The Search for Tetrahedral Shapes in Nuclei

Atlas Workshop

Lee Riedinger and Daryl Hartley

August 8, 2009

Use of stable and radioactive beams and Gammasphere to search for tetrahedral shapes

• Nuclei around N = 90 with stable beams• Nuclei around Z = 90 with stable beams• Nuclei around Z = 40 with radioactive beams• Part of the Tetranuc collaboration:

– Theory effort led by Jerzy Dudek at Strasbourg– Experimental effort led by Dominique Curien in Europe– Experiments at Cape Town in South Africa - Robert Bark and

John Sharpey Schafer– Our experimental effort focused on Gammasphere

• Each project has other goals beyond things tetrahedral

2

Predicted bands based on tetrahedral shapes

3 Pyramid-like shapes with rounded edges and corners

Dudek calculations for 156Dy

• Strong tetrahedral deformations are predicted around ‘magic numbers’: 32, 40, 56, 64, 70, 90, 132 - 136

• Top figure - do not see a minimum develop for non-zero α30

• Bottom figure - a minimum develops for non-zero α32

4

0

1

1

1

1

2

2

2

2

2

2

2

22

3

3

3

3

33

3

3

3

344

44

4

4

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

E(fyu)+Shell[e]+Correlation[PNP]

UN

IVER

S_CO

MPA

CT (D

=3, 2

3)G

p=0.

950

Gn=

0.96

0 !

Np=

35 !

Nn=

45

Dy90 Dy156 66

0.000.250.500.751.001.251.501.752.002.252.502.753.003.253.503.754.004.254.504.755.005.255.505.75

E [MeV]

Deformation "20

Def

orm

atio

n "

30

Emin=-2.47, Eo= 1.77

0

2

22

2 2

2

2

2

2

2

2

2

2

2

4

44

4

4

44

4

6

6

8

810

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-0.30-0.25-0.20-0.15-0.10-0.050.000.050.100.150.200.250.30

E(fyu)+Shell[e]+Correlation[PNP]

UN

IVER

S_CO

MPA

CT (D

=3, 2

3)G

p=0.

950

Gn=

0.96

0 !

Np=

35 !

Nn=

45

Dy90 Dy156 66

0.000.501.001.502.002.503.003.504.004.505.005.506.006.507.007.508.008.509.009.5010.0010.5011.0011.50

E [MeV]

Deformation "20

Def

orm

atio

n "

32

Emin=-2.01, Eo= 1.77

α32

α30

α20

α20

November Gammasphere measurement of 156Dy

• Used 148Nd(12C,4n) reaction so that we did not bring in too much angular momentum

• Ran for three days to get excellent data

• Looked for weak transitions in this K = 0 negative-parity band

• Looked for levels and transitions in the higher lying K = 1 negative-parity band, below I = 9

50 02 138

4 404

6 770

8 1215

10 1724

12 2285

14 2887

16 3522

18 4177

20 4858

22 5572

112933136851526

71810

92187

112637

133155

153720

174331

194979

138266

366

445

509

561

602

635

655

681

714

(450)

(518)

(565)

(611)

648

1155964

1230

7561122

5951040

972

913

870

833

156DyMissing E2

transitions from 3- through 17-

levels from earlier Riley experiment

(1988)

Ra d Warels3.ps, created 27-Apr-09 12:22:59

02

4

6

8

10

12

14

16

18

20

22

24

12

14

16

18

20

22

24

9

7

11

13

15

17

19

21

23

5

3

138

266

366

445

509

561

602

635

655

681

714

756

4

667

1033

1088

643

391

982

1100

591

359

433

527

610

421

780

685

611457

750

808

503679

970

1039

854

467405

911

449

518

868

566

340

361

221

833

608

647

681

717

808

(800)

1121

372

755

4 1159

399

1230964

377

Successful Gammasphere run on 156Dy

6

Measured branching ratios for lowest negative-parity band

7

Ra d Waredy156d1.ps, created 23-Jun-09 23:55:00

0 0

2 138

4 404

6 770

8 1215

10 1724

12 2285

14 2886

16 3522

18 4177

20 4858

22 5571

24 6328

26 7129

2 2706

4 3065

6 3498

8 4025

0 4635

2 5319

4 6069

6 6877

8 7738

92407

112708

133102

153595

174157

194771

82261

61898

41627

102707

123186

143677

164210

184779

205382

226036

9 2186

7 1809

246754

267534

11 2635

215428

236129

256876

102579

122941

143411

163961

82344

184561

205199

225872

246589

13 3153

15 3719

17 4330

19 4977

21 5658

23 6374

5 1525

62287

25 7129

154239

174781

153944

174469

195039

72163

277672

123266

10 2933

3 1367

51701

138

266

366

445

509

561

602

635

655

681

714

756

801

848

7

088

643

91

982

1100

591

359

433

527

610

421

780

685

611457

750

808

503679

861

1192

301

394

493

562

613

363

1128

1046 271

1223

446

983

605

479

491

533

569

603

654

521

970

515

452

1039

718

780

818

984

467

911

657

701

747

397

393

549

362

470

550

230

451

261

855

235

616

1129

318

600

638

673

716

172

233

657

309

449

518

868

566

258

221

833

608

647

681

717

808

(800)

1122

1121

372

755

762

486

753

796

1174

542

879

526

569

244

1393

947

7

796

902

791

598 535

560

411

238451

260

1230964

377

638

931

462

389

K = 0- ? K = 1-

151

192

B(E2)/B(E1) values in units of 106 fm2

22.7

3.1

7.7

9.9

17.7

351

591

42

< 4.5

581

302

The B(E2)/B(E1) ratios are much larger in the K = 1 negative-parity band in 156Dy

Ra d Warels3.ps, created 27-Apr-09 12:22:59

02

4

6

8

10

12

14

16

18

20

22

24

12

14

16

18

20

22

24

9

7

11

13

15

17

19

21

23

5

3

138

266

366

445

509

561

602

635

655

681

714

756

4

667

1033

1088

643

391

982

1100

591

359

433

527

610

421

780

685

611457

750

808

503679

970

1039

854

467405

911

449

518

868

566

340

361

221

833

608

647

681

717

808

(800)

1121

372

755

4 1159

399

1230964

377

Next step - measure lifetimes

8

• September Gammasphere experiment is scheduled with the25Mg(136Xe,5n)156Dy reaction

• Question is whether the B(E2)/B(E1) ratios are small due to small B(E2) (tetrahedral shape) or large B(E1) (octupole vibration)

• The lifetime of the state will vary greatly depending on whether Qt is normal or reduced

156Dy

Secondary goals of this project:• Understand family of negative-parity

bands - may not actually be a low lying K = 0- structure

• Look for “second vacuum” family of bands, as in other N = 90 nuclei

Search for tetrahedral shapes near Z = 90Candidate bands in 230-234U

9

)(15 !

) (5 !

) (7 !

) (9 !

)(11 !

0 +2 +4 +

6 +

+8

+10

12 +

14 +

16 +

! 1 ! 3

) (5 !

) (7 !

) (9 !

! 1! 3

5 !

7 !

) (9 !

) (11 !

0 +2 +

16 +

14 +

12 +

+10

+8

6 +

4 +

! 1 ! 3

! 5

! 7

! 9

! 11

! 13)(13 !

)(15 !

1 ! 3 !

)(13 !

)(11 !

! 15

2 +

4 +

+8

+10

12 +

14 +

16 +

6 +

0 +

12 +

0 +2 +

4 +

6 +

+8

+10

16 +

14 +

U138230 U140

232 U142234 U144

236

44143

296

497

741

1024

1341

1688

45

1801

1426

1085

782

522

310

149

57103

152

199

245

[311]

[270]

[225]

[176]

[123][69]

[260]

[216]

[168]

[118][66]

[253]

[211]

[163]

[113][63]

289

[346]

[298]

[334]366

1921

1532

52

170

347

578

856

1176

157

323

541

806

1112

1454

48

1828

Z. Phys. A328, 399 (1987)

231Pa(p,2n) 230Th(α,2n) 232Th(α,2n) 236U(d,pn)

236U

Propose to do multi-step Coulomb excitation of 234,236U with Gammasphere

• This lowest 1- band in 236U is different than those in other U - too low in energy and few E1s

• Second 1- band may be analogous tetrahedral candidate

• Look for ‘missing’ E2s in coulexc

10Allmond et al., PRC 79, 054610 (2009)Relative 235U(n, γ) and (n, f) cross sections from 235U(d,pγ) and (d,pf)

)(15 !

) (5 !

) (7 !

) (9 !

)(11 !

0 +2 +4 +

6 +

+8

+10

12 +

14 +

16 +

! 1 ! 3

) (5 !

) (7 !

) (9 !

! 1! 3

5 !

7 !

) (9 !

) (11 !

0 +2 +

16 +

14 +

12 +

+10

+8

6 +

4 +

! 1 ! 3

! 5

! 7

! 9

! 11

! 13)(13 !

)(15 !

1 ! 3 !

)(13 !

)(11 !

! 15

2 +

4 +

+8

+10

12 +

14 +

16 +

6 +

0 +

12 +

0 +2 +

4 +

6 +

+8

+10

16 +

14 +

U138230 U140

232 U142234 U144

236

44143

296

497

741

1024

1341

1688

45

1801

1426

1085

782

522

310

149

57103

152

199

245

[311]

[270]

[225]

[176]

[123][69]

[260]

[216]

[168]

[118][66]

[253]

[211]

[163]

[113][63]

289

[346]

[298]

[334]366

1921

1532

52

170

347

578

856

1176

157

323

541

806

1112

1454

48

1828

Secondary goal of this project: search for K = 0+ two-phonon octupole band

Recent Gammasphere work on 240Pu

• See strong E1 lines from 1- band to GSB

• Also see strong E1 lines from 0+ band to 1-band

• Explanation is that these are a family of octupole phonons

• Question is whether there is a similar 0+ band in 232,234,236U

– 0+β found at 691 keV in 232U and 810 keV in 234U by Janssens et al. - PLB156, 163 (85)

11Wang et al., PRL 102, 122501 (2009) 240Pu

GSB

1- band0+ band

Possible tetrahedral shape in 100Zr

12Hua et al., PRC 69, 014317 (2004)

• 100Zr: Z = 40, N = 60 - magic numbers• 238U(α,f) expt. - Gammasphere plus Chico - 2004• Ground state is prolate with a 2 QP sideband • Gammasphere spontaneous fission work -

spherical 0+ at 331 keV with structure on top of it - 2006

• Propose doing a Caribu experiment - coulex of a 100Zr beam, to hunt for tetrahedral bands associated with the prolate ground-state configuration

Prolate Oblate

100Zr experiment

13

Hwang et al., PRC 74, 017303 (2006) - spontaneous fission experiment inside Gammasphere

Secondary goal: measure matrix elements important for understanding shape coexistence