Triaxiality in nuclei: Theoretical aspects S. Frauendorf Department of Physics University of Notre Dame, USA IKH, Forschungszentrum Rossendorf Dresden, Germany

In collaboration with D. Almehed, UMIST V. Dimitrov, FZR, ND F. Doenau, FZR Ying-ye Zhang, UT

Triaxial shell gaps

A normal def. A large def

Phenomena in triaxial nuclei Wobbling Chiral vibrations Static chirality Tidal waves

Wobbler types

Collective Wobbler large

Aligned Wobbler 1 3 High-j particle Increases with spin

Tilted Wobbler High-j hole

High-j particle, Irrotational flow MoI realignment with 2-axis

Irrotational exchanged Cranking moments of inertia

Matsuzaki, Shimizu, Matsuyanagi, PRC 65, (R) (2002) RPA

Wobbling (A=164) No collective wobbler Transition probablities  Aligned wobbler Energies  Tilted wobbler TAC in between Constant moment of inertia ?? Lower I in other mass regions (A=105,134,190)  chirality__

Chirality

Dynamical (Particle Rotor) calculation Chiral vibration

chiral vibration chiral rotation

Chiral vibrator

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

Transition probabilities

out in out in yrast  yrare 

yrast  yrare  out in

Microscopic TAC calculations

Consequence of chirality: Two identical rotational bands. (Static approximation)

Chiral sister bands Representative nucleus observed predicted observed observed /37

Composite chiral bands

Types of chirality

Status of breaking of chiral symmetry Chiral mean field solutions do exist Chiral sister bands are seen Transition from chiral vibrations to rotations Transition matrix elements needed Sensitive to details Microscopic approach to dynamics needed

“I call any geometrical figure, or group of points, chiral, and say it has chirality, if its image in a plane mirror, ideally realized, cannot brought to coincide with itself.” Kelvin, 1904, Baltimore lectures on Molecular Dynamics and Wave Theory of Light

Chirality of molecules mirror The two enantiomers of 2-iodubutene

carvon

mirror Chirality of mass-less particles z

Chirality “I call a physical object, chiral, and say it has chirality, if its image, generated by space inversion or time reversal, cannot brought to coincide with itself by a rotation.” 11/37

Tidal wave

High-spin waves Combination of Angular momentum reorientation Triaxial deformation

yrast D. Cullen et. al

Line distance: 20keV TAC

Line distance: 200 keV

Tidal wave Less favored vibrations Mixed with p-h excitations

s ot i m K=25 i (130 ns) s o t m K= P. Chowdhury et al NPA 484, 136 (1988)

First example of a triaxial tilted Tidal Wave 10 Phonons! Softness in shows up in isomer decay Large order amplitude phonons First phase transition

Rotating mean field: Cranking model Seek a mean field solution carrying finite angular momentum. Use the variational principle with the auxillary condition The state |> is the stationary mean field solution in the frame that rotates uniformly with the angular velocity w about the z axis. In the laboratory frame it corresponds to a uniformly rotating mean field state

Can calculate molecule Very different from

    p   n  