1. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon Strength Functions of Heavy Nuclei: Achievements and Open Problems František Bečvář

2. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 The major part of the reported results were achieved thanks to hard work of my colleagues Michael Heil Jaroslav Honzátko Franz Kaeppeler Milan Krtička Rene Reifarth Ivo Tomandl Fritz Voss Klaus Wisshak – FZK Karlsruhe – NPI Řež – FZK Karlsruhe – CU Prague – LANL Los Alamos – NPI Řež – FZK Karlsruhe

3. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Outline The relation between the photon strength functions (PSFs) and the photoabsorption cross section. Fragmentation of photon strength. Brink hypothesis Models for E1 and M1 PSFs Comparison between the high-energy (n,  ) data and the photonuclear data DICEBOX algorithm as a tool for testing the validity of models for PSFs at intermediate  -ray energies Two-step  cascades: the essentials of the method and the survey of the results obtained Evidence for scissors resonances of excited nuclei Supporting results from Karlsruhe  -calorimetric measurements Comparison with the data from ( ,  ’), ( 3 He, 3 He’,  ) and ( 3 He,  ) reactions Conclusions

4. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Cornerstones of the extreme statistical model of  decay A notion of strength function (fragmentation of strength of simple nuclear states) Porter-Thomas fluctuations of partial radiation widths Brink hypothesis The principle of the detailed balance … and rather problematic absence of width correlation

5. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007  (γ, x)  γ abs =  (γ, x) +  ( γ, γ ’ ) …an energy-smoothed photoabsorption x-section EγEγ EγEγ EγEγ BnBn BnBn (γ,γ’)(γ,γ’) ≈10 eV ≈15 MeV ≈0.1 eV Photonuclear x-section Photoabsorption x-section Fragmentation of the GDER and the paradigm of the photon strength function Fluctuations

6. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Fragmentation of the GDER and the paradigm of the photon strength function  (γ, x)  γ abs =  (γ, x) +  ( γ, γ ’ ) EγEγ EγEγ EγEγ BnBn BnBn (γ,γ’)(γ,γ’) ≈10 eV ≈15 MeV ≈0.1 eV Photonuclear x-section n γ n n γ “equivalent to” The principle of the detailed balance: i i g.s. Photoabsorption x-section

7. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Fragmentation of the GDER and the paradigm of the photon strength function  (γ, x)  γ abs =  (γ, x) +  ( γ, γ ’ ) EγEγ EγEγ EγEγ BnBn BnBn (γ,γ’)(γ,γ’) ≈10 eV ≈15 MeV ≈0.1 eV Photonuclear x-section n γ n n γ “equivalent to” The principle of the detailed balance: i i g.s. = f (E1) (E γ ) E γ 3 /  (E i ) f (E1) (E γ ) = / (3 π 2 h 2 c 2 E γ ) If E1 transitions dominate Photoabsorption x-section GDR — Photon strength function

8. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007  (γ, x)  γ abs =  (γ, x) +  ( γ, γ ’ ) EγEγ EγEγ EγEγ BnBn BnBn (γ,γ’)(γ,γ’) ≈10 eV ≈15 MeV ≈0.1 eV Photonuclear x-section n γ n n γ “equivalent to” The principle of the detailed balance: i i g.s. Photoabsorption x-section = f (XL) (E γ ) E γ 2L+1 /  (E i ) In a general case Fragmentation of the GDER and the paradigm of the photon strength function f (XL) (E γ ) = / [(2L+1) π 2 h 2 c 2 E γ ] =  XL The paradigm of PSF: f (XL) and ρ are primordial, not derived quantities

9. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photoexcitation pattern does not depend on initial excitation energy of a target nucleus g.s. Quasicontinuum NRF experiments Brink hypothesis Fictitious photoexcitation experiments

10. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 n γ n n γ = i i ff = f (XL) (E γ ) E γ 2L+1 /  (E i ) f (XL) (E γ ) = / [(2L+1) π 2 h 2 c 2 E γ ] =  XL Brink hypothesis: generalization “g.s.”  “f” n γ n n γ = i i g.s. = f (XL) (E γ ) E γ 2L+1 /  (E i ) f (XL) (E γ ) = / [(2L+1) π 2 h 2 c 2 E γ ] =  XL A target in photonuclear/photoabsorption experiment is in the ground state Identical ! Photoexcitation pattern of an excited target nucleus g.s. Quasicontinuum Brink hypothesis Fictitious ( γ,γ‘) and ( γ,x ) experiments NRF experiments

11. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007  γ abs EγEγ BnBn (γ,x)(γ,x) (γ,γ')(γ,γ') (γ,γ') – NRF, g.s. only (n,γ) – two-step & n-step cascades (thermal and keV neutrons) ( 3 He, 3 He’γ), ( 3 He,αγ) Singles γ -ray spectra from (n,γ), total radiation widths  γ tot (p,p’γ) at small angles of scattering Photon strength functions: problems (γ,x) – g.s. only The Brink hypothesis and the paradigm of the photon strength function: do they hold? Is the E1 part of for energies near and below neutron threshold an extrapolation of a Lorentzian GDR? Does the energy dependence of display additional, statistically significant resonance-like structures in the region near or below the neutron threshold? To which extent the other multipolarities (M1, E2, …) contribute to photoabsorption cross section ? The main obstacles in studying PSFs: - strong Porter-Thomas fluctuations of  iγf - limited knowledge of other quantities (n,γ) at isolated neutron resonances, ARC

12. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 First evidence for validity of Brink hypothesis Data of L. M. Bollinger and G. E. Thomas, PRL 25 (1967) 1143 195 Pt(n,  ) 196 Pt at filtered neutron beam Transitions to 0 + and 2 + levels  = 4.9  0.5

13. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 L. M. Bollinger and G. E. Thomas, Phys. Rev. Lett. 18 (1967) 1143: “There is no adequate, theoretically based explanation of the E  5 dependence of the experimental widths, although an idea introduced by Brink and developed by Axel may be relevant.”  E  5 … the birth of the extreme statistical model for  decay of nuclear levels implications for complete spectroscopy of low-lying levels (ARC method) First evidence for validity of Brink hypothesis For Lorentzian E1 GDR with a constant damping width for a typical heavy nucleus: at

14. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Further evidence … ARC data from 147 Sm(n,  ) 148 Sm reaction... convincing? D. Buss and R. K. Smither, PRC 2 (1970) 1513

15. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 2. Model of Kadmenskij, Markushev and Furman: The damping width due to strongly interacting quasiparticles Kadmenskij, Matkushev, Furman (1982) … energy and temperature dependence 1. Axel-Brink model: Models used for E1 PSF An approximation for low  -ray energies Not justified for deformed nuclei At T>0 it gives a non-zero limit for E  →0 Diverges for E  → E G Landau-Migdal parameters

16. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Models used for E1 PSF 3. Model GLO: R. E. Chrien, Dubna Report No. D3, 4, 17-86-747 (1987) 4. Semi-empirical model EGLO: Divergence for E  → E G removed J. Kopecky, M. Uhl and R. E. Chrien, PRC 47 (1993) 312, adjustable parameters A good description for spherical, transitional and deformed nuclei achieved at energies E  > 6 MeV

17. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Model of Mughabghab and Dunford a generalization of KMF model for description of PSFs of deformed nuclei The damping width due to strongly interacting quasiparticles Kadmenskij, Matkushev, Furman (1982) The condition imposed on the modified width Problems: The spreading width due to the interaction between dipole and quadrupole vibrations J. Le Tourneux, Mat. Fys. Medd. Dan. Selsk. 34 (1965) 1 Summing the damping and spreading widths not fully legitimate For a typical deformed nucleus with β 2 >0.27, E G (low) ≈ 12 MeV and Γ G (low) <3.2 MeV the damping width becomes negative S. F. Mughabghab and C. L. Dunford, PLB 487 (2000) 155 … the model is not applicable to well deformed nuclei

18. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Models for M1 PSF 1. The single-particle model A constant PSF 2. The spin-flip model Analogous to AB model for E1 PSF Parameters deduced from the (p,p’  ) data 3. The scissors-resonance temperature-independent model Photon strength assumed not to depend on nuclear temperature F. Becvar et al., PRC52 (1995) 1278

19. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Comparison between photonuclear and (n,  ) data

20. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Comparison between photonuclear and (n,  ) data

21. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Comparison between photonuclear and (n,  ) data

22. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Comparison between photonuclear and (n,  ) data

23. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Comparison between photonuclear and (n,  ) data

24. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Single-Lorentzian fit Double-Lorentzian fit Comparison between photonuclear and (n,  ) data

25. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Comparison between photonuclear and (n,  ) data

26. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Behavior of photonuclear data for nuclei with N ≈ 50 No (n,  ) data

27. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Comparison between photonuclear and (n,  ) data main conclusions PSFs of spherical and transitional nuclei in  -ray energy region of 6-8 MeV are appreciably lower compared to predictions of the Axel-Brink model For spherical and transitional nuclei near A = 100 the photonuclear data also indicate a deficit of PSF with respect to predictions of the Axel-Brink model The KMF model for E1 PSF agrees with experimental data only in case of nuclei near A=100

28. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Simulation of  cascades by means of DICEBOX algorithm 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 discretization of an a priori known level-density formula – a random discretization with the Wigner-type long-range level-spacing correlations f (XL) (E γ ) E γ 2L+1 /  (E i ), 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 where the PSFs f (XL) and the density 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 Depopulating intensities are given by I if = [Σ XLf Γ i  f (XL) ] / [ Σ X΄L΄f ΄  i  f ΄ ( X΄L΄ ) ]

29. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 A straightforward approach to simulating  cascades 1-3 × 10 6 levels A complete decay scheme is known for at most 100 levels, i.e. for a 10 – 2 % fraction Probability of reaching a level after n-th step of a cascade:, where level energies. “Distant past of  cascading is irrelevant given knowleldge of the recent past” … Markovian process Necessity to generate the rest part of the decay scheme Problem: the need to generate an enormous number of depopulating intensities I ff’ = P(f ’ | f), up to 10 13 ! ~ Specificity: in line with the basic assumptions the branching intensities I if = P(f | i) are realizations pertinent to the corresponding random variables ~

30. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 A notion of a nuclear realization ≡ A set of realizations { I fi } for all possible i,f and a set of realizations { E f, J f, π f } for all levels f A nuclear realization Of these NRs only one of characterizes the behavior of a given nucleus Simulations of  cascades based on the use of various NRs lead to mutually different predictions of the cascade-related quantities To assess uncertainties of these predictions simulations of  cascades are to performed for a large number of NRs An infinite number of NRs exist for a given level-density ρ and a set of photon strength functions f (XL)

31. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Generate a level system (excitation energies, spins and parities ); take experimentally known levels and add the levels from discretization according a chosen level-density formula 0 BnBn Getting a “nuclear realization”

32. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 0 BnBn - Ascribe at random a precursors (a random generator seed) to each level of the system Getting a “nuclear realization”

33. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Ascribe at random a precursors (a random generator seed) to each level of the system Getting a “nuclear realization”

34. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Start with the neutron capturing level - Pick up its precursor γ- cascading

35. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Using this precursor generate  i  f - Deduce I  ’s γ- cascading...

36. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Generate a random number from the uniform distribution in (0,1) γ- cascading...

37. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Get the energy of the depopulating transition γ- cascading...

38. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Determine the first intermediate level - Pick up its precursor γ- cascading...

39. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Using this precursor generate  i  f for the intermediate level - Deduce I  ’s γ- cascading...

40. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Generate another random number from (0,1) γ- cascading...

41. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Get the energy of the next depopulating transition γ- cascading...

42. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Determine the next intermediate level - Pick up its precursor γ- cascading...

43. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Using this precursor generate  i  f for the intermediate level - Deduce I  ’s γ- cascading...

44. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Generate another random number from (0,1) γ- cascading...

45. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Get the energy of the next depopulating transition γ- cascading...

46. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Determine the next intermediate level - Pick up its precursor γ- cascading...

47. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Using this precursor generate  i  f for the intermediate level - Deduce I  ’s γ- cascading...

48. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Generate a random number from (0,1) γ- cascading...

49. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 - Get the energy of the next depopulating transition - This transition reaches the ground state – the cascade ends γ- cascading...

50. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 The outcome of γ -cascading - The number of steps of a given cascade is known - The procedure described is reiterated many times. Typically a set of 100 000 cascades are obtained for a given nuclear realization -The whole this process in repeated for an enough large number of other nuclear realizations - Various cascade-related quantities can be deduced and their residual Porter-Thomas r.m.s. uncertainties estimated - So also the energies of the individual transitions and the intermediate levels involved

51. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 The method of two-step γ -cascades following the thermal neutron capture Geometry: Data acquisition: - Energy E  1 - Energy E  2 - Detection-time difference Three-parametric, list-mode

52. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Spectrum of energy sums Bn-EfBn-Ef Essentials of accumulating the TSC spectra E1E1 Detection-time difference Time response function 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” × “energy sum E  1 +E  2 ”.

53. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 X 5 TSC spectrum - taken from only one of the detectors Spectrum of energy sums Bn-EfBn-Ef Essentials of accumulating the TSC spectra E1E1 Detection-time difference Time response function Energy sum E γ1 + E γ2 List-mode data i=-1 i=0 i=+1 j=-1 j=0 j=+1

54. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 TSCs in the 167 Er(n, γ ) 168 Er reaction The spectrum of  -ray energy sums

55. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 The 167 Er(n, γ ) 168 Er reaction TSCs terminating at the J π = 4 +, 264 keV level in 168 Er

56. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 DICEBOX Simulations Řež experimental data π f = + π f = - Entire absence of scissors resonances is assumed TSCs in the 167 Er(n, γ ) 168 Er reaction

57. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Scissors resonances assumed to be built on all 168 Er levels DICEBOX Simulations Řež experimental data π f = + π f = - TSCs in the 167 Er(n, γ ) 168 Er reaction

58. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 TSCs in the 167 Er(n, γ ) 168 Er reaction … still a small fraction of the overall TSC strengths 2200 2400 2600 2800 Energy of intermediate levels (keV) 2200 2400 2600 2800 Energy of intermediate levels (keV) Ground-state band  - vibrational band Non-statistical effects

59. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 TSCs in the 155 Gd(n, γ ) 156 Gd reaction DICEBOX Simulations Řež experimental data π f = + π f = - Entire absence of scissors resonances is assumed

60. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 TSCs in the 155 Gd(n, γ ) 156 Gd reaction DICEBOX Simulations Řež experimental data π f = + π f = - Scissors resonances assumed to be built on all 156 Gd levels

61. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 TSCs in the 155 Gd(n, γ ) 156 Gd reaction Origin of the two hump structure 0 B n - E f resonanting

62. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 TSCs in the 157 Gd(n, γ ) 158 Gd reaction

63. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 TSCs in the 157 Gd(n, γ ) 158 Gd reaction TSCs terminating at the J π = 4 +, 261 keV level in 158 Gd x 20

64. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 DICEBOX Simulations Řež experimental data π f = + π f = - Entire absence of scissors resonances is assumed TSCs in the 157 Gd(n, γ ) 158 Gd reaction

65. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 TSCs in the 157 Gd(n, γ ) 158 Gd reaction DICEBOX Simulations Řež experimental data π f = + π f = - Scissors resonances assumed to be built on all 158 Gd levels

66. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 E γ1 +E γ 2 = 2 E SR Sharpening the peak at the midpointof the TSC spectrum due to simultaneously resonating primary and secondary transitions TSCs in the 162 Dy(n, γ ) 163 Dy reaction A unique possibility of a sensitive test for presence of SRs built on the levels in the quasicontinuum M. Krticka et. al, PRL 92 (2004) 172501 Probability Eγ1Eγ1 Eγ2Eγ2 3/2- 6271 keV ½+ 163 Dy G.s. 5/2- 251 keV 5/2+ 162 Dy n SR Specifity of TSCs terminating at 251 keV level

67. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Entire absence of SRs is assumed TSCs in the 162 Dy(n, γ ) 163 Dy reaction

68. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 A “pygmy E1 resonance” with energy of 3 MeV assumed to be built on all levels TSCs in the 162 Dy(n, γ ) 163 Dy reaction

69. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 SRs assumed to be built only on all levels below 2.5 MeV TSCs in the 162 Dy(n, γ ) 163 Dy reaction

70. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Scissors resonances assumed to be built on all 163 Dy levels Sharpening the 3 MeV peak well reproduced TSCs in the 162 Dy(n, γ ) 163 Dy reaction plus a quantitative agreement between the predicted and simulated TSC spectra

71. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Data: E1 M1 150 Sm Gd isotopes 163 Dy Er isotopes Models for photon strength function used v.s. experimental data Models: E1 BA EGLO KMF M1 SR+SF (KMF+BA) – agrees better with the NRF data on E1/M1 ratio @ 3 MeV Photon strength functions plotted refer to the  transitions from the neutron capturing level f(E ,T f ) (MeV -3 )

72. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 SRs built on all 163 Dy levels…only on levels with E f <2.5 MeV n-step cascades following the capture of keV neutrons in 162 Dy E n = 90-100 keV

73. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 163 Dy: optimum models for photon strength functions Photon 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

74. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 0 2  B(M1)  (  N 2 ) 200 180 160140 A 4 6 Summing interval for  B(M1)  : 2.5 - 4.0 MeV Summing interval for  B(M1)  : 2.7- 3.7 MeV Redrawn from J. Enders et al., PRC 59 R1851 (1999) 164 Dy (NRF) Summing interval for  B(M1)  : 2.5 - 4.0 MeV - deduced from data in original paper of J. Margraf et al., PRC 52, 2429 (1995) Scissors-mode strength  B(M1)  : A considerable loss due to a finite summing energy interval The data from TSCs in odd 163 Dy agree well with the NRF data at least for even-even 164 Dy … Comparison between the TSC and NRF data I. NRF data for 29 even-even nuclei Value from TSCs in 163 Dy; summing interval for  B(M1)  : 2.5 - 4.0 MeV 163 Dy (TSC) Value from TSCs in 163 Dy: total sum Σ B(M1)  163 Dy (TSC) Theory of E. Lipparini and S. Stringari, Phys. Rep. 175 (1989) 103

75. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Counts per 1.2 keV Gamma-ray energy (keV) A. Nord et al., PRC 67, 034307 (2003) Spectrum of γ -rays scattered off 163 Dy Even if all 163 Dy transitions observed are M1 we get only  B(M1)  = 1.53  N 2  94 lines from 163 Dy  41 lines from 164 Dy  background lines  -ray energies 2.3-3.3 MeV:  line spacing of 7 keV Comparison between the TSC and NRF data II. NRF data for 163 Dy Even if all 163 Dy transitions observed are M1 we get only  B(M1)  = 1.53  N 2 … while TSC 163 Dy data yield total  B(M1)  = 6.2  N 2 Probably a large number of unresolved lines here... Limits of NRF?

76. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 0 2  B(M1)  (  N 2 ) 180 160140 A 4 6 Redrawn from J. Enders et al., PRC 59 R1851 (1999) 164 Dy (NRF) NRF data: summary of the results on the ssissors-mode 163 Dy (TSC) Theory Odd or odd-odd A significantly higher summed reduced M1 strengths than that seen from NRF The reputation of SR in odd nuclei seems saved Even-even SR’s damping width determined Richter’s sum rule – does not it underestimate the size of SRs ? Consequences for the constraint on parameters of the still not discovered high-lying SR, predicted by R. Hilton (1980) E. Lipparini and S. Stringari, Phys. Rep. 175 (1989) 103

77. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 E γ (MeV) f (E1) (E γ ) +f (M1) (E γ ) (MeV -3 ) Data taken from a paper of E. Melby et al., PRC 63 (2001) 044309 A 3 MeV resonance seen from ( 3 He,  ) reactions in deformed nuclei - a “pygmy resonance” of an unknown multipolarity or the SR resonance? NRF ( 3 He,  ) SR’s seen are very broad A-dependence of SR energy differs differs from that observed from NRF data - dependence of SR energy on energy of the level on which the SR resides?

78. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Data taken from A. Schiller et al., Physics of Atomic Nuclei 62 (2001) 1186 The 3 MeV resonance-like structure in the 172 Yb( 3 He, 3 He’ γ ) 172 Yb data It does not seem to be the case: – the position of the 3 MeV peak is remarkably stable with changing the initial excitation Dependence of SR energy on energy of the level on which the SR resides?

79. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Remarkable agreement Blind validation testing of the Oslo method Postulating a set of PSFs Extraction of first-generation  spectra Simulation of  cascades Construction of  -ray spectra corresponding to various initial excitations Getting a PSF The Oslo method itself should not widen the observed SR’s Postulated PSF Extracted by the Oslo method RESULTS with a SR

80. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 A comparison between the ( 3 He,  ) and NRF data on M1 strength of 166 Er and 168 Er Reaction  -ray energy interval  f (M1) (E  ) dE  /  f (E1) (E  ) dE  168 Er( ,  ΄ ) 168 Er 2.5-4.0 MeV 1.84 a) 167 Er( 3 He,α  ) 166 Er 2.5-4.0 MeV 0.34 a) Data from linear  -ray polarization measurements at Stuttgart (a sets of 46 M1 transitions and 30 E1 transitions) Effects of a temperature- or E exc - dependent E1 photon strength function?

81. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon strength functions of 148 Sm

82. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon strength functions of 148 Sm

83. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon strength functions of 148 Sm

84. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon strength functions of 148 Sm

85. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon strength functions of 148 Sm A region where crucial information on PSF is missing

86. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon strength functions of 96 Mo

87. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Photon strength functions of 96 Mo Strong correlation   f –  n (1)

88. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 R-correlation in the 173 Yb(n,  ) 174 Yb reaction at isolated resonances R-correlation: coefficient of correlation between partial radiatiation widths and reduced neutron widths averaged over final levels and resoance spins : … statistically significant Primary  transitions from resonances to the low-lying 174 Yb two-quasipartice levels F. Becvar et al., Yadernaya fizika 46 (1987) 392

89. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 9 resonances with J  = 2 - 63 partial widths 14 resonances with J  = 3 - 140 partial widths R-correlation in the 173 Yb(n,  ) 174 Yb reaction at isolated resonances and Intercept of Q : less than 1 Are correlated parts of   f decoupled from the GDR? Introduce -

90. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 SUMMARY A strong evidence for scissors-like vibrations of excited deformed nuclei Methods of TSCs and the n-step cascades (following the capture of keV neutrons) proved to be efficient tools for studying PSFs at intermediate  - ray energies of 2 – 4 MeV A deficit of photon strength in spherical and transitional nuclei at  -ray energies of 6-8 MeV Very large values of the reduced B(M1)  strength found; a deeper revision of the NRF data would be welcome The scissors M1 mode per se displays, indeed, resonance-like behavior

91. Workshop on Photon Strength Functions and Related Topics, Prague, June 17-20, 2007 Thank you