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

● Warsaw University—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

I – Total nuclear spin

J – Single-particle angular momentum

R – Collective rotation

K = Ω1+Ω

2

The K-Selection Rulefor axially symmetric systems

|K| ≤

Hindrance

Forbiddenness

Hindrance

“Reduced” Hindrance fν=F

ν1/ν

Single-particle Estimate

“Weisskopf unit”

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 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

K=16+ Isomer Activation

● Ta(178Hf,178Hf)Ta

● 73% to 86% ECoul

● Offline counting of 16+

(t1/2

=31y) isomer decay

cascade

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 ΔTOF5% in mass

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

Triple-Coincidence -ray Data

E (keV)

Cou

nt

Prompt-Delayed DataC

ount

E (keV)

178Hf Level Scheme

Iterative Fit Process for Strongly-Coupled Bands

(including the Mikhailov term)

Gam

ma

Ban

d R

elat

ive

-ra

y Y

ield

s

scat(deg)

Treatment of K-forbidden TransitionsSpin-Dependent Mixing (“SDM”) of Bohr and Mottelson

“H”

H can be written

as H(IiKiIfKf)

Log

H/H

min

Ki=0Kf=8

Ki=0Kf=6

Ki=0Kf=4

If-Kf

Rel

ativ

e -

ray

Yie

lds

scat(deg)

The Kπ=4+

Band

=

Solid/Dashed:two relative phases of <K=4|E2|GSB>and<K=4|E2| >

= (∓30%)

Gamma Band

Ground State Band

Band “A”

K=4+

Band

K=6+

IsomerBand

SecondK=8-

Band

K=8-

IsomerBand

K=16+ IsomerBand

K-allowed

K-forbidden

Deduced Population Paths

E2E2 E2

The Kπ=8- Isomer Band

Solid: Total calc. yieldDotted: γ-band pathDashed: GSB path

Rel

ativ

e -

ray

Yie

lds

scat(deg)

Matrix Elements Populating Kπ=8- Isomer Band

IGSB

I

AlagaRule

Attenuatedto preserve

isomer t1/2

Gamma Band

Ground State Band

Band “A”

K=4+

Band

K=6+

IsomerBand

SecondK=8-

Band

K=8-

IsomerBand

K=16+ IsomerBand

K-allowed

K-forbidden

Deduced Population Paths

E3E2

E3

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>

Rel

ativ

e -

ray

Yie

lds

scat(deg)

Gamma Band

Ground State Band

Band “A”

K=4+

Band

K=6+

IsomerBand

SecondK=8-

Band

K=8-

IsomerBand

K=16+ IsomerBand

K-allowed

K-forbidden

Deduced Population Paths

E2E2 E2

E2E2

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

Rel

ativ

e -

ray

Yie

ld (

norm

to 8

+G

SB

6+G

SB)

scat (deg)

Solid line: SDMDashed line: Alaga

Beam Activation ExperimentGe Detector Faraday Cup

178Hf Beam

Collimator

Ta (natural) target stack

Si Counter with aperture

Tantalum Beam Stop

Ta foil and cylindrical“catcher” stack

Raw Singles

Activity

-Ray Energy (keV)

Cou

nt

Cou

nt

-ray Energy (keV)

Doubles Activity Gated on 6+4+ in gsb

Measured Activation Function

Solid: Best fit (individual reduced m.e.)Dashed: SDM model Dotted: Linear model

Time-Averaged Mid-Target Projectile Energy (MeV)

Act

ivity

(h-1

)

Measured 16+ Band Matrix Elements<

I f K

=16

|| E

2 ||

I i K

=0>

(eb

)IGSB

Spin If in K=16+ Band

Gamma Band

Ground State Band

Band “A”

K=4+

Band

K=6+

IsomerBand

SecondK=8-

Band

K=8-

IsomerBand

K=16+ IsomerBand

K-allowed

K-forbidden

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

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.

Reduced hindrance f(IiIf) for

selected transitions in 178Hf.

The Goodness of K

Good in high-K bands.

Total breakdown ofK-conservation at

I≈12 in low-K bands.

High-K Bands

● Highly hindered transitions between high-spin, high-K states

● High-K bands align at higher spin

● Constant moments of inertia of high-K bands

Results consistent with collective alignment effects.

Expect similar behavior in other deformed nuclei.

Low-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

B(E) Reduced Transition Probabilities

Probes ofindividual

K-admixtures.

4+: probes 2≤K≤66+: probes 4≤K≤88-: probes 5≤K≤1116+: probes 14≤K≤18

from GSB

B(E) Reduced Transition Probabilities

6+: probes 4≤K≤88-: probes 5≤K≤11

Probes ofindividual

K-admixtures.

from -band

Calc. Coulomb Excitation Probability

If

16+ (99%)

GSB (0.6%)

14- band (0.1%)

14 16 18 20 22

10-1

100

10-2

10-3

10-4

K=16+

31 yK=14-

68 s

K=8-

4 s

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)

E (keV)

Cou

nt

Event-by-Event Doppler-Shift Correction

(a) Raw

(b) Corrected

for Hf-like

(c) Corrected for Xe-like

● 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

t1/2=31 yrs

The K=16+ BandBeam Activation Experiment

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.

2 Fit Technique

Present:

Previous:

2/NDF

Qo/Qobest - 1

Rel

ativ

e G

SB

-r

ay

Yie

lds

sc

at(

deg)

Rotational Bands in 178Hfbuilt on states of I=K

I – Total nuclear spin

J – Single-particle angular momentum

R – Collective rotation

K=Ω1+Ω

2

The K-Selection Rule

Electromagnetic Transition Probabilities

Electromagnetic Transition Probabilities

Electromagnetic Transition Probabilities

Electromagnetic Transition Probabilities

Eγi, α

i

Shapes and K-Conservatione.g. The Bohr Hamiltonian

Special case: axial symmetry

Images from www.europhysicsnews.com.

β-deformation γ-deformation

1P. Ring, P. Schuck, Springer-Verlag (1980). 2Chowdhury, NPA 485:136(1988). 3Sun, PLB 589:83(2004).

1Rotational alignment(K-mixing)

2Barrier penetration

3γ-softness (e.g. PSM)

For axial symmetry

Electromagnetic Selection Rules

Hindrance

Single-particle Estimate

“Weisskopf unit”

Hindrance

Single-particle Estimate

Forbiddenness

“Weisskopf unit”

Symbols

Hindrance

Forbiddenness

fν=F

ν1/ν“Reduced” Hindrance

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?