1. University of Rochester
Nuclear structure of high-K isomers: implications for controlled energy release*
D. Cline, A.B. Hayes,
University of Rochester
The K quantum number
Motivation
K-Mixing in 178Hf
The 48.6 keV, K=5- [t1/2 =141 year] isomer in 242mAm
Nuclear Structure Implications
Implications for controlled energy release
*Work supported by AFOSR and NSF
Isomeric states provide a means of storing energy that could have technological benefits if controlled depopulation of such isomers can be achieved.
This talk will focus on studies of the fundamental properties of K-isomeric states since they occur in many nuclei.

2. 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
For axially symmetric nuclei the projection of the angular momentum I on the symmetry axis, denoted by K, is a conserved quantum number.
The K selection rule forbids EM transition multipoles for which the forbiddeness v=ΔK-λ is greater than zero.
K-forbidden EM transitions are forbidden by many orders of magnitude.

3. Motivation for study of high-K isomers
Nuclear physics:
High-K states have unusually simple shell configurations providing a powerful probe of structure and residual interactions in the nuclear many-body system
High-K isomers probe the goodness of the K quantum number in nuclear structure
Quantum electronics:
Evaluate the feasibility of using long-lived isomers for controllable energy storage.
Goals
Measure the fundamental properties of isomeric states by Coulomb excitation
Ascertain the mechanism responsible for electromagnetic population and decay of highly K-forbidden isomeric states
Elucidate the feasibility of triggered depopulation of isomeric states
Knowledge of the electromagnetic properties of isomeric states is essential for studying nuclear structure and evaluating the possibility of triggering depopulation. Therefore the motivation for this work is twofold.
Nuclear Physics: High-K states have unusually simple shell model configurations
High-K isomers are a sensitive probe of the goodness of the K quantum number
Probes axial symmetry and residual interactions.
Quantum electronics:
Evaluate feasibility of using long-lived isomers for controlled energy storage
Goals:
Measure fundamental properties of isomers via heavy-ion induced Coulomb excitation.

4. CHICO* Scattering angle: 12  85 (Front Part) 95  168 (Back Part)
Ge detector
CHICO
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
Use coincident detection of reaction products recoiling from a thin target.
Measure scattering angles and time of flight.
For binary reactions these are sufficient for kinematic reconstruction of the recoil vectors masses and Q values.
This allows Doppler correction on an event by event basis and assignment of gamma transitions to the appropriate product.
Chico was designed and constructed at Rochester with NSF support specifically for use with Gammasphere, and is based on earlier such detectors we built at Rochester.
The reaction products recoil out of the target and are detected by two conical arrays of position-sensitive avalanche detectors, each housing 10 panels.
The active surface covers scattering angles between 12 and 168 degrees in θ and 280 of 360 in φ, that is 69% of a sphere.
The angle resolution is 1 in θ and 4.6 in φ.
Time resolution is 500ps.
Kinematic reconstruction for binary reactions provides a mass resolution of 5%.
Scattering angle: 12  85 (Front Part)
95  168 (Back Part)
Azimuthal angle total:  of 360
Position resolution:  1 in  and  4.6 in 
Solid angle: 69% of 4π
Time resolution:  500 ps
Mass resolution Δm/m = 5%

6. Coulomb excitation of K isomers in 178Hf
Rochester— A. B. Hayes, D. Cline, C. Y. Wu, H. Hua, M. W. Simon, R. Teng;
ANL—R. V. F. Janssens, C. J. Lister, E. F. Moore, R. C. Pardo, D. Seweryniak;
LBNL—A. O. Macchiavelli, K. Vetter; GSI—J. Gerl, Ch. Schlegel, H. J. Wollersheim;
Warsaw—P. Napiorkowski, J. Srebrny;
Yale—J. Ai, H. Amro, C. Beausang, R. F. Casten, A. A. Hecht, A. Heinz, R. Hughes, D. A. Meyer
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 to ground band 8+ E1 transition is K-hindered by a factor 1.9 x 1013]
Possible application of the 2447 keV (31 year) K= 16+ isomer for controllable energy storage. Conflicting results on possible triggering depopulation of this isomer using X-ray radiation by Collins et al (1999→) which is disputed by work of several groups.
Goal:
Elucidate pathways leading to Coulomb excitation of high-K isomers
Physical Review Letters 89 (2002) Physical Review Letters 96 (2006)
Physical Review C (2006) Submitted
The goal of this work was to elucidate the pathways that lead to Coulomb excitation of
high-K isomers. This work was motivated by the K=forbidden Coulomb excitation of the
1147 keV, K=8-, 4 second isomer in Hf. The 7-fold forbidden E1 transition is hindered
by a factor of
This work comprised Adam Hayes thesis and has been published.

7. Coulomb excitation pathways to High-K isomer bands in 178Hf
The essential conclusion of this work is that K remains a good quantum number at these spins in the high-spin K isomer bands which are strongly coupled to the deformation symmetry axis. However, K appears to break down at higher spin values in the ground and gamma bands at spins where alignment occurs.
Thus the K=6+ isomer is populated by three allowed steps or a two step process where one step is singly K forbidden.
The 8- isomer band is populated by K forbidden E3 excitation via high spin K-mixed states in the ground and gamma bands.
The K=16+ isomer is populated by the highest spin states in the ground band both by two step Coulex and mainly by gamma decay since the K=16+ band is 990 keV below the gsb 16+ state.
The Coulex yields directly measure the Eλ matrix elements which can be used to probe the spin dependence of the K admixtures in the ground and gamma bands. The data is insufficient to unambiguously determine all E2 matrix elements, thus we had to use smoothed average values as a function of spin.

8. Stimulated depopulation of the K=16+ isomer in 178Hf
The K-mixing in the ground and gamma bands at high spin results in BE2 and BE3 strengths that are not hindered, i.e. of the order of a single-particle unit. These provide a path for depopulation via heavy-ion induced Coulomb excitation. Unfortunately the depopulation probability is < 1% which is not too useful. Another possible path is via excitation of the negative-parity states but this also has a probability of <1%.
In spite of the very high sensitivity of this work, no state was observed that could mediate photo depopulation of the K=16+ isomer claimed by Collins et al.

9. Summary for 178Hf
Populated the K= 6+,8-, 14-, and 16+ isomeric bands at 10-4 probability and measured Eλ strengths
Elucidated pathways leading to Coulomb excitation of K isomers.
Showed 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.
Have identified possible Coulomb excitation paths to depopulate the K=16+ isomer in 178Hf.
No evidence of a state required to mediate photo depopulation of the K=16+ isomer claimed by Collins et al.

10. The 242mAm, 48.6keV, Kp =5-, (t1/2=141 y) isomer
Am242 has a 48.6keV K=5- isomer with a 141yr halflife. It decays 99.55% by an E4 transition to the 1-, k=0-, ground state that is hindered by a factor of 105 implying that K is conserved for these two states.
There is a I= 3-, K=o- state 4 keV above the K=5- isomer that could mediate depopulation of the isomer if the K inhibition is not applicable. .

11. Study of the 242mAm, 48.6keV, Kp =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
Motivation:
Measure coupling between K=5- isomer band and low-K bands
Experiment:
Coulomb excite a 98% pure isomer target, 500 g/cm2 242mAm on 5mg/cm2 Ni. — ~104 times greater sensitivity to matrix elements coupled to the isomer band than for 178Hf
242mAm(40Ar,40Ar)242mAm at 170 MeV using the ATLAS Linac at (Argonne)
Detect back-scattered Ar (CHICO) in coincidence with one photon in Gammasphere (101 Ge) + 5 LEPS detectors. Am recoils stopped in target
Target activity 1.6 milliCi
In the late 1960’s Livermore produced a 98% enriched 2mg sample of 242Am as a result of a 6 year project that cost multimillions of dollars at that time. Ken Moody recovered the remnants of this material and made a 500microgram/cm2 target on a 5 mg nickel backing. This turned out to be stronger than we wanted producing an activity of 1.6mCi. Fortunately the selectivity of Chico plus GS was sufficient to handle such activity.
This target was Coulomb excited by a 170 MeV Ar40 beam, the backscattered ions detected in Chico while the Am recoils were stopped in the target providing the full gamma resolution of GS.

12. 242mAm Coulomb excitation -ray spectrum
Some predicted we would not see any useful gamma data from this experiment due to the dominance internal conversion. Quite to the contrary, a remarkable gamma spectrum was obtained that it looks like the Coulex of a single superdeformed band. However, it originates from Coulomb excitation of two rotational bands with identical yields. In Coulomb excitation the ground band always is at least an order of magnitude stronger than other bands, whereas here there are two bands with identical population. The transitions labeled red are the band built on the initial K=5- isomer, and the green are from a previously unknown K=6- band.

13. Level Scheme New levels are shown in bold
Level Scheme New levels are shown in bold. Unconnected levels were not observed.
Upper and lower limits on the energies of the K=6- band were deduced by comparing discontinuities in the electron conversion branches to the known energies of the K and L edges in the calculated internal conversion coefficients. In addition two highly-converted interband gamma transitions and possibly a third were observed feeding the K=6- band from the K=5- band which located the K=6- band head at 100 keV

14.  Unidentified 99 keV and 171 keV states
243Am(d,t)242Am Grotdal et al., Physica Scripta 14, 263 (1976) 
Unidentified 99 keV and 171 keV states
The 100 keV and 172 keV energies of the 6- and 7- states in the K=6- band head are further supported by a previous observation of two unassigned states at 99 keV and 171 keV populated with the expected strength in a study of the 243Am(d,t) 242Am reaction.

15. 242Am Level Scheme New levels are shown in bold
242Am Level Scheme New levels are shown in bold. Unconnected transitions were not observed.
This shows the current level scheme derived from the partial analysis of this experiment. The new levels are shown in bold
Thus the 5- was extended from 7- to 17- , the K=3- from 7- to 15-, and the K=6- band, which is the yrast band, was unknown previously.
Decay of the K=3- band to K=5- band is seen. Unfortunately we have not yet been able to convincingly extend the K=0- gsb.
K = K = K = K = 6-

16. Gamma yields for the K=5- and K=6- following Coulomb excitation of 242Am
In-band transitions
Assuming identical mixing of the two 6- states plus strong mixing at higher spin reproduces the Coulex yields remarkably well.
This shows the in-band delta I = 2 and 1 transition yields. Even reproduce wiggles in spin dependence.

17. Interband transitions
Gamma yields for the K=5- and K=6- following Coulomb excitation of 242Am
Interband transitions
The interband transition yields also are well reproduced.

18. Coulomb excitation of the mixed K=5- and K=6- bands in 242Am
Assumptions:
Strongly-deformed axially-symmetric rotor model
ΔK=1 Coriolis band mixing
Conclusions:
Determined band wavefunctions strongly mixed; 50-50% at I = 6- to 25-75% at I = 17-
The Coriolis interaction between bands measured to be 6.8 keV at I = 6- increasing to 24 keV at I = 17-
Intrinsic quadrupole moment Q0 = 12.0 e.b
Intrinsic <K=6-|E2|K=5-> = e.b
gK-gR equals +0,080 and for intrinsic K=5- and K=6- bands
Intrinsic <K=6-|M1|K=5-> = nm,
The analysis of the Coulomb excitation yields shown plus the observed interband and in-band decays, using the above assumptions, determined the intrinsic quadrupole moment to be in good agreement with neighboring even A Pu and Cm nuclei. This determines the quadrupole collectivity.
The Coulex data require that the 6- states have complete mixing while the higher states have a 1 to 3 intensity mixture in the mixed wavefunctions
The observed magnetic properties determine the p-n shell structure.

19. Neutron-proton multiplets in 242Am New levels are shown in bold
Neutron-proton multiplets in 242Am 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/ π[523]5/2- ± ν[622]5/ π[523]5/2- ± ν[624]7/2+
The three p-n multiplets lead to the states observed. The gsb and isomer bands result from antiparallel and parallel coupling of the same proton and neutron orbits.
The new 6- band is the parallel coupling corresponding to a known K=1- band.
The K=3- and 2- comprise the third expected low-lying pair of configurations.
The delta K=1 between the K=3- and 2- also leads to first order Coriolis coupling. The K=3- band decays to the K=5- band via allowed E2 transitions. It also decays to the ground K=0- band via the K=2- Coriolis mixed component. Thus here we have a depopulation pathway between the K=5- and K=0- ground band.

20. Known K=3-  Decays New levels are shown in bold
Known K=3-  Decays New levels are shown in bold. Transitions with thin arrows from Salicio et al. Unconnected levels were not observed.
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
The delta K=1 between the K=3- and 2- also leads to first order Coriolis coupling. The K=3- band decays to the K=5- band via allowed E2 transitions. The expected branch to the K=5- admixture in the 6- band is at the limit of our sensitivity.
The K=3- band also decays to the ground K=0- band via the K=2- Coriolis mixed component. Thus here we have a depopulation pathway between the K=5- and K=0- ground band.
Salicio et al have measured transition from the I,K 3-,3 and 4-,3 states to the K=0- GSB and to the K=5- isomer with similar gammaray intensities.
The K-forbidden I,K 3-,3 to K=0- transitions have 15% to 50% gamma branches, compared to 20% I,K 3-,3 to 5-,5 branch, calculated from the measured gamma branching and E2/M1 mixing ratios. This competitive strength is consistent with a substantial K=2- admixture in the K=3- band.
The K=5- isomer decays to the I,K 1-,0 ground state by a once K-forbidden [v=1] E4 transition with a hindrance of reflecting the purity of the K-5- isomer. That is the K=1- admixture in the I,K=1-,0 ground state or of K<5 in the 5- isomer must be negligible. Note that the K=6- band cannot mix into the 5- band head resulting in a virtually pure K=5- isomeric state.
Unfortunately in our experiment we cannot see the decay from the 3- and 4- state in the K=3- band because the only observable gamma transitions are buried in the intense deexcitation gamma strength from the strongly-populated K=5- and 6- bands. However, combining the Salicio branching ratio with the wavefunctions we can derive at higher spin for the mixed K=3-/2- band should provide the needed information to evaluate possible depopulation paths. Reliable calculations of the highly-forbidden I,K 5-,5 to I,K 3-,0 4 keV BE2 should be possible using the information provided by the present study.
1    2
K-allowed

21. Nuclear Structure and Band Mixing
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
242Am
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.
Breadth and scope of these results provide a stringent test of models of nuclear structure for collective nuclei.

22. Isomer Depopulation 242mAm K=5- Isomer 178m2Hf K=16+ Isomer
No useful state found to mediate photo-depopulation
Calculated heavy-ion Coulomb depopulation (E2, E3) to ground and K=14- bands are 1% effects.
Depopulation cross sections are small.
242mAm K=5- Isomer
Heavy-ion E2 excitation of K=3- band observed ~1% at IK=3=11-
The Coriolis mixed K=3- and K=2- bands could mediate depopulation of the K=5- isomer to K=0- ground band
Measured properties sufficient to predict reliable depopulation cross sections for the K=5- isomer.
Studies of the fundamental properties of K isomers have determined the configurations and residual interactions needed to make reliable theoretical predictions of isomer depopulation mechanisms

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

24. END