1. Athens, July 9, 2008 The two-step  cascade method as a tool for studying  -ray strength functions Milan Krtička

2. Athens, July 9, 2008 Outline  The method of two-step γ-cascades following thermal neutron capture (setup at Rez near Prague)  Data processing - DICEBOX code  Examples

3. Athens, July 9, 2008 The method of two-step γ-cascades following TNC Geometry: Data acquisition: - Energy E  1 - Energy E  2 - Detection-time difference Three-parametric, list-mode

4. Athens, July 9, 2008

5. TSC spectra Detection-time difference Time response function Spectrum of energy sums Bn-EfBn-Ef Energy sum E γ1 + E γ2 List-mode data i=-1 i=0 i=+1 j=-1 j=0 j=+1 Accumulation of the TSC spectrum from, say, detector #1: The contents of the bin, belonging to the energy E  1, is incremented by q =  ij, where  ij is given by the position and the size of the corresponding window in the 2D space “detection time”דenergy sum E  1 +E  2 ”.  background-free spectrum

6. Athens, July 9, 2008 TSC spectra Detection-time difference Time response function Spectrum of energy sums Bn-EfBn-Ef Energy sum E γ1 + E γ2 List-mode data i=-1 i=0 i=+1 j=-1 j=0 j=+1 X 5 TSC spectrum - taken from only one of the detectors

7. Athens, July 9, 2008 Example of sum-energy spectra ( 57 Fe)

8. Athens, July 9, 2008 Example of a TSC spectrum Dynamic range 1:1000

9. Athens, July 9, 2008 Example of a TSC spectrum

10. Athens, July 9, 2008 Normalization of experimental spectra  Knowing intensity of one  -ray cascade  TSC intensities to all final levels can be normalized  Corrections to angular correlation and vetoing must be done 5 % 20 %

11. Athens, July 9, 2008 How to process data from this experiment?  Result of interplay of level density and  -ray SF  Comparison with predictions from decay governed by different level density formulas and  -ray strength functions  Code DICEBOX is used for making these simulations  Simulates gamma decay of a compound nucleus within extreme statistical model

12. Athens, July 9, 2008 Simulation of  cascades - DICEBOX algorithm Main assumptions:  For nuclear levels below certain “critical energy” spin, parity and decay properties are known from experiments  Energies, spins and parities of the remaining levels are assumed to be a random discretization of an a priori known level-density formula  A partial radiation width  i  f (XL), characterizing a decay of a level i to a level f, is a random realization of a chi-square-distributed quantity the expectation value of which is equal to f (XL) (E γ ) E γ 2L+1 /  (E i ), where f (XL) and ρ are also a priori known  Selection rules governing the  decay are fully observed  Any pair of partial radiation widths  i  f (XL) is statistically uncorrelated

13. Athens, July 9, 2008 Modelling within ESM Outcomes from modelling are compared with experimental data Deterministic character of random number generators is exploited Simulation of the decay:  “nuclear realization” (10 6 levels  10 12   f )  “precursors” are introduced  fluctuations originating from nuclear realizations cannot be suppressed

14. Athens, July 9, 2008 Main feature of DICEBOX  There exists infinite number of artificial nuclei (nuclear realizations), obtained with the same set of level density and  -ray SFs models that differ in exact number of levels and intensities of transitions between each pair of them  leads to different predictions from different nuclear realizations  DICEBOX allows us to treat predictions from different nuclear realizations  The size of fluctuations from different nuclear realizations depend on the (observable) quantity - in our case intensity of TSC cascades - and nucleus  Due to fluctuations only “integral” quantities can be compared  Simulation of detector response must be applied

15. Athens, July 9, 2008 Results of GEANT3 simulations - 95 Mo(n,  ) 96 Mo

16. Athens, July 9, 2008 Example of a TSC spectrum Wide-bin TSC spectra  E  = 2 MeV Integrated TSC spectra

17. Athens, July 9, 2008 Examples of spectra ( 96 Mo) Integrated TSC Simulation Experiment

18. Athens, July 9, 2008 Some features of TSC spectra (1) 100 nuclear realizations Problems with presentation of results distribution of values from 1400 nuclear realizations 2235 keV

19. Athens, July 9, 2008 Some features of TSC spectra (2)

20. Athens, July 9, 2008 And some results

21. Athens, July 9, 2008 TSCs in the 162Dy(n,γ)163Dy reaction Entire absence of SRs is assumed DICEBOX Simulations Řež experimental data π f = - π f = + 1/2 + M1 E1

22. Athens, July 9, 2008 TSCs in the 162Dy(n,γ)163Dy reaction A “pygmy E1 resonance” with energy of 3 MeV assumed to be built on all levels

23. Athens, July 9, 2008 TSCs in the 162Dy(n,γ)163Dy reaction SRs assumed to be built only on all levels below 2.5 MeV

24. Athens, July 9, 2008 TSCs in the 162Dy(n,γ)163Dy reaction Scissors resonances assumed to be built on all 163 Dy levels

25. Athens, July 9, 2008 163 Dy: models for photon strength function used  -ray strength functions plotted refer to the  transitions to the ground state of 163 Dy KMF+BA SR SF EGLO f(E ,T=0) (MeV -3 ) The role of E1 transitions to or from the ground state is reduced

26. Athens, July 9, 2008 TSCs in the 167 Er(n,γ) 168 Er reaction Entire absence of scissors resonances is assumed

27. Athens, July 9, 2008 TSCs in the 167 Er(n,γ) 168 Er reaction Scissors resonances assumed to be built on all 168 Er levels

28. Athens, July 9, 2008 Enhanced PSF at low energies - 96 Mo

29. Athens, July 9, 2008 Enhanced PSF at low energies - 96 Mo

30. Athens, July 9, 2008 Enhanced PSF at low energies - 96 Mo

31. Athens, July 9, 2008 Enhanced PSF at low energies - 96 Mo Pictures with comparison similar but correct statistical analysis excludes also this model at 99.8 % confidence level Krticka et al., PRC 77 054319 (2008)  the enhancement is very weak if any analysis of data from DANCE confirm this

32. Athens, July 9, 2008 Pygmy resonance in 198 Au revisited

33. Athens, July 9, 2008 Pygmy resonance in 198 Au revisited No pygmy resonance postulated

34. Athens, July 9, 2008 Pygmy resonance in 198 Au revisited Pygmy resonance at 5.9 MeV

35. Athens, July 9, 2008 Pygmy resonance in 198 Au revisited Abrupt suppression of PSF below 5 MeV The best fit obtained – it does not seem that there is a pygmy resonance in 198 Au

36. Athens, July 9, 2008 PSF used Exactly the same fit describes perfectly also data obtained with DANCE 4  detector

37. Athens, July 9, 2008 Spectra from 4  ball (DANCE, n_TOF, …) E1E1 E2E2 E3E3 E4E4

38. Athens, July 9, 2008 data from the Karlsruhe 4  BaF 2  calorimeter Pygmy resonance at 5.5 MeVNo pygmy resonance postulatedSuppression of PSF below 5 MeV … but postulating a pygmy resonance leads to too large total radiation width No difference in fits Pygmy resonance in 198 Au revisited

39. Athens, July 9, 2008

40. Conclusions  Measurement of TSC cascades provides valuable information on  -ray strength functions  DICEBOX simulations can be used for obtaining information of  -ray strength functions from many experiments Special thanks to: F. Becvar Charles University, Prague, Czech Republic I. Tomandl, J. Honzatko Nuclear Physics Institute, Rez, Czech Republic G. Mitchell NCSU

41. Athens, July 9, 2008 Thank you for your attention