1. 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 ● Warsaw University—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 178 Hf K-Selection Rule & Hindrance Motivation Two Experiments Results Conclusions Future work

3. I – Total nuclear spin J – Single-particle angular momentum R – Collective rotation K = Ω 1 +Ω 2 The K-Selection Rule for axially symmetric systems |  K| ≤

4. Hindrance Forbiddenness Hindrance “Reduced” Hindrance f ν =F ν 1/ν Single-particle Estimate “Weisskopf unit”

5. Motivation ● Mystery of Coulomb excitation of the (t 1/2 =4s) K=8 - isomer in 178 Hf (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. Two Coulomb Excitation Experiments Online Experiment ● 178 Hf( 136 Xe, 136 Xe) 178 Hf ● 650 MeV (96% E Coul ) ● 0.5 mg/cm 2 (thin) 89% 178 Hf pure target ● CHICO + Gammasphere ● Prompt  -rays from many rotational bands K=16+ Isomer Activation ● Ta( 178 Hf, 178 Hf)Ta ● 73% to 86% E Coul ● Offline counting of 16 + (t 1/2 =31y) isomer decay cascade 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. Triple-Coincidence  -ray Data E  (keV) Count

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

10. 178 Hf Level Scheme

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

12. Treatment of K-forbidden Transitions Spin-Dependent Mixing (“SDM”) of Bohr and Mottelson “H” H can be written as H(I i K i  I f K f ) Log H/H min K i =0  K f =8 K i =0  K f =6 K i =0  K f =4 I f -K f

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

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

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

16. Matrix Elements Populating K π =8 - Isomer Band I GSB II Alaga Rule Attenuated to preserve isomer t 1/2

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

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

19. The K π =6 + Isomer Band No fitting. Calculation: two choices of relative phase of and Relative  -ray Yields  scat (deg)

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

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

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

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

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

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

26. Measured 16 + Band Matrix Elements (eb) I GSB Spin I f in K=16 + Band

27. Gamma Band Ground State Band Band “A” K=4 + Band K=6 + Isomer Band Second K=8 - Band K=8 - Isomer Band K=16 + Isomer Band K-allowed K-forbidden 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 a Calculated from b b M.B. Smith, et al., PRC 68, 031302 (2003) c R.B. Firestone Table of Isotopes, vol. 2 (Wiley & Sons, New York, 1996) 8 th ed. Reduced hindrance f (I i  I f ) for selected transitions in 178 Hf.

31. The Goodness of K Good in high-K bands. Total breakdown of K-conservation at I≈12 in low-K bands. High-K Bands ● Highly hindered transitions between high-spin, high-K states ● High-K bands align at higher spin ● Constant moments of inertia of high-K bands Results consistent with collective alignment effects. Expect similar behavior in other deformed nuclei. Low-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

32. B(E ) Reduced Transition Probabilities 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 from GSB

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

34. Calc. Coulomb Excitation Probability IfIf 16 + (99%) GSB (0.6%) 14 - band (0.1%) 1416182022 10 -1 10 0 10 -2 10 -3 10 -4 K=16 + 31 y K=14 - 68  s K=8 - 4 s GSB Calculated Depopulation of 178m2 Hf 58 Ni on 178m2 Hf, 80% Coulomb barrier (230 MeV)

35. Summary ● Populated at least 3 high-K isomer bands in 178 Hf 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 242m Am+ 40 Ar 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 - t 1/2 =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. E  (keV) Count Event-by-Event Doppler-Shift Correction (a) Raw (b) Corrected for Hf-like (c) Corrected for Xe-like

40. ● Activation on natural tantalum targets ● 72% to 88% Coulomb barrier ● Scattered 178 Hf 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 t 1/2 =31 yrs The K=16+ Band Beam Activation Experiment

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.  2 Fit Technique Present: Previous:  2 /NDF Q o /Q o best - 1 Relative GSB  -ray Yields  sc at ( deg)

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

44. I – Total nuclear spin J – Single-particle angular momentum R – Collective rotation K=Ω 1 +Ω 2 The K-Selection Rule

45. Electromagnetic Transition Probabilities

48. E γ i, α i

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

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

51. For axial symmetry Electromagnetic Selection Rules

52. Hindrance Single-particle Estimate “Weisskopf unit”

53. Hindrance Single-particle Estimate Forbiddenness “Weisskopf unit”

54. Symbols Hindrance Forbiddenness f ν =F ν 1/ν “Reduced” Hindrance

55. The K π =8 - Isomer Band ● Matrix elements should – Preserve the 4s half-life, – Not have discontinuities with increasing spin, – Remain below reasonable physical upper bounds. ● Possibilities: – Population via GSB,  -band, or some higher-K band? Second 8- band important? – Multipolarity? E1, E3, E5? – Systematics: SDM, Alaga, some modification?

56. The K π =8 - Isomer Band ● Matrix elements should – Preserve the 4s half-life, – Not have discontinuities with increasing spin, – Remain below reasonable physical upper bounds. ● Possibilities: – Population via GSB,  -band, or some higher-K band? Second 8- band important? – Multipolarity? E1, E3, E5? – Systematics: SDM, Alaga, some modification?