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

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- 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| ≤

Forbiddenness

Single-particle Estimate

“Weisskopf

unit”

Hindrance

Hindrance

“Reduced” Hindrancefν=Fν1/ν

- 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

Online 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

CHICO Resolution:

1 degree in

4.7 degrees in

500 ps in ΔTOF

5% in mass

Trigger: p + p + (at least one ray)

Count

E (keV)

Count

E (keV)

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

“H”

H can be written as H(IiKiIfKf)

Relative -ray Yields

scat(deg)

=

(∓30%)

=

Solid/Dashed:

two relative

phases of

<K=4|E2|GSB>

and

<K=4|E2| >

K-allowed

K-forbidden

K=4+Band

Gamma Band

K=16+IsomerBand

Band “A”

K=6+IsomerBand

K=8-IsomerBand

SecondK=8-Band

Ground State Band

E2

E2

E2

Relative -ray Yields

Solid: Total calc. yield

Dotted: γ-band path

Dashed: GSB path

scat(deg)

IGSB

I

AlagaRule

Attenuatedto preserve isomer t1/2

K-allowed

K-forbidden

K=4+Band

Band “A”

K=16+IsomerBand

Gamma Band

K=6+IsomerBand

K=8-IsomerBand

SecondK=8-Band

Ground State Band

E3

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)

Relative -ray Yields

scat(deg)

K-allowed

K-forbidden

K=4+Band

Gamma Band

Band “A”

K=16+IsomerBand

K=6+IsomerBand

K=8-IsomerBand

SecondK=8-Band

Ground State Band

E2

E2

E2

E2

E2

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

Solid line: SDMDashed line: Alaga

scat (deg)

Ge Detector

Faraday Cup

Collimator

178Hf Beam

Ta (natural) target stack

Tantalum Beam Stop

Ta foil and cylindrical“catcher” stack

Si Counter with aperture

Count

-Ray Energy (keV)

Count

-ray Energy (keV)

Activity (h-1)

Time-Averaged Mid-Target Projectile Energy (MeV)

Solid: Best fit (individual reduced m.e.)

Dashed: SDM model Dotted: Linear model

IGSB

<If K=16|| E2 || Ii K=0> (eb)

Spin If in K=16+ Band

K-allowed

K-forbidden

K=4+Band

Band “A”

K=16+IsomerBand

Gamma Band

K=6+IsomerBand

K=8-IsomerBand

SecondK=8-Band

Ground State Band

E2 Excitation & Feed

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

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

Hindrance Systematics

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

Good 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.

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

from -band

Probes of

individual

K-admixtures.

6+: probes 4≤K≤8

8-:

probes 5≤K≤11

Calc. Coulomb Excitation Probability

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

- 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.

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

- 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)

END

Phys. Rev. C 75, 034308 (2007)

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

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

(a) Raw

Count

(b) Corrected for Hf-like

(c) Corrected for Xe-like

E (keV)

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

- 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.

Relative GSB -ray Yields

2/NDF

scat(deg)

Qo/Qobest - 1

2 Fit Technique

Present:

Previous:

The K-Selection Rule

I – Total nuclear spin

J – Single-particle angular momentum

R – Collective rotation

K=Ω1+Ω2

Electromagnetic Transition Probabilities

Electromagnetic Transition Probabilities

Electromagnetic Transition Probabilities

Electromagnetic Transition Probabilities

Eγi, αi

Shapes and K-Conservatione.g. The Bohr Hamiltonian

γ-deformation

β-deformation

Special case: axial symmetry

Images from www.europhysicsnews.com.

1Rotational 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

For axial symmetry

Hindrance

Single-particle Estimate

“Weisskopf

unit”

Hindrance

Single-particle Estimate

“Weisskopf

unit”

Forbiddenness

Symbols

Forbiddenness

Hindrance

“Reduced” Hindrance

fν=Fν1/ν

- 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?

- 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?