Transcript Slide 1

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?
Nucleons are not on fixed positions.
What is rotating?
Bohr and Mottelson
The nuclear surface
Collective model accounts for the appearance of
rotational bands E I(I+1), Alaga rules for e.m. transitions and
many more phenomena.
2
Decay+detector
HI+small arrays
Nucleonic
orbitals –
gyroscopes
HI+large arrays
Collective
rotation
Interplay
between
collective
and sp.
degrees of
freedom
3
Spinning clockwork of gyroscopes
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?
Deformed density / potential
Orientation of the gyroscopes
Deformed potential aligns the
partially filled orbitals
Partially filled orbitals are
highly tropic
1.0
overlap
0.8
0.6
0.4
Nuclus is oriented –
rotational band
0.2
Well deformed
174
Hf
0.0
-90
0
90

180
270
5
How is angular momentum generated?
HCl
Moving masses
or currents in a liquid
are not too useful concepts
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 axis
Gradual – rotational band
Abrupt – band crossing, no bands
Moments of inertia for I>20
(no pairing) differ strongly from
rigid body value
Microscopic cranking
Calculations do well in
reproducing the moments
of inertia.
With and without pairing.
M. A. Deleplanque et al.
Phys. Rev. C69, 044309 (2004)
7
Magnetic Rotation
1.0
overlap
0.8
0.6
0.4
0.2
0.0
-90
0
90
180
270

Weakly deformed
199
Pb
8
The shears effect
TAC

Long transverse magnetic dipole vectors, strong B(M1)
9
Better data needed for studying interplay between shape of
potential and orientation of orbitals.
Qt  qi1 3/ 2  qh9 / 2  qi123/ 2
10
Terminating bands
A. Afanasjev et al. Phys. Rep. 322, 1 (99)
Deformed density / potential
Orientation of the gyroscopes
11
Instability after termination
M. Riley
E. S..Paul
et al.
@Gammasphere
termination
Calculations:
I. Ragnarsson
Coexistence of sd, hd, with wd
12
After termination, several alignments,
substantial rearrangement of orbitals
instability
new shape, bands
Symmetries at high spin
Determine the parity-spin-multiplicity sequence of the bands
Combination of
Shape (time even)
With
Angular momentum (time odd)
13
223
Th
Tilted reflection asymmetric nucleus
2
E-0.0074I [MeV]
Parity doubling
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
-0.08
223
Th
<60keV
erpp(+,+)
ermp(-,+)
erpm(+,-)
ermm(-,-)
4
6
8
10
I
12
14
Best case of reflection asymmetry. Must be better studied!
16
14
Good simplex
S  Rz ( ) P  1
S | e i | simplex
parit y  (  ) I 
Several examples in mass 230 region
Substantial staggering
15
Weak reflection symmetry breaking
Driven by rotation
S=(E--E+)[MeV]
0.8
0.6
240
0.4
222
Pu
Staggering
Parameter S
Th
0.2
226
Th
0.0
0
5
10
15
20
25
30
35
I
Changes sign!
16
Condensation of non-rotating vs. rotating
octupole phonons
1.0
n=3
0.8
0.6
E'n-E'0
0.4
n=2
j=3 phonon
condensation
n=1
0.2
0.0
n=0
-0.2
 ph  rot  c
-0.4
0.00
Angular momentum
0.05
0.10
0.15
rotational frequency
+
 rot
 ph  vib / 3
j=0 phonon
j=3 phonon
17
harmonic (non-interacting) phonons
220
3.0
2.5
2.0
E0
E1
E2
E3
1.5
E
c
Ra
Data: J.F.Smith et al.PRL 75, 1050(95)
Plot :R. Jolos, Brentano PRC 60, 064317 (99)
n=3
1.0
n=2
0.5
0.0
n=1
n=0
0
5
10
15
20
I
an harmonic (interacting) phonons
3.0
2.5
Ea
Eb
Ec
Ed
E
2.0
0-2
1.5
n=3
1.0
n=2
exp
n=1
0.5
0.0
1-3
n=0
0
5
10
I
15
20
18
0.8
_
240
Pu
+
2.5
226
1.7
3.0
222
0.1
Th
S=(E--E+)[MeV]
I
30
28
26
24
22
20
18
16
14
12
10
8
6
4
2
0
0.0
240
0.4
222
Pu
Th
0.2
226
Th
0.0
Th
0.2
0.6
0.3
0
5
10
15
[MeV]
Rotating octupole does not
completely lock to the rotating
quadrupole.
20
I
+
25
30
35
 rot
 ph  rot
-
19
1.0
n=3
0.8
0.6
E'n-E'0
0.4
n=2
j=3 phonon
condensation
n=1
0.2
0.0
n=0
-0.2
-0.4
0.00
0.05
0.10
0.15

X. Wang, R.V.F. Janssens, I.
Wiedenhoever et al. to be
published.
Preliminary
20
Chirality
Consequence of chirality: Two identical rotational bands.
21
band 2
134Pr
h11/2 h11/2
band 1
K. Starosta et al.
Results of the
Gammasphere
GS2K009
experiment.
Come as
close as 20keV
Strong
Transitions
2 -> 1
22
Soft chiral vibrations
Shape
Unharmonicites
Must be even,
because symmetry
is spontaneously
broken
Microscopic RPA calculations (D. Almehed’s talk)
Decreasing energy (about 2 units of alignment)
Strong transitions 2->1, weak 1->2
Tiny interaction between 0 and 1 phonon states (<20 keV)
Systematic appearance of sister bands
Difficult to explain otherwise.
32
Triaxial Rotor
with microscopic
moments of inertia
Rigid shape
IBFFM
Soft shape
A. Tonev et al. PRL 96, 052501 (2006)
Q /Q  2
0
t
1
t
C. Petrache et al.
PRL
24

Transition
Quadrupole
moment
1.5
1.25
Q2
1
larger
0.75
smaller
0.5
0.25
0
0
0.25
0.5
0.75
1
1.25
Q2  0
1.5

  30o , deformsfor other
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 vibrator
Harmonic approximation
Frozen alignment
H  A1 ( J1  j ) 2  A3 ( J 3  j ) 2  A2 J 22
1/ 2
2 j 
I  J1  

W 
1
 1 
J1 
J
2 j  2 
1
Ai 
I  I 1/ 2
2 Ji
J2  J1
J
Full triaxial rotor + particle + hole (frozen)
26
24
22
20
18
16
14
12
10
8
6
4
2
0
jp,jn frozen
=30
o
chiral rotor
chiral vibrator
om1
om2
0.0
0.2
0.4
0.6
0.8
[MeV]
1.0
1.2
1.4
[8] K. Starosta et al., Physical Review Letters 86, 971 (2001)
600
134Pr - a chiral vibrator,
which does not make it.
E2E1TPR(J-TAC)
E2E1exp
500
400
E2-E1[keV]
134
Pr
300
200
Calculation:
Triaxial rotor with
Cranking MoI
+particle+hole
100
V<25keV
0
-100
-200
8
10
12
14
16
18
20
134
Pr
J
J
I
24
22
20
18
16
14
12
10
8
6
4
2
0
om1e
om2e
om1o
om2o
Experiment
0
100
200
300
400
[kEV]
500
600
24
22
20
18
16
14
12
10
8
6
4
2
0
om1e
om2e
om1o
om2o
134
Pr
TPR (J-TAC)
0
100
200
300
400
[keV]
500
600

jh

J

jp
Frozen alignment

jh
Coupling to particles

jh

J

J

jp

jp
Additional alignment
Tiny interaction between states!
600
E2E1TPR(J-TAC)
E2E1exp
500
112
400
E2-E1[keV]
134
Pr
300
Ru | V | 18keV
200
104
100
V<25keV
0
Rh | V | 1keV
-100
-200
8
10
12
14
16
18
20
I
134
Pr | V | 25keV ( 17keV )
But strong cross talk!!??
Rs ( )
1
Rl ( )

jh

jp

R
4 irreducible representations of group D2 h
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!!!
Ri ( )
0.6
2.0
BE2so11
BE2so12
BE2so21
BE2so22
0.3
1.6
2
B(M1,I->I-1)[N ]
2
B(E2,I->I-2)[eb ]
0.4
TPR(J-TAC)
vib rot
1.8
TPR(J-TAC)
0.5
vib rot
0.2
0.1
1.4
1.2
BM1o11
BM1o12
BM1021
BM1o22
1.0
0.8
0.6
0.4
0.2
0.0
8
10
Strong interband
12
14
I
16
18
20
0.0
8
10
12
14
I
16
18
20
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->1 weak decay 1->2 .
Problem: different inband B(E2)
Coupling to deformation degrees of freedom seems important
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
Moment of inertia
has the rigid body value
velocityfield
v L (r)  j(r) / m (r)
in body fixed frame
v B (r)  v L (r )   e x  r
generated by the
p-orbitals
Deformed harmonic oscillator
N=Z=4 (equilibrium shape)
Moments of inertia for I>20
M. A. Deleplanque et al.
Phys. Rev. C69, 044309 (2004)
rotational alignment
Backbends
K-isomers
Combination of many orbitals
-> classical periodic orbits
Velocity field in body fixed frame
of unpaired N=94 nuclides