Goodness of the K quantum number in deformed nucleiD. 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) 178Hf 2) 242mAm

Low-lying high-K isomers in 178Hf

• Weisskopf hindrance factors FW for high-K isomer decay range from 103 -1013

• Reduced hindrance factors fν range from 24 – 165 per degree of forbiddenness

• Thus K is a good quantum number implying axial symmetry

Coulomb excitation of high-K isomers in 178Hf

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 178Hf by 650 MeV 136Xe; Chico/Gammasphere, (1999)

Physical Review Letters 89 (2002) 242501

2) Excitation function for 16+ isomer of 178Hf beam at 73%—86% barrier (2003)Physical Review Letters 96 (2006) 042505Physical Review C75 (2007) 034308Adam Hayes; Ph.D. thesis, Rochester, (2005)

3) Coulomb excitation of 985 MeV 178Hf beam by a 208Pb target (2008)

Ge detectorCHICO

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

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.html

Coulomb excitation of 178Hf by 650 MeV 136XeA.B. Hayes1, D. Cline1, C.Y. Wu1, M.W. Simon1, R. Teng1, J. Gerl2, Ch. Schlegel2, H.J.Wollersheim2, A.O. Macchiavelli3, K. Vetter3, P. Napiorkowski4, J. Srebrny4

1)Rochester, 2)GSI, 3)LBNL, 4)Warsaw

Physical Review Letters 89 (2002) 242501

178Hf Beam Activation for K=16+, 31 yr Isomer A.B. Hayes1, D. Cline1, C.Y. Wu1, H. Amro2, C. Beausang2, D. Meyer2, R. Casten2,

A. Heinz2, A. Hecht2, R. Hughes2, C. Lister3, D. Seweryniak3

1)Rochester, 2)Yale, 3)ANL

• 858 MeV 178Hf beam from Argonne ATLAS facility Coulomb excited by stack of five 1mg/cm2 Ta foils at 73%—86% Coulomb barrier

• Measured 178m2Hf , K=16+ [31 year] isomer activity in Ta catcher foils

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

• 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 IGSB

>12, Igamma>12

• B(Eλ) values saturate at

~1 W.u.

K-Mixing in Low-K Wave Functions of 178Hf

Summary for prior 178Hf 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.

Coulomb excitation of 985 MeV 178Hf beam by a 208Pb targetA.B. Hayes1, D. Cline1, C.Y. Wu2, M.P. Carpenter3, J.J. Carroll4, D.M Cullen5,

R.V.F. Janssens3, S.A. Karamian6, T. Lauritsen3, N.M. Lumley5, P.J.R. Mason5, S.V. Rigby7, D. Seweryniak3, T.P.D. Swan8, P.M. Walker8, S. Zhu3

1)Rochester, 2)LLNL, 3)ANL, 4)Youngstown, 5Manchester, 6Dubna, 7Liverpool, 8Surrey

• Chico plus Gammasphere using 93 Ge detectors

• Target was 500μg/cm2 208Pb, (99.86% enrichment) on 40μg/cm2 carbon backing

• Ran 0.6 pnA 178Hf beam for ~100hours at 90% of the Coulomb barrier

• Collected 2.75x109 p-p-γ events: 50 times more than prior experiment

• Contamination of 179Hf 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

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

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

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

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

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

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

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

Hindrances for B(E1) transitions to the K=8- (4.0s) isomer band

Conclusions:• Hindrance is reduced by a factor of 109 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

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

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

K isomers in 178Hf: Summary

• Greatly expanded the nuclear spectroscopic information for 178Hf.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 178Hf

• 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 Eλ matrix elements.

Motivation:

1. Measure coupling between K=5- isomer band and low-K bands

Experiment:

1. Coulomb excite a 98% pure isomeric target, 480 g/cm2 242mAm on 5mg/cm2 Ni.

~103 times greater sensitivity to the isomer band than 178Hf

2. 242mAm(40Ar,40Ar)242mAm 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 242mAm, 48.6keV, K =5-, (t1/2=141 y) isomer

A.B. Hayes1, D. Cline1, K.J. Moody2, C.Y. Wu2, J.A. Becker2, M.P. Carpenter3, J.J. Carroll4, D. Gohlke4, J.P. Greene3, A.A. Hecht3, R.V.F. Janssens3, S.A. Karamian5 T. Lauritsen3, C.J. Lister3,

A.O. Macchiavelli6, R.A. Macri2, R. Propri4, D. Seweryniak3, X. Wang3, R. Wheeler4, S. Zhu3

1) Rochester, 2) LLNL, 3) ANL, 4)Youngstown, 5) Dubna, 6) LBNL

The 242mAm, 48.6keV, K =5-, (t1/2=141 y) isomer

242mAm Coulomb excitation -ray spectrum

242Am Level SchemeNew levels are shown in bold.

Unconnected transitions were not observed.

K = 0- K = 3- K = 5- K = 6-

Neutron-proton multiplets in 242AmNew 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+

Coriolis band mixing for the K=5- and K=6- bands in 242Am

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 Q0 = 12.0 e.b

• Intrinsic <K=6-|E2|K=5-> = -0.180 e.b

• gK-gR equals +0,080 and +0.100 for intrinsic K=5- and K=6- bands

• Intrinsic <K=6-|M1|K=5-> = -0.280 nm

Gamma-ray yield data AlagaMixing

Known K=3- DecaysNew 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

K-isomers in 242Am: 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: g9/2, i11/2 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 178Hf

K 1 j K 0.63

PK ,K 1 0.5

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.

This work was supported by:

• Air Force Office of Scientific Research

• National Science Foundation

• U.S. Department of Energy

Acknowledgements

Summary

• Mixing consistent with Coriolis theoryChasman’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 242Am Contrasts with high-K mixing in 178Hf

K 1 j K 0.63

PK ,K 1 0.5

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

Moment of Inertia vs. Rotational Frequency

Summary

• A 98% pure 242mAm 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

Nuclear Structure and Band Mixing242Am

• 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.

178Hf

• 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.

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: g9/2, i11/2 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 178Hf

K 1 j K 0.63

PK ,K 1 0.5