A close up of the spinning nucleus

S. Frauendorf

Department of Physics

University of Notre Dame, USA

IKH, Forschungszentrum Rossendorf

Dresden, Germany

How is the nucleus rotating?

What is rotating?

The nuclear surface

Nucleons are not on fixed positions.

Collective model accounts for the appearance of rotational bands E I(I+1), Alaga rules for e.m. transitions andmany more phenomena.

Bohr and Mottelson

2

HI+small arrays

HI+large arrays

Decay+detector

Collectiverotation

Interplaybetweencollective and sp.degrees offreedom

Nucleonicorbitals –gyroscopes

Spinning clockwork of gyroscopes

Nucleonicorbitals –gyroscopes

3

Aspects of the close up

• How does orientation come about?

• How is angular momentum generated?

• Examples: magnetic rotation, band termination and recurrence

• Weak symmetry breaking at high spin

• Examples: reflection asymmetry, chirality

4

How does orientation come about?

Orientation of the gyroscopes

Deformed density / potential

Deformed potential aligns thepartially filled orbitals

Partially filled orbitals are highly tropic

Nuclus is oriented – rotational band

Well deformed Hf174 -90 0 90 180 2700.0

0.2

0.4

0.6

0.8

1.0

over

lap

5

How is angular momentum generated?

Moving massesor currents in a liquidare not too useful concepts HCl

rigid

irrotational

Myth: Without pairing the nucleus rotates like a rigid body. 6

Angular momentum is generated by alignment of the spin of the orbitals with the rotational axisGradual – rotational bandAbrupt – band crossing, no bands

Microscopic cranking Calculations do well inreproducing the momentsof inertia.With and without pairing.

Moments of inertia for I>20 (no pairing) differ strongly from rigid body value

M. A. Deleplanque et al. Phys. Rev. C69, 044309 (2004)

7

Magnetic Rotation

-90 0 90 180 2700.0

0.2

0.4

0.6

0.8

1.0

over

lap

Weakly deformed Pb199

8

TAC

Long transverse magnetic dipole vectors, strong B(M1)

The shears effect

9

2

2/132/92/13

ihit qqqQ

Better data needed for studying interplay between shape ofpotential and orientation of orbitals.

10

Terminating bandsA. Afanasjev et al. Phys. Rep. 322, 1 (99)

Orientation of the gyroscopes

Deformed density / potential

11

Instability after termination

After termination, several alignments, substantial rearrangement of orbitals

Coexistence of sd, hd, with wd

new shape, bandsinstability

M. RileyE. S..Paulet al.@Gammasphere

Calculations:I. Ragnarsson

termination

12

Symmetries at high spin

Combination of Shape (time even)With Angular momentum (time odd)

Determine the parity-spin-multiplicity sequence of the bands

13

Th223

Parity doubling

Best case of reflection asymmetry. Must be better studied!

4 6 8 10 12 14 16

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

223Th

E-0

.007

4I2 [M

eV]

I

erpp(+,+) ermp(-,+) erpm(+,-) ermm(-,-)

<60keV

Tilted reflection asymmetric nucleus

14

Good simplex

Several examples in mass 230 region

Substantial staggering

I

i

z

e

)(parity

simplex ||

1)(

S

PRS

15

Weak reflection symmetry breaking

Driven by rotation

0 5 10 15 20 25 30 35

0.0

0.2

0.4

0.6

0.8

240Pu

222Th226Th

S=

(E--E

+)[

MeV

]

I

StaggeringParameter S

Changes sign!

16

Condensation of non-rotating vs. rotatingoctupole phonons

0.00 0.05 0.10 0.15

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

j=3 phonon condensation

n=3

n=2

n=0

n=1

E' n-

E' 0

+

-

+

-

+

-

j=0 phonon j=3 phonon

3/vibph rot

Angular momentum rotational frequency

crotph

17

exp

n=0

n=1n=2

n=3

0 5 10 15 200.0

0.5

1.0

1.5

2.0

2.5

3.0

E

I

E0 E1 E2 E3

0 5 10 15 200.0

0.5

1.0

1.5

2.0

2.5

3.0

E

I

Ea Eb Ec Ed

n=0

n=1n=2

n=3

harmonic (non-interacting) phonons

an harmonic (interacting) phonons

0-2 1-3

Data: J.F.Smith et al.PRL 75, 1050(95)Plot :R. Jolos, Brentano PRC 60, 064317 (99)

Ra220

c

18

02468

1012141618202224262830

0.0 0.1 0.2 0.3

222Th3.0

2.5

1.7

_

+

226Th

240Pu

[MeV]

I

0 5 10 15 20 25 30 35

0.0

0.2

0.4

0.6

0.8

240Pu

222Th226Th

S=

(E--E

+)[

MeV

]I

Rotating octupole does not completely lock to the rotating quadrupole.

+

-

+

-

+

-

rotph rot

19

0.00 0.05 0.10 0.15

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

j=3 phonon condensation

n=3

n=2

n=0

n=1

E' n-

E' 0

X. Wang, R.V.F. Janssens, I. Wiedenhoever et al. to be published.

Preliminary

20

Consequence of chirality: Two identical rotational bands.

Chirality

21

band 2 band 1134Pr

h11/2 h11/2

Come as close as 20keV

StrongTransitions2 -> 1

K. Starosta et al.K. Starosta et al.Results of the Results of the GammasphereGammasphereGS2K009 GS2K009 experiment.experiment.

22

Soft chiral vibrations

Shape

Microscopic RPA calculations (D. Almehed’s talk)

Decreasing energy (about 2 units of alignment)Strong transitions 2->1, weak 1->2Tiny interaction between 0 and 1 phonon states (<20 keV)Systematic appearance of sister bands

Difficult to explain otherwise.

UnharmonicitesMust be even,because symmetryis spontaneouslybroken

32

Triaxial Rotorwith microscopicmoments of inertia

Rigid shape

IBFFM

Soft shape

A. Tonev et al. PRL 96, 052501 (2006) 2/ 10 tt QQC. Petrache et al.PRL 24

0 0.25 0.5 0.75 1 1.25 1.50

0.25

0.5

0.75

1

1.25

1.5

02 Q

2Q

Transition Quadrupolemoment

other for deforms ,30o

larger

smaller

25

Summary

• Close up refined our concept of how nuclei are rotating: assembly of gyroscopes

• Rich and unexpected response as compared to non-nuclear systems

• Rotation driven crossover between different discrete symmetries resolved

• Chirality of rotating nuclei appears as a soft an harmonic vibration

26

Congratulations!

27

Loss and onset of orientation

Geometrical picture vs. TAC

Chiral vibratorFrozen alignment

2/1 2

1

12

12

)()(

12

2/1

2

1

1

222

233

211

IIA

j

Ij

JAjJAjJAH

ii

W

J

J JJJ

J

Harmonic approximation

02468

101214161820222426

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

chiral rotor

chiral vibrator

jp,j

n frozen

=30o

[MeV]

J

om1 om2

Full triaxial rotor + particle + hole (frozen)

[8] K. Starosta et al., Physical Review Letters 86, 971 (2001)

8 10 12 14 16 18 20-200

-100

0

100

200

300

400

500

600

134Pr

V<25keV

E2-

E1[

keV

]

I

E2E1TPR(J-TAC) E2E1exp

0

2

4

6

8

10

12

14

16

18

20

22

24

0 100 200 300 400 500 600

TPR (J-TAC)

134Pr

[keV]

J

om1e om2e om1o om2o

02468

1012141618202224

0 100 200 300 400 500 600

134Pr

[kEV]

J

om1e om2e om1o om2o

134Pr - a chiral vibrator,which does not make it.

Experiment

Calculation:Triaxial rotor with Cranking MoI +particle+hole

Frozen alignment Coupling to particles

pj

hj

J

pj

hj

J

hj

pj

J

Additional alignment

Tiny interaction between states!

8 10 12 14 16 18 20-200

-100

0

100

200

300

400

500

600

134Pr

V<25keV

E2-

E1[

keV

]

I

E2E1TPR(J-TAC) E2E1exp keVV 18||Ru 112

)17(25||Pr 134 keVkeVV

keVV 1||Rh 104

But strong cross talk!!??

4 irreducible representations of group2 belong to even I and 2 to odd I. For each I, one is 0-phonon and one is 1-phonon.

)(iR)(sR )(lR1

hD2

The 1-phonon goes below the 0-phonon!!!

hj

pj R

8 10 12 14 16 18 20

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

TPR(J-TAC)

B(M

1,I-

>I-

1)[

N

2 ]

I

BM1o11 BM1o12 BM1021 BM1o22

8 10 12 14 16 18 200.0

0.1

0.2

0.3

0.4

0.5

0.6

TPR(J-TAC)

B(E

2,I-

>I-

2)[e

b2 ]

I

BE2so11 BE2so12 BE2so21 BE2so22

vib rotvib rot

Strong interband

Strong decay 2->1 weak decay 1->2 .

Cross over of the two bands (Intermediate MoI maximal)

Almost no interaction between bands 1 and 2 (manifestation of D_2)

Evidence for chiral vibration

Problem: different inband B(E2)

Coupling to deformation degrees of freedom seems important

Two close bands, same dynamic MoI, 1-2 units difference in alignment

Do not cross

Conclusions

• So far no static chirality – look at TSD

• Evidence for dynamic chirality

• Chiral vibrators exotic: One phonon crosses zero phonon

• Coupling to deformation degrees

)()(

frame fixedbody in

rervrv xLB

Deformed harmonic oscillatorN=Z=4 (equilibrium shape)

)(/)()(

fieldvelocity

rrjrv mL

Moment of inertiahas the rigid body value

generated by thep-orbitals

rotational alignmentBackbends

K-isomers

M. A. Deleplanque et al. Phys. Rev. C69, 044309 (2004)

Moments of inertia for I>20

Combination of many orbitals-> classical periodic orbits

Velocity field in body fixed frame of unpaired N=94 nuclides