Experimental evidence for ChiralityS. Frauendorf

Department of Physics

University of Notre Dame

USA

IKH, Forschungszentrum

Rossendorf, Dresden

Germany

In collaboration withJ. Meng, PKUV. Dimitrov, ISUF. Doenau, FZRU. Garg, NDK. Starosta, MSUS. Zhu, ANL

Consequence of chirality: Two identical rotational bands.

The prototype of a chiral rotor

Frauendorf, Meng, Frauendorf, Meng, Nucl. Phys. A617, 131 (1997Nucl. Phys. A617, 131 (1997) )

Particle – Rotor model:

Frauendorf, Meng, Nuclear Physics A617, 131 (1997)Frauendorf, Meng, Nuclear Physics A617, 131 (1997)

Doenau, Frauendorf, Zhang, PRC , in preparation

312 ,

Dynamical (Particle Rotor) calculation

Chiral vibration

Frozen alignment approximation:

They are numbers

One dimensional -very well suited for analysis.

312 44 JJJ

chiralvibration

chiralrotation

jJ crit 3

24

out

in

out

out

in

in

yrast yrare

out

in

312 ,

Dynamical (Particle Rotor) calculation

Chiral vibration

chiralregime

2/112/11 21 jj

8 10 12 14 16 18 20 22 24 26 28 300.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

=90o

E2-

E1

I

omega1 E2E1

rotEE 3.012

10 12 14 16 18 20 22

0.0

0.1

0.2

0.3

0.4

=90o

1->1 1->2 2->1 2->2

B(E

2,I-

>I-

2)

I

8 10 12 14 16 18 20 22-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

=90o

1->1 1->2 2->1 2->2

B(M

1,I-

>I-

1)

I

8 10 12 14 16 18 20 22

0.0

0.1

0.2

0.3

0.4

0.5

=90o

1->1 1->2 2->1 2->2

B(E

2,I-

>I-

1)

I

band 2 band 1134Pr

h11/2 h11/2

10 12 14 16 18 20 220

100

200

300

400

500

600

700

800

900

1000

backbend

134Prexperiment

E2-

E1

I

E2E1 omega1

10 15 20 250.0

0.2

0.4

0.6

0.8

1.0

=90o 1:2E

2-E

1

I

omega1 E2E1

2/192/11 21 jj

10 15 20 25

0.00

0.05

0.10

0.15

0.20

0.25

0.30 =90o 1:2B

(E2

,I->

I-1

)

I

BE2u(11) BE2u(12) BE2u(21) BE2u(22)

10 15 20 25

0

1

2

3

4

5

=90o 1:2

B(M

1,I-

>I-

1)

I

BM1(11) BM1(12) BM1(21) BM1(22)

10 15 20 25-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40 =90o 1:2

B(E

2,I-

>I-

2)

I

BE2s(11) BE2s(12) BE2s(21) BE2s(22)

Microscopic moments of inertia

Cranking of the core about the 3 axes

1:4:1:: 321 JJJIrrotational flow

1:55.3:52.1:: 321 JJJ

o3018.0

10 12 14 16 18 20 220

100

200

300

400

500

600

700

800

900

1000

PR + TAC

E2-

E1

I

E2E1 omega1

10 12 14 16 18 20 220

100

200

300

400

500

600

700

800

900

1000

backbend

134Prexperiment

E2-

E1

I

E2E1 omega1

10 12 14 16 18 20 220.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

PR + TAC

B(M

1,I-

>I-

1)

I

BM111 BM112 BM121 BM122

10 12 14 16 18 20 22

0.0

0.1

0.2

0.3

0.4

0.5

0.6

PR + TAC

B(E

2,I-

>I-

2)

I

BE2s11 BE2s12 BE2s21 BE2s22

10 12 14 16 18 20 220

100

200

300

400

500

600

700

800

900

1000

PR + TAC

E2-

E1

I

E2E1 omega1

10

12

13

14

15

16

17

18

19

11 10

12

13

14

15

16

17

18

19

11

112 2

10 15 20 25

0

1

2

3

4

5

=80o

B(M

1,I-

>I-

1)

I

BM1(11) BM1(12) BM1(21) BM1(22)

10 12 14 16 18 20 22 240.0

0.1

0.2

0.3

0.4

0.5

=80o

B(E

2,I-

>I-

2)

I

BE2s(11) BE2s(12) BE2s(21) BE2s(22)

10 15 20 250.0

0.1

0.2

0.3

0.4

0.5

=80o

B(E

2,I

->I-

1)

X Axis Title

BE2u(11) BE2u(12) BE2u(21) BE2u(22)

10 15 20 250.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

=80o

E2-

E1

I

E2E1 omega1

5910445 Rh 2/11

12/9 hg

C. Vaman et alPhys. Rev. Lett.92, 032501 (2004)

10 15 20 25

0.00

0.05

0.10

0.15

0.20

0.25

0.30 =90o 1:2B

(E2

,I->

I-1

)

I

BE2u(11) BE2u(12) BE2u(21) BE2u(22)

10 15 20 25

0

1

2

3

4

5

=90o 1:2

B(M

1,I-

>I-

1)

I

BM1(11) BM1(12) BM1(21) BM1(22)

10 15 20 25-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40 =90o 1:2

B(E

2,I-

>I-

2)

I

BE2s(11) BE2s(12) BE2s(21) BE2s(22)

S. Zhu et al.Phys. Rev. Lett. 91, 132501 (2003)

Composite chiral band in 7513560 Nd

Chiral sister bands

Representativenucleus I

observed13 0.21 145910445 Rh 2/11

12/9 hg

13 0.21 4011118877 Ir

2/912/9 gg

447935 Br

12/132/13

ii

13 0.21 14

predicted

predicted

9316269 Tm 1

2/112/13ii predicted45 0.32 26

12/112/11

hh observed13 0.18 267513459 Pr

31/37

Chiral vibrator

2/1 2

1

12

12

)()(2/1

2

1

1

222

233

211

IIA

j

Ij

JAjJAjJAH

ii

W

J

JJ

J

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

Conclusions

Energy condition rotEE 3.012 met for several cases.

Left-right coupling (LRC) displaces the two bands

LCR makes the transition rates in the two bands somewhat different.Seen in BM1/BE2. Lifetimes needed.

LCR distributes the classical transition strength between intrabandand interband transitions. Sensitive to details. Inter/Intra not a good indicator for chirality.

B(intra)+B(inter) can be compared with classical strength (from TAC).

New regions : A=190, A=162 TSD