1. T he Decline and Fall of β-Vibrations Newton: by William Blake (1757-1827) Newton: by Godfrey Kneller 1689 John Sharpey-Schafer University of the Western Cape South Africa 6/11/2014ISPUN141

2. Bohr & Mottelson Vol II Page 363 !! Ben on his Bike 2008 6/11/2014ISPUN142

3. 6/11/2014ISPUN143 So, WHAT are the 0 2 + states ??

4. Two Neutron Transfer to 154 Gd (N=90) N.B. Log 10 scale Shahabuddin et al; NP A340 (1980) 109 K π = 2 + Bandhead 6/11/2014ISPUN144 01+01+ 02+02+ 03+03+ 04+04+

5. J V Maher et al. PRL 25 (1970) 302 238 U(p,t) 236 U 17 MeV θ = 30º 02+02+ 0 2 + NOT a β-vibration NOR a pairing vibration 6/11/2014ISPUN145

6. 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 0 2 + 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) 0 2 + 0 1 + 6/11/2014ISPUN146

7. 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 0 2 + 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

8. 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

9. 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

10. [505]11/2 - 681 keV │0 2 + > K π =15/2 - =2 γ + + [505]11/2 - 155 64 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 +

11. 1000 1200 1400 800 600 400 200 0 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]1/2 + 681 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

12. [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 0 2 + 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

13. 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

14. Systematics of Energies of 0 2 + and [505]11/2 - states for Z = 60-68 and N = 86-98 02+02+ [505]11/2 - 6/11/2014ISPUN1414

15. 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

16. 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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18. 6/11/2014ISPUN1418

19. THE PROBLEM for ( 3 He,n) Two Proton Stripping: 1. 1. How to get good resolution ΔE n ≈ 2 keV 2. 2. 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: 1. 1. 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 0 2 + levels We would like 2 proton transfer data to compare

20. 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

21. Fast Neutrons from ( 3 He,n) Statistical Neutrons from ( 3 He,xn) γ-rays from targetγ-rays from beam stop 59 27 Co 32 ( 3 He,n) 61 29 Cu 32 ISPUN14216/11/2014 Papka et al., Eur. Phys. J. A50, 158 (2014)

22. 148 Nd( 3 He,n) 150 Sm 150 Sm 6/11/2014ISPUN1422 Paul Papka

23. 6/11/2014ISPUN1423 Summary: Why are 0 2 + states not β-Vibrations ? 1. There are no 2 phonon states [Kulp et al., PR C77, 061301 (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 0 1 + built on 0 2 + Why are the 0 2 + states in N=88,90 [505]11/2 - Pairing Isomers ? 1. The coupling of the [505]11/2 - odd neutron to 0 2 + 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

24. 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