T he Decline and Fall of β-Vibrations Newton: by William Blake ( ) Newton: by Godfrey Kneller 1689 John Sharpey-Schafer University of the Western Cape South Africa 6/11/2014ISPUN141

Bohr & Mottelson Vol II Page 363 !! Ben on his Bike /11/2014ISPUN142

6/11/2014ISPUN143 So, WHAT are the states ??

Two Neutron Transfer to 154 Gd (N=90) N.B. Log 10 scale Shahabuddin et al; NP A340 (1980) 109 K π = 2 + Bandhead 6/11/2014ISPUN

J V Maher et al. PRL 25 (1970) U(p,t) 236 U 17 MeV θ = 30º NOT a β-vibration NOR a pairing vibration 6/11/2014ISPUN145

Configuration Dependent or Quadrupole Pairing R. E. Griffin, A. D. Jackson and A. B. Volkov, Phys. Lett. 36B, 281 (1971). Suggested that Δ pp ≈ Δ oo >> Δ op for Actinide Nuclei where states were observed in (p,t) that were not pairing- or β-vibrations. Suppose there are n prolate and n oblate degenerate levels at the Fermi Surface; Assume that each pairing matrix element is the same for the same type -a BUT the prolate-oblate matrix elements are very weak –εa Then if the prolate n*n matrix is A, the oblate matrix is also A The matrix for the total system is; A εA εA A Then there are (2n-2) states with ZERO energy and 2 states with energies E 1,2 = -(1 ± ε) na (2n-2) /11/2014ISPUN146

Configuration Dependent or Quadrupole Pairing R. E. Griffin, A. D. Jackson and A. B. Volkov, Phys. Lett. 36B, 281 (1971). Suggested that Δ pp ≈ Δ oo >> Δ op for Actinide Nuclei where states were observed in (p,t) that were not pairing- or β-vibrations. W. I. van Rij and S. H. Kahana, Phys. Rev. Lett. 28, 50 (1972). S. K. Abdulvagabova, S. P. Ivanova and N. I. Pyatov, Phys. Lett. 38B, 251 (1972). D. R. Bès, R. A. Broglia and B. Nilsson, Phys. Lett. 40B, 338 (1972). took up the suggestion I. Ragnarsson and R. A. Broglia, Nucl. Phys. A263, 315 (1976). coined the term “pairing isomers” for these 0 + states 6/11/2014ISPUN147

Single-Particle Quadrupole Moments in a deformed W-S potential A=155 A=239 N=90 [505]11/2 - Abdulvagabova, Ivanova & Pyatov Phys. Lett. 28B (1972) 215 Low Density of Oblate s-p States Below the Fermi Surface qνqν qνqν ενεν ενεν 6/11/2014ISPUN148

What is the │0 2 + > Configuration ? nothing ۞ (t,p) & (p,t) │0 2 + > is 2p n - 2h n this gives J π but nothing on the orbit. ۞ Single particle transfer would give l n but does not populate │0 2 + >. NOT In { │0 2 + > + neutron }, look to see which orbit does NOT couple to │0 2 + >. 6/11/2014ISPUN149

[505]11/ keV │0 2 + > K π =15/2 - =2 γ + + [505]11/ Gd 91 High-K states JFS-S et al. EPJ A47 (2011) 6 6/11/2014ISPUN1410 Tshifhwa Madiba en familie [505]11/2 - is BLOCKED from coupling to the core 0 2 +

ExEx (keV) [521]3/2 - [651]3/2 + [505]11/2 - │0 2 + > BLOCKED 155 Gd 91 Seen by Schmidt et al; J. Phys. G12(1986)411 in (n,γ) (d,p) & (d,t) [642]5/2 + [402]5/2 + [532]3/2 - [400]1/ keV K=3/2 - K=3/2 + {K=11/2 - } K γ =2 K=1/2 - =2-Ω K=1/2 + =2-Ω K=15/2 - =2+Ω 996 keV 6/11/2014ISPUN1411

[660]1/2 + “Prolate” [505]11/2 - “Oblate” Configuration Dependent or Quadrupole Pairing; Assume Δ pp ≈ Δ oo >> Δ op 82 Neutrons Prolate Deformation => R. E. Griffin, A. D. Jackson and A. B. Volkov, Phys. Lett. 36B, 281 (1971). W. I. van Rij and S. H. Kahana, Phys. Rev. Lett. 28, 50 (1972). S. K. Abdulvagabova, S. P. Ivanova and N. I. Pyatov, Phys. Lett. 38B, 251 (1972). D. R. Bès, R. A. Broglia and B. Nilsson, Phys. Lett. 40B, 338 (1972). I. Ragnarsson and R. A. Broglia, Nucl. Phys. A263, 315 (1976). First Excited states in even-even nuclei are NOT β-vibrations. In N=88,90 nuclei they are “PAIRING ISOMERS” ISPUN1412 Flying Fish [505]11/2 - orbital 6/11/2014

162 Yb 92 gsb 163 Yb 93 gsb [521]3/2 - Jerry Garrett et al, Phys. Lett. B 118, 297 (1982) Full Unblocked Pairing Pairing Reduced by Odd Neutron (Blocking) 155 Dy 89 [505]11/2 - even-even even-odd The Extruded [505]11/2 - orbital does NOT partake in the Monopole neutron Pairing 6/11/2014ISPUN14 13 Jerry Garrett

Systematics of Energies of and [505]11/2 - states for Z = and N = [505]11/2 - 6/11/2014ISPUN1414

E gnd state = ½ ħω β + ħω γ E x (0,0,2,2) = ħω γ + ħ 2 / I K = 2 Gamma Vibration Band Head Energy ħ ω γ keV 6/11/2014ISPUN1415

150 Sm( 12 C,4n) 158 Er 65 MeV Tshepo Dinoko, PhD Thesis, UWC 6/11/2014ISPUN1416 Tshepo Dinoko N=90

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6/11/2014ISPUN1418

THE PROBLEM for ( 3 He,n) Two Proton Stripping: How to get good resolution ΔE n ≈ 2 keV How to separate the 1 in 1000 ( 3 He,n) direct reaction events from the flood of ( 3 He,xn) fusion-evaporation events ?? THE SOLUTION: Use HPGe detectors having ΔE γ ≈ 2 keV 2.(i) Note that Q (3He,n) ≈ + 7 MeV E n ≈ 32 MeV Fast while Q (3He,xn) ≈ - 17 MeV E n < 6 MeV Slow (ii) To 0 + states, the ( 3 He,n) cross-section peaks at 0° while for ( 3 He,xn) all neutrons are emitted isotropically ie. the direct reaction L=0 neutrons to 0 n + states are focused at 0° While the evaporation neutrons are emitted in all directions. ISPUN14196/11/2014 We have 2 neutron transfer data to levels We would like 2 proton transfer data to compare

AFRODITE 9 HPGe Clovers in BGO shields target beam stop 12 Neutron detectors Each 10x10x60 cm ~2.0m Pb γ-ray shielding wall 25 MeV 3 He beam Schematic set-up for ( 3 He,n) experiments AFRODITE = AFRican Omnipurpose Detector for Innovative Technologies and Experiments ISPUN14206/11/2014

Fast Neutrons from ( 3 He,n) Statistical Neutrons from ( 3 He,xn) γ-rays from targetγ-rays from beam stop Co 32 ( 3 He,n) Cu 32 ISPUN14216/11/2014 Papka et al., Eur. Phys. J. A50, 158 (2014)

148 Nd( 3 He,n) 150 Sm 150 Sm 6/11/2014ISPUN1422 Paul Papka

6/11/2014ISPUN1423 Summary: Why are states not β-Vibrations ? 1. There are no 2 phonon states [Kulp et al., PR C77, (2011)] 2. Strongly populated in 2n transfer, Weakly in 2p transfer; {a truly collective state would not have uneven properties} 3. There are Congruent states to built on Why are the states in N=88,90 [505]11/2 - Pairing Isomers ? 1. The coupling of the [505]11/2 - odd neutron to is BLOCKED 2. The back-bending frequency ħω c is NOT reduced by blocking and is therefore not involved in the monopole pairing 3. The Explanation of Griffiths, Jackson and Volkov is more than adequate

6/11/2014ISPUN1424 Many thanks to all my collaborators: Rob Bark, iThemba LABS Suzan Bvumbi, University of Johannesburg Tshepo Dinoko, University of Western Cape Pete Jones, iThemba LABS Amel Korichi, CSNSM Orsay Kati Juhász, University of Debrecen Elena Lawrie, iThemba LABS Kobus Lawrie, iThemba LABS Kevin Li, University of Stellenbosch Tshifhwa Madiba, University of Western Cape Siyabonga Majola, University of Cape Town Ani Minkova, University of Sofia Simon Mullins, iThemba LABS Barna Nyakó, ATOMKI Debrecen Paul Papka, University of Stellenbosch David Roux, University of Western Cape Maciej Stankiewicz, University of Cape Town Preston Vymers, University of Johannesburg Mathis Wiedeking, iThemba LABS And many others