A close up of the spinning nucleus
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A close up of the spinning nucleus
S. Frauendorf
Department of Physics
University of Notre Dame, USA
IKH, Forschungszentrum Rossendorf
Dresden, Germany
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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
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HI+small arrays
HI+large arrays
Decay+detector
Collectiverotation
Interplaybetweencollective and sp.degrees offreedom
Nucleonicorbitals –gyroscopes
Spinning clockwork of gyroscopes
Nucleonicorbitals –gyroscopes
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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
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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
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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
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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)
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Magnetic Rotation
-90 0 90 180 2700.0
0.2
0.4
0.6
0.8
1.0
over
lap
Weakly deformed Pb199
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TAC
Long transverse magnetic dipole vectors, strong B(M1)
The shears effect
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2
2/132/92/13
ihit qqqQ
Better data needed for studying interplay between shape ofpotential and orientation of orbitals.
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Terminating bandsA. Afanasjev et al. Phys. Rep. 322, 1 (99)
Orientation of the gyroscopes
Deformed density / potential
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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
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Symmetries at high spin
Combination of Shape (time even)With Angular momentum (time odd)
Determine the parity-spin-multiplicity sequence of the bands
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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
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Good simplex
Several examples in mass 230 region
Substantial staggering
I
i
z
e
)(parity
simplex ||
1)(
S
PRS
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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!
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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
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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
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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
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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
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Consequence of chirality: Two identical rotational bands.
Chirality
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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.
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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
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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
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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
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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
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Congratulations!
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Loss and onset of orientation
Geometrical picture vs. TAC
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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)
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[8] K. Starosta et al., Physical Review Letters 86, 971 (2001)
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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
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Frozen alignment Coupling to particles
pj
hj
J
pj
hj
J
hj
pj
J
Additional alignment
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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!!??
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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
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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
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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
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Do not cross
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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
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)()(
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
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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