Structure of hot nuclear states
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1 Structure of hot nuclear states Teng Lek Khoo Argonne National Laboratory 2nd Workshop on Level Density and Gamma Strength Oslo, May 11-15, /25/09 T. L. Level Density and Gamma Strength W'shop 1
2 Samuel Taylor Coleridge The Rime of the Ancient Mariner And the Albatross begins to be avenged. Water, water, every where, And all the boards did shrink ; Water, water, every where, Nor any drop to drink. γs, γs every where, And all the spectra did shrink ; γs, γs every where, Nor any physicist to drink. 5/25/09 T. L. Level Density and Gamma Strength W'shop 2
3 Lauritsen et al. h 124 Xe, l max ~ 80 ; ~1/2 of γs unresolved, from hot states. 5/25/09 T. L. Level Density and Gamma Strength W'shop 3
4 Topics Phase transitions Fission barriers and l max in Superheavy Nuclei Order to chaos transition in superdeformed nuclei Ergodic superdeformed bands Information extracted from γ spectra. Theoretical description of γ spectrum requires knowledge of ρ & S γ. 5/25/09 T. L. Level Density and Gamma Strength W'shop 4
5 γs detected with & Berkeley 5/25/09 T. L. Level Density and Gamma Strength W'shop 5
6 Adventures in the βγ plane & above Rotation around symmetry axis Oblate s.p. prolate J ~ J 0 ( β) J 0 = J rigid sphere J ~ J 0 (1-0.6β) Collective oblate prolate s.p. Collective & aligned-particle rotation of nuclei 5/25/09 T. L. Level Density and Gamma Strength W'shop 6
7 Magnetization vs. T/T c symmetry broken ordered phase deformed β vs. T, I=0 170 Er, Goodman symmetry restored disordered phase spherical γ vs. T, I=60, 40, 20 h γ = 0 0, prolate 164 Er, Goodman γ = 60 0, oblate Phase Transitions Universality class Critical exponent β Order param (1 T/T c ) β 5/25/09 T. L. Level Density and Gamma Strength W'shop 7!
8 5/25/09 T. L. Level Density and Gamma Strength W'shop 8
9 Prolate (γ=0 0 ) & oblate (γ=60 0 ) states in N=88, 90 nuclei N 86, e.g. 152 Dy. Particle alignment (γ=60 0, oblate), yrast isomers. N = 88, 90, e.g. 154,156 Dy. Both prolate & oblate rotational & terminating bands. N 92, e.g. 158 Dy, prolate rotors (γ=0 0 ). 5/25/09 T. L. Level Density and Gamma Strength W'shop 9
10 154 Dy, Ma et al., PRL 61, 46 (1988), PRC 70, (2004) collectivity returns collective singleparticle 5/25/09 T. L. Level Density and Gamma Strength W'shop 10
11 prolate 5/25/09 T. L. Level Density and Gamma Strength W'shop 11
12 Cascade A oblate & prolate zones 2 peaks Ma et al., PRL 84, 5967 (2000) Theory THFB Experiment Remanent signatures of phase transition at finite temperature in a mesoscopic system Cascade B oblate zone 1 peak 5/25/09 T. L. Level Density and Gamma Strength W'shop 12
13 Superheavy nuclei: at the limits of Z,I,E * What are the limits? Physics questions. B f (I,E*,Z,N) & E shell (I,E*,Z,N). Variation with I, E* (as well as Z, N) incisive tests of shell structure. Spectroscopy detailed tests of E sp, e(ω), E band (I), J (1,2) (i.e. E/ I, 2 E/ 2 I). 5/25/09 T. L. Level Density and Gamma Strength W'shop 13
14 ρ, S γ in SHN ρ, S γ in SHN with transfer reactions, e.g. 249 Cf(d,p), (α, 3 He), (d,t), ( 3 He,α) Any new aspects, e.g. near top of fission barrier? 5/25/09 T. L. Level Density and Gamma Strength W'shop 14
15 How delicate are superheavy nuclei? How fragile are these loosely-bound nuclei, barely held together shell-created barriers? If you tickle them, will they laugh and fall apart? If you spin them, will they fission immediately? 5/25/09 T. L. Level Density and Gamma Strength W'shop 15
16 5/25/09 T. L. Level Density and Gamma Strength W'shop 16
17 5/25/09 T. L. Level Density and Gamma Strength W'shop 17
18 Initial states for γ decay to g.s. 5/25/09 T. L. Level Density and Gamma Strength W'shop 18
19 M. Asai 1,10, D. Grayson 1 5/25/09 T. L. Level Density and Gamma Strength W'shop 19
20 I max ( 254 No) > I max ( 220 Th)! (b) 220 Th 90 B f ( 254 No) > B f ( 220 Th) >5 MeV ~8 MeV σ( 254 No) ~ σ( 220 Th)/ Yb( 48 Ca,4n) I max =20 Yield (arbitrary units) I (hbar) 223 MeV 219 MeV (a) 254 No Pb( 48 Ca,2n) I max =32 I max =20 5/25/09 T. L. Level Density and Gamma Strength W'shop 20
21 Excited SD states (chaotic regime) Excited SD states (ergodic regime) 4. ND yrast cascade to ground state Double cycle of chaos order 5/25/09 Potential Energy Surface at single spin T. L. Level Density and Gamma Strength W'shop 21
22 Hackman et al. Lauritsen et al. 5/25/09 T. L. Level Density and Gamma Strength W'shop 22
23 5/25/09 T. L. Level Density and Gamma Strength W'shop 23
24 194 Hg SD gated Lopez-Martens et al. E γ E γ correlations Slice c) Discrete SD bands, A~190 Cuts perpendicular to diagonal 5/25/09 T. L. Level Density and Gamma Strength W'shop 24
25 Observations: new phenomenon Exceptionally narrow SD ridges (~10 kev vs. ~50 kev for ND). Ridge exhausts ~100% of E2 total strength (vs. ~10% for ND). No detectable broad component with rotational damping Γ rot ~300 kev. Number of bands contributing to the ridge ~150 (vs. ~30 for ND). Cf. FWHM SD ~ 10 kev vs. FWHM ND ~ 350 kev Narrow ridge implies E2 transitions flow within parallel rotational bands with nearly identical J (2). J (2) identical to that of SD band 1. Theory predicted narrow ridges (Matsuo and Yoshida). suggests that ~2-8 (4, average) basis configurations in excited SD states; from U= MeV. Predicted by Mottelson 5/25/09 T. L. Level Density and Gamma Strength W'shop 25
26 U damping 1.6 MeV Golden region Only narrow ridge P narrow ~1 n band high, ~150 Γ ~ 10 kev U mix ~1.2 MeV, Γ µ >D 2, (n mix >2, n branch =1-2) mixing Low 2Δϖ 194 Hg SD 1.0 MeV Onset mixing & damping Medium 2Δϖ 152 Dy, SD High 2Δϖ Yb, ND U damp U mix damping Γ wide = Γ rot ~300 kev n branch >2 n band low~30 P narrow ~0.1 5/25/09 T. L. Level Density and Gamma Strength W'shop 26
27 Γ E2 < D < Γ µ kev Ergodic condition 2Δω < Γ µ ~25 ~40 kev chaotic intrinsic-motion Chaotic, orderly rotational decay ergodic bands chaotic rotational decay rotational damping n branch ~1 >2 Motional narrowing conditions for ergodic bands small " $ 0 # " i! SD states in A 190 small Coriolis intn. large ε, Κ Large ε, Α 5/25/09 T. L. Level Density and Gamma Strength W'shop 27
28 Small Δϖ ~identical J (2) identical bands. Ergodic and identical bands intimately connected. 5/25/09 T. L. Level Density and Gamma Strength W'shop 28
29 Excitation Energy above yrast line, U [MeV] From Order to Chaos Chaotic Quantum numbers lost (except I, π) no selection rules. Statistical spectrum. Transitions strengths unpredictable, governed by Porter-Thomas fluctuations. Ergodic Mostly chaotic, with: (a) complicated wavefunctions and (b) Porter-Thomas fluctuations in all transitions except collective E2 transitions, with rotational band structure preserved. Unique in 194 Hg. Ordered Good quantum numbers selection rules. Well-defined spectrum; equi-spaced (picket-fence) sharp lines from rotation of a cold SD object. 5/25/09 T. L. Level Density and Gamma Strength W'shop 29
30 Summary 1. Phase transitions along and above the yrast line. 2. Superheavy nuclei: survive to I = 32 hbar; shell structure robust to high spin. 3. Superdeformed bands: double cycle of chaos-to-order transition; new ergodic regime with orderly E2 flow in chaotic states. 5/25/09 T. L. Level Density and Gamma Strength W'shop 30
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