Rare earth nuclei p resolved lines - interacting bands – magnitude of interactions –

1. Landscapes and fluctuations of two-dimensional rotational g - spectra –coupling between rotational and thermal motion • Introduction: • p cascades of rotational transitions p ordered or chaotic intrinsic and rotational motion: discrete bands – ergodic bands – damping of rotational motion M. Matsuo S. Leoni A. Bracco E. Vigezzi R.A. Broglia B. Herskind S. Åberg T.L. Khoo A.P. Lopez-Martens T. Lauritsen T. Døssing • Rare earth nuclei • p resolved lines - interacting bands – magnitude of interactions – • level spacing distributions • p damped rotational motion – strength distributions – scaling laws • p landscapes and fluctuations are powerful tools to investigate • interacting bands and rotational damping Niigata, Milano, Copenhagen, Argonne,Orsay • 194Hg – superdeformed bands • p ~ 100 discrete unresolved bands • p ergodic rotational bands or precursors to ergodic bands

2. g – ray cascades of deformed nuclei: CN formation n Particle evaporation a unresolved (unresolvable?) gamma rays, mostly E2’s Resolve from coincidences D. RADFORD Quasicontinuum spectra F. STEPHENS and D. DIAMOND B. HERSKIND and S. LEONI I..Y. LEE and C. BAKTASH T-L KHOO and A.P. LOPEZ-MARTENS energy resolvable gamma rays, mostly E2’s angular momentum

3. Rotational and intrinsic motion Rotational motion ordered chaotic ergodic bands damping of rotationalmotion chaotic Intrinsic motion Rare earth nucleus discrete bands ordered

4. 163Er – interacting bands LI,LII BEG/BFH AFG AEH C A B AEG Hagemann et al., Nucl.Phys. A618 (1997) 199

5. Infer: mixed bands higher up in energy Same magnitude of interaction E-Eyrast = 1.5 MeV T ~ 1/3 MeV d2 ~ 6 keV Nbranch ~ 5 HAB <-> FABef |V| ~ 10 keV E-Eyrast = 400 keV d2 ~ 50 keV

6. Magnitude of interactions experimental, from level crossings surface – d interaction DK

7. Calculations of interacting bands • Cranked Nilsson potential • Surface delta interaction M. Matsuo et al. Nucl. Phys. A617(1997)1 Configuration mixing with residual interaction Cranking np-nh basis bands

8. Level spacings

9. E1 - E2 Eg - Eg coincidence spectra E2 one band E1 Many bands Rotational damping

10. E1 E1 + E2 - E2 Mixing and Damping D I = 0: spreading of basis band state over energy interval D I = -4: two steps in a cascade I I - 2 compound damping width I - 4 Gcomp mean filed mean field + residual interaction Gnarrow Gwide D I = -2: one step in a cascade I - 2 I E2 Grot rotational damping width E E1

11. Narrow component in g-g correlation g-g correlation Eg2 Eg1 Matsuo et al. PLB465(1999)1 1. Doorway states keep rotational correlation 2. The correlation is smeared by Gcomp » G P 2 D / narrow comp

12. I 2 4s(I) s(E1 – E2) ~ a I U1/4 Grot~4s(w) a I U1/4 Gnarrow ~ 2 Gcomp ar2 a U3/2 2 Gnarrow r Pnarrow ~ Exponentially decreasing 8s(w)2 Gcomp Grot= aI2 U-1 Eg - Eg schematic two-step strength funcions n Motional narrowing E2 E1 Energy U Angular momentum

13. Flow in cascades asymptotic flow line: U a I2 1 MeV I below motional narrowing: energy GrotaI U ¼ ~ Eg3/2 GcompaU 3/2~ Eg3 yrast line above motional narrowing: GrotaI2 U -1~ const 30 60 angular momentum

14. Perspective plot of g-g spectra 168Yb Fluctuation analysis: Large fluctuations: few underlying transitions. Small fluctuations: many underlying transitions. valley ridges • Unresolved, yet discrete, bands on the ridges • - Damped transitions in the valley AnalysisofQuasi-Continuumg-gspectra with respect to both shape and fluctuations • Shape anlysis: • Width of ridge • Width and depth of valley • => Extract Grot and Gcomp Døssing, Herskind, Leoni, Bracco, Broglia, Matsuo, Vigezzi, Phys. Rep. 268(1996)1

15. I+2 I I-2 I+2 I I-2 Fluctuation analysis Ridge • unresolved, yet discrete, bands ridge Counts [arb. unit] Eg1-Eg2 [keV] Valley • strongly interacting bands  valley Counts [arb. unit] Eg1-Eg2 [keV]

16. Grot I+2 I I-2 I+2 I I-2 Experimental evidence for rotational damping Discrete bands about ~ 30 discrete bands of the four p s’s up to U ~ 800 keV cranking model level density r(U,N,Z) Rotational Damping Fragmented decay of weak transitions in the valley A. Bracco et al.,PRL76(1996)4484

17. Landscapes => GcompandGrot 18O+150Nd163Er+5n @ 87,93 MeV v/c =0.96 % Imax 40, Umax4 MeV 3x109g-g-g events <Eg>=960 keV I = 32  Total I3/2 <Eg>=900 keV I = 30  Total Gcomp 20 keV Grot  150 – 200 keV P ~ 10 % I30-40 1)Sorting of163Er matrix 2) Subtraction of ALLknown transitions by RADWARE 3) Subtraction of E1xE1 and E2xE1 background 4) Spectral Shape Analysis of Ridge-Valley structure narr S. Leoni et al., PRL93(2004)022501-1

18. Experimental damping width data const Matsuo et. al., Cranked mean field Laurtizen et. al., schematic, cranked oscillator I3/2 F.S. Stephens et. al., Phys. Rev. Lett 88 (2002)142501

19. probed regions in I and U: wide component from valley shape 1 MeV I valley fluctuations, narrow component energy ridge fluctuations yrast line 30 60 angular momentum

20. Ergodic bands Damping of rotational motion Ergodic bands Discrete rotational bands Ergodic bands: chaotic internal States, E2 transitions along bands observed until now search in superdeformed nuclei estimated Grot < d B. Mottelson, S Åberg

21. Cascades including SD band feeding decay along Weak rotational transitions along excited superdeformed bands energy Cold ND decay decay out angular momentum

22. Gated spectra – 194Hg SD -gated ND -gated E2-bump Decay-out bump

23. g - g gated spectra - 194 Hg Eg (keV) 600 700 800 900 Eg (keV)

24. Extract from gated spectra in 194 Hg: first ridge 1.0 second ridge 0.5 0.0 yrast band 32 FWHM(keV) DE(keV) intensity E2 - bump 30 10 0 200 Npath 100 600 700 800 900 Transition energy (keV)

25. Ergodic bands ? about 4 components of basis bands in each mixed state precursor to ergodic bands, motional narrowing sets in when band mixing sets in Calculated bands, 194Hg

26. Shell effects in rotational damping s(w) : dispersion in rotational frequency 168Yb proton ~ Grot

27. s(w)2 Gcomp s(w)2 Gcomp Grot = Grot = 8 8 Precursor to ergodic bands Ergodic bands: chaotic internal States, E2 transitions along bands < d E(I) – Erigid(I) Precursor to ergodic bands: motional narrowing for all mixed bands: < d2 angular momentum I

28. I 2 4s(I) s(E1 – E2) ~ 8s(w)2 Gcomp Grot= aI 2U-1 Schematic strength functions with ergodic bands discrete bands > rotational damping discrete bands > ergodic bands > rotational damping 8s(w)2 Gcomp Gridge= aI 2U-1 2 Gcomp r Exponentially decreasing Glong~ s(w) a I U1/4

29. Conclusions Powerfull techniques to study the elusive spectra of unresolved g-rays Rare-earth nuclei: • Onset of damping around U ~ 800 keV • cranking model level density r(U,N,Z) • damping confirmed, Grot ~~ 200 keV • information on Gcomp not so convincing Superdeformed 194Hg nucleus: • no damping • hints of ergodic bands – precursor to ergodic bands Perspectives: • better theories (pf shell model) • g - ray tracking detection

30. Volcano 50-100

31. Volcano 20-50

32. J (2) ~ 77 2/ MeV Tilted planes in g -g -g spectra (α,2n) => 122Xe N=3: x+3y-4z = ±δ x x x N=2: x+2y-3z = ±δ z y z N=1: x+y-2z = ±δ y z y