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Collective Excitations of Deformed Nuclei and their Coupling to Single Particle States

Collective Excitations of Deformed Nuclei and their Coupling to Single Particle States. J. F. Sharpey-Schafer Physics Department, University of Western Cape, Belleville, South Africa. Bohr & Mottelson Vol II Page 363 !!. Nikšić et al. PRL 99 (2007) 092502. Li et al. PR C79(2009) 054301.

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Collective Excitations of Deformed Nuclei and their Coupling to Single Particle States

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  1. Collective Excitations of Deformed Nuclei and their Coupling to Single Particle States J. F. Sharpey-Schafer Physics Department, University of Western Cape, Belleville, South Africa.

  2. Bohr & Mottelson Vol II Page 363 !!

  3. Nikšić et al. PRL 99 (2007) 092502 Li et al. PR C79(2009) 054301 Self-consistent Relativistic Mean Field +BCS

  4. 15464Gd90 JFS-S et al. EPJ A47 (2011) 5

  5. Congruence of first & second Vacuum structures in 154Gd & 152Sm

  6. Configuration DependentorQuadrupole Pairing R. E. Griffin, A. D. Jackson and A. B. Volkov, Phys. Lett. 36B, 281 (1971). Suggested that Δpp ≈ Δoo >> Δop for Actnide Nuclei where 02+ 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

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

  8. Configuration Dependent or Quadrupole Pairing; Assume Δpp≈ Δoo>> Δop Nilsson Diagram N~90 [505]11/2- “Oblate” [521]3/2- 90 [660]1/2+ “Prolate”

  9. What is the│02+ > Configuration ? • (t,p) & (p,t) │02+ > is 2pn- 2hn this gives Jπbut nothing on the orbit. • Single particle transfer would give lnbut does not populate │02+ >. In { │02+ > + neutron }, look to see which orbit does NOT couple to │02+ >.

  10. Gsb β Canadian Journal of Physics 51 (1973) 1369 McMaster Løvhøiden, Burke & Waddington 157Gd(p,t)155Gd

  11. Kπ=15/2- =2γ+ + [505]11/2- 155Gd91 High-K Decay Scheme Missing │02+ > coupling [505]11/2-

  12. K=1/2+ =2-Ω 1400 K=15/2- =2+Ω Ex 155Gd91 1200 (keV) 996 keV K=1/2- =2-Ω 1000 Kγ=2 800 K=3/2+ {K=11/2-} BLOCKED 681 keV 600 K=3/2- 400 │02+ > [400]1/2+ [532]3/2- 200 [402]5/2+ [642]5/2+ [505]11/2- [651]3/2+ 0 Seen by Schmidt et al; J. Phys. G12(1986)411 in (n,γ) (d,p) & (d,t) [521]3/2-

  13. Egnd state = ½ ħωβ + ħωγ Ex (0,0,2,2) = ħωγ + ħ2/I K = 2 Gamma Vibration Band Head Energy

  14. Systematics of the strength of the E2 transitions from the 2γ+γ-bandhead to the ground state in a series of deformed nuclei.

  15. M1s 1. ΔK=2 kills the M1 component in J → J out-of-band transitions. Hence not much p-h component in the 2γ+ states unless all the components manage to cancel out ?? 2. In-band M1 transitions are very weak, demonstrating that gK ≈ gR

  16. The way the Soloviev qp-phonon model (QPM) works is as follows; 1] He postulates that collective phonons exist. He does not know how or what. V. G. Soloviev, Nucl. Phys. 69, 1-36 (1965) 2] So he defines a phonon operator; Qi Ψ = 0 (his equ 6) And collective states are given by; Qi+ Ψ (his equ 7) And [Qi,Qj+] = δij (his equ 8) 3] As he has no clue at all what the Qi are, he assumes they can be expanded in terms of 2qp wave functions. That is in terms of particle hole states and nothing more complex. 4] To do this he needs an interaction which he assumes is of the multipole-multipole type. 5] The phonon energy he then finds using the variation principle for Qi+ Ψ(his equ 10). But to do this he has to fit experimental data as his Hamiltonian has unknown constants κn , κp , κnp (his equ 3) which govern the strengths of the neutron-neutron, proton-proton and neutron-proton interactions. Later he gets fed up and puts all these κ s equal !! 6] In reference; V. G. Soloviev and N. Yu. Shirikova, Z. Phys. A301, 263-269 (1981) , he concludes “that the two-phonon states cannot exist in deformed nuclei” (his abstract). This is because anti-symmetrization and the Pauli principle pushes up the two-phonon energy to 2.5 times twice the phonon energy in his model. At these energies the two-phonon states are well above the pairing gap and will get mixed to hell !!!

  17. Two Neutron Transfer to 154Gd (N=90) Kπ = 2+ Bandhead Shahabuddin et al; NP A340 (1980) 109 N.B. Log10 scale

  18. Proton Stripping to 154Gd Kπ = 2+ band NB; Log10 Scale K=0+ │02+ > 0 2 4 O. P. Jolly; PhD thesis (1976), McMaster + Denis Burke & Jim Waddington

  19. Gammasphere Data Nov. 2008 K=2 γ-band ground state band aligned i13/2 band 2nd vacuum 156Dyfrom the 148Nd(12C,4n)156Dy reaction Spin I ( ħ ) Siyabonga Majola et al., to be published

  20. K=2 γ-band built on the aligned i13/2 band ground state band aligned i13/2 band 156Dyfrom the 148Nd(12C,4n)156Dy reaction Spin I ( ħ )

  21. Some even-even nuclei in which the γ-band has been observed above 15+ NucleusBeamHighest Spin ReachedReference Species Energy (MeV) Yrast band γ-even γ-odd 104Mo ff (fission fragment) 20+ 18+ 17+ [49] 154Gd α 45 24+ 16+ 17+ [3] 156Dy 12C 65 32+ 28+ 27+ [50] 156Er 48Ca 215 26+ 26+ 15+ [51] 160Er 48Ca 215 50+ - 43+ [52] 162Dy 118Sn 780 Coulex 24+ 18+ 17+ [53] 164Dy 118Sn 780 Coulex. 22+ 18+ 11+ [53] 164Er 9Be 59 24+ 14+ 19+ [54] 164Er 18O 70 24+ 18+ 21+ [55,56] 170Er 238U 1358 Coulex. 26+ 18+ 19+ [57] 180Hf 136Xe 750 Coulex. 18+ 16+ 13+ [58] 238U 209Bi 1130 & 1330 Coulex 30+ 26+ 27+ [59]

  22. 238U146 γ-band gsb Ward et al., Nucl Phys A600 (1996) 88 Coulex; 209Bi beam on thick target

  23. 16567Ho98 Coulex Thick target 209Bi beam 5.4 Mev/u Chalk River 8π Odd Proton Coupled to core γ-Vibration K< K> gsb G Gervais, Dave Radford et al. Nucl Phys A624 (1997) 257 γ=2+ gsb=7/2- K<=3/2- K>=11/2-

  24. 10442Mo62 10542Mo63 10341Nb62 Two Phonon Excitations ?? Jian-Guo Wang et al Nucl Phys A834 (2010) 94c

  25. 116Cd(48Ca,6n)156Er 215 MeV J M Rees, E S Paul et al Phys. Rev. C83 (2011) 044314 Z = 68 N = 88 Gammasphere Data, ANL

  26. 16068Er92 Odd Spin γ-band in 160Er Gammasphere data; Ollier et al., Phys. Rev. C83 (2011) 044309

  27. 16468Er96 γ-band S-band gsb Steve Yates et al., PR C21 (1980) 2366 150Nd(18O,4n)164Er and Coulex with 136Xe

  28. 16468Er96 Steve Yates et al., PR C21 (1980) 2366 150Nd(18O,4n)164Er and Coulex with 136Xe

  29. Summary of Experimental Data onγ-Bands • 1. B(E2) decays out-of-band to ground state band; • ΔK = 2 hence no M1 strength. Mixing ratios δ >>1 • M1 & g-factors; in-band transitions ΔJ = 1 are very weak or zero. • Transfer reactions (pick-up & stripping) zero or very weak. Rare exceptions ? • Some bands Signature split, others not. • Connected to γ-deformation ?? • 5. Alignments; ALL γ-bands track their intrinsic configuration. • 6. K>/K< splitting in odd nuclei; very few examples

  30. Theory ?? • Rotation-Vibration Model; based on Bohr Hamiltionan • Phonon/Boson Models; [Bés, Soloviev, Piepenbring…….] • Start with Nilsson potential + BCS => Quasi-particles • Assume Phonons/Bosons exist and then invent an interaction to • produce them !! Then fiddle with the interaction and the truncation. • IBA, X(5) and other fairy tales ! • RPA etc, more sucessful ? • Triaxial Projected Shell Model (TPSM) [Hara, Sun, Shiekh et al] • Hopeful ??

  31. CONCLUSIONS ?? • More data at low and high spins might help ? • Coulex is a good way of connecting to real collective structures and keeps the spectra less complicated. • Are Kπ = 2+ “γ-vibrational” bands just a projection of the Zero Point Motion on the symmetry axis or are they more of a traditional Boson/Phonon ?? • Do RPA or TPSM help ? • Non-Microscopic Models are no use at all. [IBA, X(5)…..] • Unlike phantom β-vibrations, γ-vibrations are a REAL collective motion !!

  32. Many thanks to all my colleagues SOUTH AFRICAU.S.A.CANADAFRANCE L L Riedinger D L Hartley C Beausang M Almond M P Carpenter C J Chiara P E Garrett F G Kondev W D Kulp III T Lauritsen E A McCutchan M A Riley J L Wood C H Wu S Zu D Curien J Dudeck N Schunk S M Mullins R A Bark E A Lawrie J J Lawrie J Kau F Komati P Maine S H T Murray N J Ncapayi P Vymers P Papka iThemba LABS + Stellenbosch Univ. S P Bvumbi S N T Majola Univ. of Western JFS-S Cape T E Madiba D G Roux A Minkova Univ. of Sofia J Timár ATOMKI, Debrecen iThemba LABS Rhodes University

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