Dynamic and Static Chirality

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Dynamic and Static Chirality

• S. Frauendorf
• Department of Physics
• University of Notre Dame, USA
• IKH, Forschungszentrum Rossendorf
• Dresden, Germany

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In collaboration with
Ying-ye Zhang, UT Knoxville F. Doenau, FZ
Rossendorf S. Brant, U. Zagreb
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Chirality of molecules
mirror
The two enantiomers of 2-iodubutene
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New type of chirality
Chirality Changed
invariant
Molecules Massless particles space
inversion time reversal
Nuclei time
reversal space inversion
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Consequence of static chirality Two identical
rotational bands.
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The prototype of a chiral rotor
Frauendorf, Meng, Nucl. Phys. A617, 131 (1997)
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Left-right tunneling
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Triaxial rotor proton particle neutron hole
Chiral vibration
Chiral vibration
Nuclear chirality - a transient phenomenon
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For most chiral molecules the two enantiomers
Live long enough such that they can be
separated. experiments that show the rotation of
the polarization plane are possible.
Breaking of chiral symmetry is not very strong in
nuclei. Substantial left-right tunneling in
chiral rotors (static chirality) A soft
collective mode reaching the chiral
sectors Chiral vibrators (dynamic chirality)
No quantity that measures chirality directly so
far suggested. Combination of indirect evidence
from models.
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Transition rates static chirality
The mixing phase d depends on details, hard to
predict.
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Static chirality - chiral rotor
Two DI1 bands with small separation (as
compared to rotational frequency).
Similar transition rates in the sister bands.
Outband/Inband ratios depend on details. Sum of
B(1-gt1)B(1-gt2) about equal to B(2-gt2)B(2-gt1).
The function I(w) extrapolates to the origin.
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ph11/2 nh11/2
134Pr
Transitions 2-gt1 prevail
No upbend extrapolating to zero
Results of the Gammasphere GS2K009 experiment.
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Transition probabilities in 134Pr
D. Tonev et al. PRL in print EUROBALL
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C. Petrache et al. PRL in print GAMMASPHERE
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pg9/2 nh11/2
104Rh
C. Vaman et al. PRL 92,032501 (2004)
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Composite chiral band in
S. Zhu et al. Phys. Rev. Lett. 91, 132501 (2003)
J. Timar et al. Phys. Lett. B 598, 178 (2004)
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J. Timar et al. Phys. Lett. B 598, 178 (2004)
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Two quasi neutron configuration chiral?
Y. X. Luo et al. in preparation GAMMASPHERE
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No clear evidence for static chirality
Close bands with same parity observed.
Bands either parallel or cross, do nor merge.
Kink in I(w) and follwing extrapolation to origin
???
Transition probabilities not symmetric.
What about dynamic chirality ?
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Chiral vibrator
Frozen alignment
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8 K. Starosta et al., Physical Review Letters
86, 971 (2001)
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134Pr - a chiral vibrator,which does not make it.
Calculation Triaxial rotor with Cranking MoI
particlehole
Experiment
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Coupling to particles
Frozen alignment
Additional alignment
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Tiny interaction between states!
But strong cross talk!!??
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4 irreducible representations of group 2 belong
to even I and 2 to odd I. For each I, one is
0-phonon and one is 1-phonon.
The 1-phonon goes below the 0-phonon!!!
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vib rot
vib rot
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Evidence for chiral vibration
Two close bands, same dynamic MoI, 1-2 units
difference in alignment
Cross over of the two bands (Intermediate MoI
maximal)
Almost no interaction between bands 1 and 2
(manifestation of D_2)
Strong decay 2-gt1 weak decay 1-gt2 .
Problem different inband B(E2)
Coupling to deformation degrees of freedom seems
important
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Transition Quadrupole moment
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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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Microscopic moments of inertia
Irrotational flow
Cranking of the core about the 3 axes
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Particle Rotor model
Frauendorf, Meng, Nuclear Physics A617, 131 (1997)
Doenau, Frauendorf, Zhang, PRC , in preparation
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Frozen alignment approximation
They are numbers
One dimensional - very well suited for analysis.
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chiral vibration
chiral rotation
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out
in
out
in
in
in
out
out
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in
in
out
out
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