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The Loss of K-Selection in 178 Hf A. B. Hayes “Next Generation Isomers” workshop, 2 nd April, 2007

The Loss of K-Selection in 178 Hf A. B. Hayes “Next Generation Isomers” workshop, 2 nd April, 2007. U. Rochester — D. Cline, C. Y. Wu, H. Hua, M. W. Simon, R. Teng LBNL (Lawrence Berkeley) — A. O. Macchiavelli, K. Vetter GSI — J. Gerl, Ch. Schlegel, H. J. Wollersheim

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The Loss of K-Selection in 178 Hf A. B. Hayes “Next Generation Isomers” workshop, 2 nd April, 2007

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  1. The Loss of K-Selection in 178HfA. B. Hayes “Next Generation Isomers” workshop, 2nd April, 2007 • U. Rochester—D. Cline, C. Y. Wu, H. Hua, M. W. Simon, R. Teng • LBNL (Lawrence Berkeley)—A. O. Macchiavelli, K. Vetter • GSI—J. Gerl, Ch. Schlegel, H. J. Wollersheim • WarsawUniversity—P. Napiorkowski, J. Srebrny • ANL (Argonne National Laboratory)—R.V.F. Janssens, C. J. Lister, E. F. Moore, R. C. Pardo, D. Sewereniak • WNSL, Yale University—J. Ai, H. Amro, C. Beausang, R. F. Casten, A. A. Hecht, A. Heinz, R. Hughes, D. A. Meyer

  2. The Loss of K-Selection in 178Hf K-Selection Rule & Hindrance Motivation Two Experiments Results Conclusions Future work

  3. The K-Selection Rulefor axially symmetric systems I – Total nuclear spin J – Single-particle angular momentum R – Collective rotation K = Ω1+Ω2 |K| ≤ 

  4. Forbiddenness Single-particle Estimate “Weisskopf unit” Hindrance Hindrance “Reduced” Hindrancefν=Fν1/ν

  5. Motivation • Mystery of Coulomb excitation of the (t1/2=4s) K=8- isomer in 178Hf (Hamilton 1983, Xie 1993) • These two experiments measured the total isomer cross sections • Unknown which transitions responsible for large K • Can we generalize K-selection violations to other nuclei? • Practical interests—high energy-density storage and release

  6. K=16+Isomer Activation Ta(178Hf,178Hf)Ta 73% to 86% ECoul Offline counting of 16+ (t1/2=31y) isomer decay cascade Two Coulomb Excitation Experiments Online Experiment • 178Hf(136Xe,136Xe)178Hf • 650 MeV (96% ECoul) • 0.5 mg/cm2 (thin) 89% 178Hf pure target • CHICO + Gammasphere • Prompt -rays from many rotational bands Both Experiments: Fit matrix elements with semi-classical Coulomb-excitation code GOSIA

  7. Online Experiment — CHICO and Gammasphere CHICO Resolution: 1 degree in  4.7 degrees in  500 ps in ΔTOF 5% in mass Trigger: p + p +  (at least one  ray)

  8. Count E (keV) Triple-Coincidence -ray Data

  9. Count E (keV) Prompt-Delayed Data

  10. 178Hf Level Scheme

  11. Iterative Fit Process for Strongly-Coupled Bands Gamma Band Relative -ray Yields (including the Mikhailov term) scat(deg)

  12. Ki=0Kf=8 Ki=0Kf=6 Ki=0Kf=4 Log H/Hmin If-Kf Treatment of K-forbidden TransitionsSpin-Dependent Mixing (“SDM”) of Bohr and Mottelson “H” H can be written as H(IiKiIfKf)

  13. Relative -ray Yields scat(deg) = (∓30%) = The Kπ=4+Band Solid/Dashed: two relative phases of <K=4|E2|GSB> and <K=4|E2|  >

  14. K-allowed K-forbidden K=4+Band Gamma Band K=16+IsomerBand Band “A” K=6+IsomerBand K=8-IsomerBand SecondK=8-Band Ground State Band Deduced Population Paths E2 E2 E2

  15. The Kπ=8- Isomer Band Relative -ray Yields Solid: Total calc. yield Dotted: γ-band path Dashed: GSB path scat(deg)

  16. IGSB I Matrix Elements Populating Kπ=8- Isomer Band AlagaRule Attenuatedto preserve isomer t1/2

  17. K-allowed K-forbidden K=4+Band Band “A” K=16+IsomerBand Gamma Band K=6+IsomerBand K=8-IsomerBand SecondK=8-Band Ground State Band Deduced Population Paths E3 E3 E2

  18. Measured and Predicted 8- Isomer Band Coulomb Excitation Cross Sections • Hamilton:178Hf(136Xe,136Xe)178Hf • GSB Ifeed/ICoul.exc.≈ 0.9% Present calculation: 0.5% Xie:178Hf(130Te,130Te)178Hf 560—620 MeV σisom = 2.7—7.5 mb Present calculation: 16—38 mb, ≈ 5 Xie's measurements)

  19. The Kπ=6+ Isomer BandNo fitting. Calculation: two choices of relative phase of <K=6|E2|K=4> and <K=6|E2|K=2> Relative -ray Yields scat(deg)

  20. K-allowed K-forbidden K=4+Band Gamma Band Band “A” K=16+IsomerBand K=6+IsomerBand K=8-IsomerBand SecondK=8-Band Ground State Band Deduced Population Paths E2 E2 E2 E2 E2

  21. The K=16+ BandOnline expt. - Prompt -ray yields Relative -ray Yield (norm to 8+GSB6+GSB) Solid line: SDMDashed line: Alaga scat (deg)

  22. Beam Activation Experiment Ge Detector Faraday Cup Collimator 178Hf Beam Ta (natural) target stack Tantalum Beam Stop Ta foil and cylindrical“catcher” stack Si Counter with aperture

  23. Raw Singles Activity Count -Ray Energy (keV)

  24. Count -ray Energy (keV) Doubles Activity Gated on 6+4+ in gsb

  25. Measured Activation Function Activity (h-1) Time-Averaged Mid-Target Projectile Energy (MeV) Solid: Best fit (individual reduced m.e.) Dashed: SDM model Dotted: Linear model

  26. IGSB <If K=16|| E2 || Ii K=0> (eb) Spin If in K=16+ Band Measured 16+ Band Matrix Elements

  27. K-allowed K-forbidden K=4+Band Band “A” K=16+IsomerBand Gamma Band K=6+IsomerBand K=8-IsomerBand SecondK=8-Band Ground State Band Deduced Population Paths E2 Excitation & Feed

  28. Results and Conclusions • Moments of Inertia • Hindrance systematics • K-mixing • Comment on energy storage

  29. Moments of Inertia 16+ inertia from Mullins et al. PLB393,279 & B400,401 (1997)

  30. Hindrance Systematics Reduced hindrance f(IiIf) forselected transitions in 178Hf. aCalculated from bbM.B. Smith, et al., PRC 68, 031302 (2003)cR.B. Firestone Table of Isotopes, vol. 2 (Wiley & Sons, New York, 1996) 8th ed.

  31. Highly hindered transitions between high-spin, high-K states • High-K bands align at higher spin • Constant moments of inertia of high-K bands High-K Bands • Rapid loss of hindrance with increasing spin in the low-K bands • Up-bends in the moments of inertia of the GSB and the -band Low-K Bands The Goodness of K Good in high-K bands. Total breakdown of K-conservation at I≈12 in low-K bands. Results consistent with collective alignment effects. Expect similar behavior in other deformed nuclei.

  32. B(E) Reduced Transition Probabilities from GSB Probes of individual K-admixtures. 4+: probes 2≤K≤6 6+: probes 4≤K≤8 8-: probes 5≤K≤11 16+: probes 14≤K≤18

  33. B(E) Reduced Transition Probabilities from -band Probes of individual K-admixtures. 6+: probes 4≤K≤8 8-: probes 5≤K≤11

  34. Calc. Coulomb Excitation Probability 100 16+ (99%) 10-1 10-2 GSB (0.6%) K=16+31 y 10-3 K=14-68 s 10-4 14- band (0.1%) 14 16 18 20 22 K=8-4 s If GSB Calculated Depopulation of 178m2Hf58Ni on 178m2Hf, 80% Coulomb barrier (230 MeV)

  35. Summary • Populated at least 3 high-K isomer bands in 178Hf electromagnetically. • Deduced population paths and measured EM matrix elements coupling 4+, 6+, 8- and 16+ bands. • Found rapid loss of K-conservation in low-K bands, consistent with rotational alignment. • Collective effects⇒should apply to other quadrupole-deformed nuclei. • Heavy ion Coulomb depopulation of the 31 year isomer is a <1% effect. No levels found that would support claims of stimulated emission.

  36. Current Work 242mAm+40Ar Coulomb excitation at 80% barrier at ATLAS • First Coulomb excitation of a nearly pure (98%) isomer target • Selectively excited states coupled to the K=5- t1/2=141 y isomer • Strong K=1 mixing between the K=5- isomer band and a previously unobserved K=6- band • Weak (~1%) multiple Coulomb excitation channel to a K=3- band known to decay to the ground state

  37. Possibilities for FAIR Studies • Coulomb excitation of secondary isomer beams • Storage ring to select isomer states by mass? • Select isomer states indirectly by scattering energy? • Increased selectivity of m.e. coupled to isomers • Extend isomer excitation studies to shorter-lived isomers (<<1s)

  38. END Phys. Rev. C 75, 034308 (2007) Phys. Rev. Lett. 96, 042505 (2006) Phys. Rev. Lett. 89, 242501 (2002)

  39. (a) Raw Count (b) Corrected for Hf-like (c) Corrected for Xe-like E (keV) Event-by-Event Doppler-Shift Correction

  40. The K=16+ BandBeam Activation Experiment t1/2=31 yrs • Activation on natural tantalum targets • 72% to 88% Coulomb barrier • Scattered 178Hf ions trapped in Ta catchers • Activity measured offline • Four-point activation function • Two 4-crystal Ge detectors • Analysis combines data of Hf+Xe and Ta+Hf experiments

  41. Lessons from K≦4 Band Fits • Quadrupole moment GSB: K=2: K=4: • The Alaga rule and the Mikhailov rule are successful. • The SDM model works, at least for low K, low spin. • Isomer bands can be treated as perturbations to the Coulomb excitation yields.

  42. Relative GSB -ray Yields 2/NDF scat(deg) Qo/Qobest - 1 2 Fit Technique Present: Previous:

  43. Rotational Bands in 178Hfbuilt on states of I=K

  44. The K-Selection Rule I – Total nuclear spin J – Single-particle angular momentum R – Collective rotation K=Ω1+Ω2

  45. Electromagnetic Transition Probabilities

  46. Electromagnetic Transition Probabilities

  47. Electromagnetic Transition Probabilities

  48. Electromagnetic Transition Probabilities Eγi, αi

  49. Shapes and K-Conservatione.g. The Bohr Hamiltonian γ-deformation β-deformation Special case: axial symmetry Images from www.europhysicsnews.com.

  50. 1Rotational alignment (K-mixing) 2Barrier penetration 3γ-softness (e.g. PSM) 1P. Ring, P. Schuck, Springer-Verlag (1980). 2Chowdhury, NPA 485:136(1988). 3Sun, PLB 589:83(2004).

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