saddle-point approximation

  46. Results and Model Predictions: 58Ni, Jp = 2+

  47. Wavelet analysis

  48. Wavelet analysis

  49. Wavelet analysis

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