Oslo-07-TD Landscapes and fluctuations of two-dimensional rotational  - spectra – coupling between rotational and thermal motion 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 194 Hg – superdeformed bands p ~ 100 discrete unresolved bands p ergodic rotational bands or precursors to ergodic bands 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 Niigata, Milano, Copenhagen, Argonne,Orsay Introduction: p cascades of rotational transitions p ordered or chaotic intrinsic and rotational motion: discrete bands – ergodic bands – damping of rotational motion

Oslo-07-TD  – ray cascades of deformed nuclei: angular momentum energy CN formation n  Particle evaporation unresolved (unresolvable?) gamma rays, mostly E2’s resolvable 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

Oslo-07-TD Rotational and intrinsic motion Rotational motion Intrinsic motion ordered chaotic Rare earth nucleus ergodic bands discrete bands damping of rotational motion

Oslo-07-TD 163 Er – interacting bands Hagemann et al., Nucl.Phys. A618 (1997) 199 C A AEH BEG/BFH AFG LI,LII BAEG

Oslo-07-TD Infer: mixed bands higher up in energy HAB FABef |V| ~ 10 keV E-E yrast = 400 keV d 2 ~ 50 keV E-E yrast = 1.5 MeV T ~ 1/3 MeV d 2 ~ 6 keV N branch ~ 5 Same magnitude of interaction

Oslo-07-TD Magnitude of interactions KK experimental, from level crossings surface –  interaction

Oslo-07-TD Calculations of interacting bands M. Matsuo et al. Nucl. Phys. A617(1997)1 Cranking np-nh basis bands Configuration mixing with residual interaction Cranked Nilsson potential Surface delta interaction

Oslo-07-TD Level spacings

Oslo-07-TD E  - E  coincidence spectra E 1 - E 2 one band Rotational damping Many bands E2E2 E1E1

Oslo-07-TD Mixing and Damping  I = 0: spreading of basis band state over energy interval mean filed mean field + residual interaction  I = -2: one step in a cascade  I = -4: two steps in a cascade  narrow  rot  comp  wide E2E2 E1E1 E1E1 + E 2 E1E1 - E 2 compound damping width rotational damping width I I - 4 I - 2 I E

Oslo-07-TD Narrow component in  -  correlation  correlation 1. Doorway states keep rotational correlation 2. The correlation is smeared by  comp EE EE compnarrow /2  DP Matsuo et al. PLB465(1999)1

Oslo-07-TD E  - E  schematic two-step strength funcions U Energy Angular momentum n E1E1 E2E2 Motional narrowing  (E 1 – E 2 ) ~ 4(I)4(I) I 2  narrow ~ 2  comp P narrow ~  I 2 U -1    comp  rot   rot   2  narrow   Exponentially decreasing   2   U 3/2   I U 1/4

Oslo-07-TD Flow in cascades angular momentum energy I 1 MeV yrast line asymptotic flow line: U  I 2  comp  U 3/2 ~ E  3  rot  I U ¼ ~ E  3/2  rot  I 2 U -1 ~ const below motional narrowing: above motional narrowing:

Oslo-07-TD Perspective plot of  spectra Analysis of Quasi - Continuum  spectra with respect to both shape and fluctuations 168 Yb valley ridges Døssing, Herskind, Leoni, Bracco, Broglia, Matsuo, Vigezzi, Phys. Rep. 268(1996)1 Fluctuation analysis: Large fluctuations: few underlying transitions. Small fluctuations: many underlying transitions. - Unresolved, yet discrete, bands on the ridges - Damped transitions in the valley Shape anlysis: -Width of ridge -Width and depth of valley => Extract  rot and  comp

Oslo-07-TD I+2 I I-2 Counts [arb. unit] Valley E  1 -E  2 [keV] I+2 I I-2 Counts [arb. unit] Ridge E  1 -E  2 [keV]  strongly interacting bands  valley  unresolved, yet discrete, bands  ridge Fluctuation analysis

Oslo-07-TD Experimental evidence for rotational damping Rotational Damping  rot I+2 I I-2 Discrete bands I+2 I I-2 A. Bracco et al., PRL76(1996)4484 about ~ 30 discrete bands of the four  ’s up to U ~ 800 keV cranking model level density  (U,N,Z) Fragmented decay of weak transitions in the valley

Oslo-07-TD 18 O+ 150 Nd  ,93 MeV v/c =0.96 % I max  40 , U max  4 MeV 3x10 9  events 1) Sorting of 163 Er matrix 2) Subtraction of ALL known transitions by RADWARE 3) Subtraction of E1xE1 and E2xE1 background 4) Spectral Shape Analysis of Ridge-Valley structure I = 30  =900 keV I = 32  =960 keV Total  comp  20 keV  rot  150 – 200 keV P ~ 10 % I   Landscapes =>  comp and  rot S. Leoni et al., PRL93(2004) narr I 3/2

Oslo-07-TD Experimental damping width I 3/2 const F.S. Stephens et. al., Phys. Rev. Lett 88 (2002) data Matsuo et. al., Cranked mean field Laurtizen et. al., schematic, cranked oscillator

Oslo-07-TD probed regions in I and U: angular momentum energy ridge fluctuations wide component from valley shape valley fluctuations, narrow component I 1 MeV yrast line

Oslo-07-TD Ergodic bands estimated  rot Ergodic bands: chaotic internal States, E2 transitions along bands  d Ergodic bands Discrete rotational bands Damping of rotational motion observed until now search in superdeformed nuclei B. Mottelson, S Åberg

Oslo-07-TD Cascades including SD band angular momentum energy feeding decay out Cold ND decay decay along Weak rotational transitions along excited superdeformed bands

Oslo-07-TD Gated spectra – 194 Hg SD -gated ND -gated E2- bump Decay-out bump

Oslo-07-TD  gated spectra Hg E  (keV)

Oslo-07-TD Extract from gated spectra in 194 Hg: Transition energy (keV) N path FWHM(keV)  E(keV) intensity first ridge second ridge yrast band E2 - bump

Oslo-07-TD 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, 194 Hg

Oslo-07-TD Shell effects in rotational damping  : dispersion in rotational frequency ~  rot 168 Yb proton

Oslo-07-TD Precursor to ergodic bands angular momentum I E(I) – E rigid (I)    comp  rot  Ergodic bands: chaotic internal States, E2 transitions along bands Precursor to ergodic bands: motional narrowing for all mixed bands:  d  d 2    comp  rot 

Oslo-07-TD Schematic strength functions with ergodic bands  (E 1 – E 2 ) ~ 4(I)4(I) I 2 Exponentially decreasing   I U 1/4  I 2 U -1    comp  ridge   I 2 U -1    comp  rot   long ~ 2  comp    ) discrete bands > rotational damping discrete bands > ergodic bands > rotational damping

Oslo-07-TD Conclusions Powerfull techniques to study the elusive spectra of unresolved  -rays Onset of damping around U ~ 800 keV cranking model level density  (U,N,Z) damping confirmed,  rot ~~ 200 keV information on  comp not so convincing Rare-earth nuclei: Superdeformed 194 Hg nucleus: no damping hints of ergodic bands – precursor to ergodic bands Perspectives: better theories (pf shell model)  - ray tracking detection

Oslo-07-TD Volcano

Oslo-07-TD Volcano 20-50

Oslo-07-TD Tilted planes in  spectra => 122 Xe J (2) ~ 77  2 / MeV N=3: x+3y-4z = ±δ N=2: x+2y-3z = ±δ N=1: x+y-2z = ±δ (α,2n) x x x y y y z z z