The loss of k selection in 178 hf a b hayes next generation isomers workshop 2 nd april 2007
Sponsored Links
This presentation is the property of its rightful owner.
1 / 56

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


  • 72 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

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

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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| ≤ 


Forbiddenness

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 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

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)

Triple-Coincidence -ray Data


Count

E (keV)

Prompt-Delayed Data


178Hf Level Scheme


Iterative Fit Process for Strongly-Coupled Bands

Gamma Band Relative -ray Yields

(including the Mikhailov term)

scat(deg)


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)


Relative -ray Yields

scat(deg)

=

(∓30%)

=

The Kπ=4+Band

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

Deduced Population Paths

E2

E2

E2


The Kπ=8- Isomer Band

Relative -ray Yields

Solid: Total calc. yield

Dotted: γ-band path

Dashed: GSB path

scat(deg)


IGSB

I

Matrix Elements Populating Kπ=8- Isomer Band

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

Deduced Population Paths

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)


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-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+ BandOnline expt. - Prompt -ray yields

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


Raw Singles Activity

Count

-Ray Energy (keV)


Count

-ray Energy (keV)

Doubles Activity Gated on 6+4+ in gsb


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


IGSB

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

Spin If in K=16+ Band

Measured 16+ Band Matrix Elements


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

  • 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)


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.


  • 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

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 Probabilities

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

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


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

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

  • 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)

Event-by-Event Doppler-Shift Correction


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

  • 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:


Rotational Bands in 178Hfbuilt on states of I=K


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


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 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?


  • Login