1. Goodness of the K quantum number in deformed nuclei D. Cline, A.B. Hayes, University of Rochester Why study K? The existence of high-K long-lived isomeric states is evidence for axial symmetry High-K states are a powerful probe of nuclear structure Goals: Exploit K-forbidden EM transitions to probe the goodness of K Measure spin dependence of the K-mixing for collective bands built on K-isomers Nuclei studied: 1) 178 Hf 2) 242m Am

2. Low-lying high-K isomers in 178 Hf Weisskopf hindrance factors F W for high-K isomer decay range from 10 3 -10 13 Reduced hindrance factors f ν range from 24 – 165 per degree of forbiddenness Thus K is a good quantum number implying axial symmetry

3. Coulomb excitation of high-K isomers in 178 Hf Motivation: Highly K-forbidden Coulomb excitation of the 1147 keV (4 sec) K=8 - isomer was observed by Hamilton et al (1982) and confirmed by Xie et al (1993) [N.B. 8 - to ground band 8 + E1 transition has B(E1:8 - →8 + ) = 5.1(3)x10 -14 W.u.] X-ray triggered depopulation of the 2447 keV (31 year) K= 16 + isomer claimed by Collins et al (1999→). Refuted by Ahmad et al. (2001→) Goal: Elucidate pathways leading to Coulomb excitation of the K=8 - isomer Experiments: 1)Coulomb excitation of 178 Hf by 650 MeV 136 Xe; Chico/Gammasphere, (1999) Physical Review Letters 89 (2002) 242501 2)Excitation function for 16 + isomer of 178 Hf beam at 73%—86% barrier (2003) Physical Review Letters 96 (2006) 042505 Physical Review C75 (2007) 034308 Adam Hayes; Ph.D. thesis, Rochester, (2005) 3)Coulomb excitation of 985 MeV 178 Hf beam by a 208 Pb target (2008)

4. Ge detector CHICO Scattering angle: 12   85  (Front Part) 95   168  (Back Part) Azimuthal angle total: 280  of 360  Position resolution:  1  in  and  4.6  in  Solid angle: 69% of 4π Time resolution:  500 ps Mass resolution Δm/m = 5% CHICO * M.W.Simon, D. Cline, C.Y. Wu R.W. Gray, R. Teng. C. Long Nucl. Inst. Meth. A452 (2000) 205 * Work supported by the NSF

6. Coulomb excitation data analysis Gamma-ray spectra analyzed using Radware: D.C. Radford; Nucl. Inst. Meth. A361 (1995) 297 Eλ matrix elements fit to Coulomb excitation yields using the Rochester semi-classical least-squares search code Gosia: T. Czosnyka, D. Cline, C.Y.Wu, (University of Rochester, 1980, Major updates 2008-09) Can fit <1000 matrix elements coupling 100 levels to thousands of data Website:http://www.pas.rochester.edu/~cline/Gosia/index.htmlhttp://www.pas.rochester.edu/~cline/Gosia/index.html

7. Coulomb excitation of 178 Hf by 650 MeV 136 Xe A.B. Hayes 1, D. Cline 1, C.Y. Wu 1, M.W. Simon 1, R. Teng 1, J. Gerl 2, Ch. Schlegel 2, H.J.Wollersheim 2, A.O. Macchiavelli 3, K. Vetter 3, P. Napiorkowski 4, J. Srebrny 4 1) Rochester, 2) GSI, 3) LBNL, 4) Warsaw Physical Review Letters 89 (2002) 242501

8. 178 Hf Beam Activation for K=16 +, 31 yr Isomer A.B. Hayes 1, D. Cline 1, C.Y. Wu 1, H. Amro 2, C. Beausang 2, D. Meyer 2, R. Casten 2, A. Heinz 2, A. Hecht 2, R. Hughes 2, C. Lister 3, D. Seweryniak 3 1) Rochester, 2) Yale, 3) ANL 858 MeV 178 Hf beam from Argonne ATLAS facility Coulomb excited by stack of five 1mg/cm 2 Ta foils at 73%—86% Coulomb barrier Measured 178m2 Hf, K=16 + [31 year] isomer activity in Ta catcher foils

9. Coulomb excitation pathways to High-K isomer bands in 178 Hf

10. Probe four ranges of K in the GSB GSB→4 + : 2≤K≤6 GSB→6 + : 4≤K≤8 GSB→8 - : 5≤K≤11 GSB→16 + : 14≤K≤18 Wave functions are mixed for I GSB >12, I gamma >12 B(Eλ) values saturate at ~1 W.u. K-Mixing in Low-K Wave Functions of 178 Hf

11. Summary for prior 178 Hf work Populated the K= 6 +, 8 -, 14 -, and 16 + isomeric bands at 10 -4 probability Elucidated possible pathways leading to Coulomb excitation of K isomers. Measured average B(Eλ) strengths The data imply that there is massive break down of the K quantum number at high spin in the ground band and gamma band whereas K is conserved in high-K bands. No evidence of a state required to mediate photo depopulation of the K=16 + isomer claimed by Collins et al. Observation of direct γ-ray transitions from the ground to K=16 + bands at high spin would confirm our hypothesis.

12. Coulomb excitation of 985 MeV 178 Hf beam by a 208 Pb target A.B. Hayes 1, D. Cline 1, C.Y. Wu 2, M.P. Carpenter 3, J.J. Carroll 4, D.M Cullen 5, R.V.F. Janssens 3, S.A. Karamian 6, T. Lauritsen 3, N.M. Lumley 5, P.J.R. Mason 5, S.V. Rigby 7, D. Seweryniak 3, T.P.D. Swan 8, P.M. Walker 8, S. Zhu 3 1) Rochester, 2) LLNL, 3) ANL, 4) Youngstown, 5 Manchester, 6 Dubna, 7 Liverpool, 8 Surrey Chico plus Gammasphere using 93 Ge detectors Target was 500μg/cm 2 208 Pb, (99.86% enrichment) on 40μg/cm 2 carbon backing Ran 0.6 pnA 178 Hf beam for ~100hours at 90% of the Coulomb barrier Collected 2.75x10 9 p-p-γ events: 50 times more than prior experiment Contamination of 179 Hf etc <10 -4 : 100 times better than prior experiment Observed 368 transitions connecting 185 levels in 18 collective bands Extended collective bands up to spin 26ħ: Added ~57 new levels

13. γ-ray spectrum gated on transitions in the K=16 + isomer band Triple γ-γ-γ spectrum gated on the 377keV (18 + →17 + ) plus 398keV (19 + →18 + ) peaks Clean well-resolved spectra Peak to background ratio ~100:1 Peak areas up to several thousand counts

14. Positive-parity states energies versus I(I+1) for 178 Hf

15. Kinematic moments of inertia for positive-parity states in 178 Hf

16. Kinematic moments of inertia for negative-parity states in 178 Hf

17. γ-decay feeding of the K=6 + (77ns) isomer band

18. Hindrances for B(M1) transitions to the K=6 + (77ns) isomer band Conclusion: Reduced hindrance at higher spins suggests increase in K-mixing Mixing is large at spins where S-band crosses the γ–band and K=6 + bands

19. γ-decay feeding to the K=8 - (4.0s) isomer band

20. Hindrances for B(E1) transitions to the K=8 - (4.0s) isomer band Conclusions: Hindrance is reduced by a factor of 10 9 for E1 transitions from the S band Compelling evidence for appreciable K mixing in the S band The E3 excitation provides the dominant pathways in Coulomb excitation

21. γ-decay feeding to the K=16 + (31y) isomer band

22. Hindrances for B(E2/M1) transitions to the K=16 + (31y) isomer band Conclusions: Expected direct γ-ray feeding from the gsb at high spin not observed Possible K=14 + band feeds strongly into the K=16 + isomer band Possible allowed Coulomb excitation pathway would be via the S→K=14 + →K=16 + Angular distribution analysis needed to confirm spin and multi-polarity assignments

23. K isomers in 178 Hf: Summary Greatly expanded the nuclear spectroscopic information for 178 Hf. Observe 368 transitions involving 185 levels in 18 rotational bands Confirmed large breakdown of K at higher spins in lower K bands Discovered important pathways for Coulomb excitation of K-isomer bands in 178 Hf The predicted direct γ-ray branches from the ground to K=16 + band were not observed These preliminary results consistent with importance of the Coriolis term in K mixing Coulomb excitation and γ-ray angular distribution analyses required to elucidate fully the detailed Coulomb-excitation pathways and contributing E λ matrix elements.

24. Motivation: 1.Measure coupling between K=5 - isomer band and low-K bands Experiment: 1.Coulomb excite a 98% pure isomeric target, 480  g/cm 2 242m Am on 5mg/cm 2 Ni. ~10 3 times greater sensitivity to the isomer band than 178 Hf 2. 242m Am( 40 Ar, 40 Ar) 242m Am at 170 MeV using ATLAS (Argonne) 3.Used CHICO plus Gammasphere (101 Ge) + 5 LEPS detectors. 4.Am recoils stopped in target 5.Target activity 1.6 milliCurie: Count rates of 1MHz alphas plus 500kHz x-rays Study of the 242m Am, 48.6keV, K  =5 -, (t 1/2 =141 y) isomer A.B. Hayes 1, D. Cline 1, K.J. Moody 2, C.Y. Wu 2, J.A. Becker 2, M.P. Carpenter 3, J.J. Carroll 4, D. Gohlke 4, J.P. Greene 3, A.A. Hecht 3, R.V.F. Janssens 3, S.A. Karamian 5 T. Lauritsen 3, C.J. Lister 3, A.O. Macchiavelli 6, R.A. Macri 2, R. Propri 4, D. Seweryniak 3, X. Wang 3, R. Wheeler 4, S. Zhu 3 1) Rochester, 2) LLNL, 3) ANL, 4) Youngstown, 5) Dubna, 6) LBNL

25. The 242m Am, 48.6keV, K  =5 -, (t 1/2 =141 y) isomer

26. 242m Am Coulomb excitation  -ray spectrum

27. 242 Am Level Scheme New levels are shown in bold. Unconnected transitions were not observed. K = 0 - K = 3 - K = 5 - K = 6 -

28. Neutron-proton multiplets in 242 Am New levels are shown in bold. Previously known levels from Salicio et al., Phys. Rev. C 37, 2371 (1988). π[523]5/2 - ± ν[631]1/2 + π[523]5/2 - ± ν[622]5/2 + π[523]5/2 - ± ν[624]7/2 +

29. Coriolis band mixing for the K=5 - and K=6 - bands in 242 Am Assumptions: Strongly-deformed axially-symmetric rotor model ΔK=1 Coriolis band mixing Results: Determined wavefunctions strongly mixed; 50-50% at I = 6 - to 25-75% at I = 17 - Measured Coriolis interaction increases from 6.8 keV [I = 6 - ] to 24 keV [I = 17 - ] Intrinsic quadrupole moment Q 0 = 12.0 e.b Intrinsic = -0.180 e.b g K -g R equals +0,080 and +0.100 for intrinsic K=5 - and K=6 - bands Intrinsic = -0.280 nm

30. Gamma-ray yield data Alaga Mixing

32. Known K=3 -  Decays New levels are shown in bold. Transitions with thin arrows from Salicio et al. Unconnected levels were not observed. 1   2 K-allowed K-forbidden transitions to K=0 - band have comparable strength to K-allowed transitions to the K=5 - band Explanation  K=2 - / K=3 - Coriolis mixing

33. K-isomers in 242 Am: Summary Added 29 new states Identified 6- rotational band nearly degenerate with 5- isomer band Alaga Rule applied to observed states does not reproduce Coulomb excitation Rotor + two-state mixing model recovers Alaga rule (no shell model predictions used) Mixing between 5-, 6- bands reaches ~40% Alignment: g 9/2, i 11/2 neutrons Mixing consistent with Coriolis theory –Chasman’s calculated gives GSB population? –No indication of GSB yield –3 - band head known to decay to g.s. (82% including conversion)  Observed population of tentative 3- band could give highly converted decay to g.s. <10% Strong  K=1 mixing by degeneracy, in contrast to high-  K mixing in 178 Hf

34. K-mixing in strongly-deformed nuclei Coulomb excitation has the experimental sensitivity sufficient to study the evolution of K-mixing with spin of rotational bands built on isomeric states starting from either the ground or isomer state. Demonstrated that isomers can be directly Coulomb excited by identified pathways and multipoles not available to isomer decay Directly measure Eλ plus M1 matrix elements which probe nuclear structure of the rotational bands built on the unusual configurations that lead to isomerism. Results consistent with Coriolis effects playing a significant role in the onset of K-mixing at higher spin in the rotational bands.

35. This work was supported by: Air Force Office of Scientific Research National Science Foundation U.S. Department of Energy Acknowledgements

37. Summary Mixing consistent with Coriolis theory Chasman’s calculated (for mass 244) gives GSB population? –No indication of GSB yield –3- band head known to decay to g.s. (82% including conversion)  Observed population of 3- band implies highly converted decay to g.s. <10% Strong  K=1 mixing via degeneracy in 242 Am Contrasts with high-  K mixing in 178 Hf

38. K Quantum Number K is the projection of the total spin I on the nuclear symmetry axis K is a conserved quantum number for axially symmetric nuclei K-selection rule:  K  – is the multipole order of EM transition Degree of forbiddenness =  K - –Transition is “ -times” forbidden

39. Moment of Inertia vs. Rotational Frequency

40. Summary A 98% pure 242m Am K=5 - isomer target Coulomb excited to I~18 30 states added including discovery of a new K=6 - band Unexpectedly strong K=5 - to K=6 -  K=1 Coriolis coupling Provided an accurate measure of residual interactions K=5 - isomer state coupled to I,K=1,0 - ground state through K=3 - band—consistent with ΔK=1 Coriolis mixing with K=2 - band Coriolis coupling between the K=3 - and 2 - bands in being investigated The coupling of the mixed K=3 - - 2 - bands with the K=5 - and K=0 - bands is being investigated

41. Nuclear Structure and Band Mixing 242 Am Complete  K=1 Coriolis mixing of K=5 - and K= 6 - bands due to level degeneracy K=2 - and K=3 - bands Coriolis mixed: decay by comparable E2 strengths to both ground K=0 - and isomeric K=5 - bands ~1 s.p.u. Detailed knowledge of the  K=1 mixed wave functions, Coriolis interaction strength, and intrinsic E2 plus M1 properties. 178 Hf Measured E2 and E3 coupling of K=0+, 2+ bands to K=4+,6+,8-,16+ isomer bands Discovered complete breakdown of K at high spin in nominal low-K bands; whereas K is well conserved for high-K bands K-forbidden transition strengths ~ few single-particle units at high spin (I~12) Results consistent with Coriolis mixing Breadth and scope of these results provide a stringent test of models of nuclear structure for collective nuclei.

42. Summary Added 29 new states Identified 6- rotational band nearly degenerate with 5- isomer band Alaga Rule applied to observed states does not reproduce Coulomb excitation Rotor + two-state mixing model recovers Alaga rule (no shell model predictions used) Mixing between 5-, 6- bands reaches ~40% Alignment: g 9/2, i 11/2 neutrons Mixing consistent with Coriolis theory –Chasman’s calculated gives GSB population? –No indication of GSB yield –3 - band head known to decay to g.s. (82% including conversion)  Observed population of tentative 3- band could give highly converted decay to g.s. <10% Strong  K=1 mixing by degeneracy, in contrast to high-  K mixing in 178 Hf