The loss of k selection in 178 hf a b hayes next generation isomers workshop 2 nd april 2007
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The Loss of K-Selection in 178 Hf A. B. Hayes “Next Generation Isomers” workshop, 2 nd 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

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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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The loss of k selection in 178 hf a b hayes next generation isomers workshop 2 nd april 2007

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 a b hayes next generation isomers workshop 2nd april 2007

The Loss of K-Selection in 178Hf

K-Selection Rule & Hindrance

Motivation

Two Experiments

Results

Conclusions

Future work


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

The K-Selection Rulefor axially symmetric systems

I – Total nuclear spin

J – Single-particle angular momentum

R – Collective rotation

K = Ω1+Ω2

|K| ≤ 


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Forbiddenness

Single-particle Estimate

“Weisskopf

unit”

Hindrance

Hindrance

“Reduced” Hindrancefν=Fν1/ν


Motivation

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


Two coulomb excitation experiments

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 Experiments

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


Online experiment chico and gammasphere

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)


Triple coincidence ray data

Count

E (keV)

Triple-Coincidence -ray Data


Prompt delayed data

Count

E (keV)

Prompt-Delayed Data


178 hf level scheme

178Hf Level Scheme


Iterative fit process for strongly coupled bands

Iterative Fit Process for Strongly-Coupled Bands

Gamma Band Relative -ray Yields

(including the Mikhailov term)

scat(deg)


Treatment of k forbidden transitions spin dependent mixing sdm of bohr and mottelson

Ki=0Kf=8

Ki=0Kf=6

Ki=0Kf=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(IiKiIfKf)


The k 4 band

Relative -ray Yields

scat(deg)

=

(∓30%)

=

The Kπ=4+Band

Solid/Dashed:

two relative

phases of

<K=4|E2|GSB>

and

<K=4|E2|  >


Deduced population paths

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

Deduced Population Paths

E2

E2

E2


The k 8 isomer band

The Kπ=8- Isomer Band

Relative -ray Yields

Solid: Total calc. yield

Dotted: γ-band path

Dashed: GSB path

scat(deg)


Matrix elements populating k 8 isomer band

IGSB

I

Matrix Elements Populating Kπ=8- Isomer Band

AlagaRule

Attenuatedto preserve isomer t1/2


Deduced population paths1

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

Deduced Population Paths

E3

E3

E2


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

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 loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

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)


Deduced population paths2

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

Deduced Population Paths

E2

E2

E2

E2

E2


The k 16 band online expt prompt ray yields

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

Relative -ray Yield (norm to 8+GSB6+GSB)

Solid line: SDMDashed line: Alaga

scat (deg)


Beam activation experiment

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


Raw singles activity

Raw Singles Activity

Count

-Ray Energy (keV)


Doubles activity gated on 6 4 in gsb

Count

-ray Energy (keV)

Doubles Activity Gated on 6+4+ in gsb


Measured activation function

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


Measured 16 band matrix elements

IGSB

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

Spin If in K=16+ Band

Measured 16+ Band Matrix Elements


Deduced population paths3

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

Deduced Population Paths

E2 Excitation & Feed


Results and conclusions

Results and Conclusions

  • Moments of Inertia

  • Hindrance systematics

  • K-mixing

  • Comment on energy storage


Moments of inertia

Moments of Inertia

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


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Hindrance Systematics

Reduced hindrance f(IiIf) 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.


The goodness of k

  • 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 K

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.


B e reduced transition probabilities

B(E) 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 reduced transition probabilities1

B(E) Reduced Transition Probabilities

from -band

Probes of

individual

K-admixtures.

6+: probes 4≤K≤8

8-:

probes 5≤K≤11


Calculated depopulation of 178m2 hf 58 ni on 178m2 hf 80 coulomb barrier 230 mev

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

Calculated Depopulation of 178m2Hf58Ni on 178m2Hf, 80% Coulomb barrier (230 MeV)


Summary

Summary

  • 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

Current Work

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 fair studies

Possibilities for FAIR 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)


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

END

Phys. Rev. C 75, 034308 (2007)

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

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


Event by event doppler shift correction

(a) Raw

Count

(b) Corrected for Hf-like

(c) Corrected for Xe-like

E (keV)

Event-by-Event Doppler-Shift Correction


The k 16 band beam activation experiment

The K=16+ BandBeam 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 4 band fits

Lessons from K≦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.


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Relative GSB -ray Yields

2/NDF

scat(deg)

Qo/Qobest - 1

2 Fit Technique

Present:

Previous:


Rotational bands in 178 hf built on states of i k

Rotational Bands in 178Hfbuilt on states of I=K


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

The K-Selection Rule

I – Total nuclear spin

J – Single-particle angular momentum

R – Collective rotation

K=Ω1+Ω2


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Electromagnetic Transition Probabilities


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Electromagnetic Transition Probabilities


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Electromagnetic Transition Probabilities


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Electromagnetic Transition Probabilities

Eγi, αi


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Shapes and K-Conservatione.g. The Bohr Hamiltonian

γ-deformation

β-deformation

Special case: axial symmetry

Images from www.europhysicsnews.com.


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

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).


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Electromagnetic Selection Rules

For axial symmetry


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Hindrance

Single-particle Estimate

“Weisskopf

unit”


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Hindrance

Single-particle Estimate

“Weisskopf

unit”

Forbiddenness


The loss of k selection in 178hf a b hayes next generation isomers workshop 2nd april 2007

Symbols

Forbiddenness

Hindrance

“Reduced” Hindrance

fν=Fν1/ν


The k 8 isomer band1

The Kπ=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 8 isomer band2

The Kπ=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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