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

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

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### END states

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

The Loss of K-Selection in 178Hf

K-Selection Rule & Hindrance

Motivation

Two Experiments

Results

Conclusions

Future work

The K-Selection Rulefor axially symmetric systems

I – Total nuclear spin

J – Single-particle angular momentum

R – Collective rotation

K = Ω1+Ω2

|K| ≤

Single-particle Estimate

“Weisskopf

unit”

Hindrance

Hindrance

“Reduced” Hindrancefν=Fν1/ν

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

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 ExperimentsOnline 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

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)

178Hf Level Scheme

Iterative Fit Process for Strongly-Coupled Bands

Gamma Band Relative -ray Yields

(including the Mikhailov term)

scat(deg)

Ki=0Kf=8

Ki=0Kf=6

Ki=0Kf=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(IiKiIfKf)

Relative -ray Yields

scat(deg)

=

(∓30%)

=

The Kπ=4+BandSolid/Dashed:

two relative

phases of

<K=4|E2|GSB>

and

<K=4|E2| >

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 PathsE2

E2

E2

The Kπ=8- Isomer Band

Relative -ray Yields

Solid: Total calc. yield

Dotted: γ-band path

Dashed: GSB path

scat(deg)

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 PathsE3

E3

E2

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)

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)

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 PathsE2

E2

E2

E2

E2

The K=16+ BandOnline expt. - Prompt -ray yields

Relative -ray Yield (norm to 8+GSB6+GSB)

Solid line: SDMDashed line: Alaga

scat (deg)

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

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

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 PathsE2 Excitation & Feed

Results and Conclusions

- Moments of Inertia
- Hindrance systematics
- K-mixing
- Comment on energy storage

Moments of Inertia

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

Reduced hindrance f(IiIf) 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.

- 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 KGood 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.

B(E states) 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

B(E states) Reduced Transition Probabilities

from -band

Probes of

individual

K-admixtures.

6+: probes 4≤K≤8

8-:

probes 5≤K≤11

Calc. Coulomb Excitation Probability states

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)Summary states

- 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.

Current Work states

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

Possibilities for statesFAIR 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)

Phys. Rev. C 75, 034308 (2007)

Phys. Rev. Lett. 96, 042505 (2006)

Phys. Rev. Lett. 89, 242501 (2002)

(a) Raw states

Count

(b) Corrected for Hf-like

(c) Corrected for Xe-like

E (keV)

Event-by-Event Doppler-Shift CorrectionThe K=16+ Band statesBeam 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

Lessons from K states≦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.

Rotational Bands in states178Hfbuilt on states of I=K

The K-Selection Rule states

I – Total nuclear spin

J – Single-particle angular momentum

R – Collective rotation

K=Ω1+Ω2

Electromagnetic Transition Probabilities states

Eγi, αi

Shapes and K-Conservation statese.g. The Bohr Hamiltonian

γ-deformation

β-deformation

Special case: axial symmetry

Images from www.europhysicsnews.com.

1 statesRotational 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).

Electromagnetic Selection Rules states

For axial symmetry

The K statesπ=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?

The K statesπ=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?

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