Collective Excitations in Exotic NucleiDavid Radford (ORNL)

RIA Summer School, August 2002

I Nuclear Excitations: Single particle motion vs. Collective motionCollective Modes: Rotations and Vibrations

II Experimental Techniques and Examples of Results• Gamma-Ray Spectroscopy• Giant Resonances• Intermediate-Energy Coulomb Excitation

III Towards RIA•Learning to do Nuclear Structure Measurements with

Post-accelerated Radioactive Ion Beams•Experiments with Heavy Neutron-rich Beams at the HRIBF

0 20 40 60 80 100 120 1400

10

20

30

40

50

60

70

80Z

Yields for the Rare Isotope Accelerator Facility

Mass Separated Intensities (ions/s)

Stable isotopes

> 1012

1010-10

12

108-10

10

106-10

8

104-10

6

102-10

4

1 -102

T1/2

= 1 sec

100 KW

400 MeV/u

r-processpath

Neutron drip

line???

Neutron drip

line???

1-100/day

mass separatedyields [/s]

rp-processpathrp-processpath

N (A-Z)N (A-Z)

The Holifield Radioactive Ion Beam Facility

25 MV tandemelectrostaticaccelerator

RIBinjectorplatform

RIB target/ion source

RIB injectorelectronics ORIC

K=105 cyclotron

Target/ion sourceremote handlingsystem

Recoil massspectrometerOn-line isotope

separator

Spinspectrometer

Nuclearreactions

Isobarseparator

Daresburyrecoilseparator

Stable beaminjector

Oak Ridge National LaboratoryPhysics Division

Some HRIBF beam currents

Singly stripped - suitable for Coulex For doubly stripped, divide by five

104

105

106

107

108

Ions

/s o

n ta

rget

113Ag

118AgN = 82126Sn

132Sn

127Sb

134Sb

132Te

136Te

Proton-induced fission of uraniumUC target

HRIBF will be the only facility that can accelerate thesebeams above the Coulomb barrier for at least 4 - 5 years.

Total of over 100 beams with at least 103 ions/s.

Goal: Physics measurements with neutron-rich RIBS

These n-rich RIBs provide a unique opportunity for a whole class of measurementsthat could never before be applied to nuclei on the n-rich side of stability.

To do these studies, we want to learn how to do the following types of measurementswith RIBs:

Coulomb excitation

B(E2) values transition matrix elements

Static quadrupole moments by reorientation nuclear shape

Fusion-evaporation; spectroscopy

band structure, etc.

Transfer reactions

e.g. (d,p) (3He,d) Spectroscopic factors

shell-model wavefunctions

Fusion-Evaporation

- Ideal for studies athigh angular momentum

- Tends towards proton-rich

n

n

Targetnucleus

10-22 sec

10-19 sec

10-15 sec

n

⇒ ⇒ ⇒

⇓CompoundFormation

FastFission

hω ~0.75 MeV~2x1020 Hz

⇒

Ix

Ix

γ

BeamNucleus

Fusion

p

Groundstate

Rotation

10-9 sec

400 440 480 520 560 600

Beam Energy (MeV)

134Te on 9Be

100

300

500

700

900

(m

b)

440 480 520 560 600 640

Beam Energy (MeV)

134Te on 13C

100

300

500

700

900

(m

b)

EvapOR cross section calculationsNeutron-rich RIBs, light targets

4n 139Ba

5n 138Ba

6n 137Ba

4n 143Ce

5n 142Ce

6n 141Ce

4n-evaporation products from 132Snon most n-rich stable targets

Mo42TcRu

RhPd46

AgCd

InSn50

SbTe

IXe54

CsBa

LaCe58

PrNd

PmSm62

EuGd

TbDy66

HoEr

TmYb70

LuHf

42 46 50 54 58 62 66 70 74 78 82 86

90

94

98

102

106

110

114

118

122

02

4

6

8

10

12

14

16

18

20

22

24

26

28

30

7

9

11

13

15

17

19

21

23

5

3

25

27

29

31

(9)

(11)

(13)

(15)

(17)

(7)

(12)

(14)

(16)

(18)

(10)

8

10

12

14

16

18

20

22

24

26

28

30

65

(7)

6

4

14

16

12

10

11

13

15

17

19

21

23

9

(8)

18

(9 )

(11 )

(13 )

(15 )

(17 )

(10 )

(12 )

(14 )

(16 )

(18 )

(20 )

(8)

(10)

(12)

(14)

(16)

(9)

(11)

(13)

(15)

(17)(19 )

02

4

6

8

32

4

1

50113

171

224

270

310

345

376

404

429

453

475

497

516

538

486

207

249

286

317

344

368

391

413

159

551

109

612

423

362

302

244

184

587

619

647

552

435

457

479

502

841

264

301

330

350

795

751

222

889

946

320

356

384

921

900

881

281

975

704

252

288

316

328

321

328

353

380

686

664

634

586

504

403

974

980

963

907

832

407

434

458

755

(683)

718

798

627

711613

522683

728

597

943

361

582

958325

927

618

288

910

640814

307

339

368

811

804

796

395

420

443

504

465

787

778

270

544

240

1005

392

974

570

1166

204

245

287

327

993

224

267

308

346

382

98

106

118

148

160

168

210

206

247

285

319

348

227

267

302

333

362

(99)

(108)

(120)

127

139

146

156

368

139

128

179

418

433

(404)

618

583

(163)

(170)

(179)

(183)

Band A

Beta DoubleGamma

Gamma

Ground band

Octupole bands

K=0- K=1-

232Th Coulomb Excited by 209Bi at E = 6 MeV/u

"Unsafe Coulex" - some contribution from nuclear interactions

No absolute B(E2)’s extracted

D. Ward et al., Private Communication.

Intermediate energy Coulomb excitation- Ideally suited for beam-fragmentation products

• Ebeam ≈ 40 MeV/nucl.• β ≈ 0.3, γ ≈ 1.05• bmin ≈ 20 fm• “touching spheres”

1.2(AS1/3+AAu

1/3)= 11 fm• σ ~ 100 mb• target ~ 100 mg/cm2

• K. Alder et al., Rev. Mod. Phys. 28, 432 (1956).

• A. Winther and K. Alder, Nucl. Phys. A 319, 518 (1979).

• C.A. Bertulani and G. Baur, Phys. Rep. 163, 300 (1988).

• T. Glasmacher, Ann. Rev. Nucl. Part. Sci. 48 (1998), 1.

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bmin

Sθmaxbmin = a 0 cot ( θmax /2) / γ

a0 =ZS ZAu e2

m0c2 β2

Zero degree detector

Energy spectra in target and projectile frames for 40S+197Au

40S

2+

0+

γ

0 keV

891 keV

500 15001000

β = 0

β = 0.27

Energy (keV)

Cou

nts

/ (10

keV

)

197Au3/2+

γ

0 keV

547.5 keV7/2+

100

50

80

6040

20

0

0

150

H. Scheit et al. Phys. Rev. Lett. 77 (1996) 3967

Reaction Rates

NReactions

NBeam Particles

= 6 10-7

At

= cross section, mb t = target thickness, mg/cm2

A = mass of target, a.m.u.

Derive: NA = 6 1023 atoms/mole 1 barn = 100 fm2

Beam Requirements

Two days to do experiment ~1.7 105 s At least 100 counts detected

A) Intermediate Energy Coulex; sd-shell nuclei

~ 100 mb t ~ 100 mg/cm2 A = 197

NR/NB ~ 3 10-5 = 0.2 N /NB ~ 6 10-6

N = 100 NB ~ 1.7 107

100 s-1 Beam

A) Low Energy Coulex; 132Sn Region

~ 10 mb t ~ 1 mg/cm2 A = 12

NR/NB ~ 5 10-7 = 0.02 N /NB ~ 10-8

N = 100 NB ~ 1010

6 104 s-1 Beam

Experimental Challenges

Beams are radioactive

Stopped/scattered beam can give huge background

- Good tandem beam quality, careful tuning

Beams are weak

, rates comparable to room background

- Require clean trigger (usually HyBall)

Beams are isobar cocktails, i.e. contaminated

- Can be helped by high-resolution -ray detection

Require light targets, inverse kinematics

Large recoil velocity, Doppler broadening

- Segmented clover array CLARION

Setup for experiments with neutron-rich RIBS

Target

Metal foil

X-raydetector

Recoil Detectors

CLARION

HyBall

11 segmented clover Ge detectors10 smaller Ge detectors

95 CsI detectors with photodiodes

Foil plus multichannel plate

50 cm downstream from targetand at RMS achromat

MoTcRuRhPdAgCdInSnSbTeIXeCsBaLaCe

PrNd

Pm

62 66 70 74 78 82

HRIBF test experiment12

C(118

Ag,4n)126

I, 12

C(118

Ag,5n)125

I at 500 MeV9Be(

118Ag,4n)

123Sb at 455 MeV

118Ag

125I

126I

123Sb

118Ag Test Experiment: Particle-Gamma Coincidences

118Ag on Be and C targets

Small 118Sn component of beam (~10%)

Gammas gated by charged particles:

HyBall particle ID spectra:

12C

α

p

9BeαE

nerg

yE

nerg

y

Particle ID

Particle ID

500 MeV 118Ag,Sn on 12C

455 MeV 118Ag,Sn on 9Be

200 600 1000 1400Eγ (keV)

20

60

100

140

180

5

15

25

35

45

5

15

25

35

α-gated

p-gated

12C-gated118Ag

123Sb + α3n

126Te + p3n

118Sn 2+ 0+

6+ 4+

2+ 0+4+ 2+

7- 6+

Fusion-Evaporation Reactions

100 300 500 700 900E (keV)

50

150

250

350

450

550

650

0

10

20

Cou

nts

per

Cha

nnel

0

10

20

0

10

20

12C(118Ag,5n)125I at 500 MeV γγ gates

~106 118Ag /s for 33 hours

Projection

125I, 126I

381 keV gate

580 keV gate

891 keV gate31/2- 27/2-

TACγγ -Recoil

5/2

9/2

11/2

15/2

19/2

23/2

27/2

31/2

35/2

7/2

11/2

15/2

9/2

13/2

17/2

21/2

13/2

7/2

11/2

15/2

19/2

704

381

580

614

506

891

779

648

114

655

786

948

482

608

684

850

596

435

333

173

489

801

536168

637

698

841

125I

D. Balabanski et al.Private comm.122Sn(7Li, 4n)

Coulomb Excitation Measurements Near 132Sn

PdAgCdInSnSbTeIXeCsBaLaCe

66 70 74 78 82 86

118Ag

126Sn 128Sn

132Te 134Te 136Te

Example: A = 136 Coulex

396 MeV 136Te + 136Ba

on 0.83 mg/cm2 C target

200 400 600 800 1000 1200 1400

60

140

UngatedDoppler corrected

200 400 600 800 1000 1200 1400

150

350

UngatedNot Doppler corrected

200 400 600 800 1000 1200 1400

6

14

22Te2+ 0+

Ba2+ 0+

Prompt carbon gateDoppler corrected

Particle ID Spectra:

C

protons

C

protons

Ring 1 7-14

oRing 328-44

o

Coulex Results: Sn & Te Spectra

200 600 1000 1400E (keV)

200

600

1000

1400

50

150

250

350

450

200 600 1000 1400E (keV)

0

10

20

30

0

10

20

30

40

0

20

40

60

A = 136

A = 134

A = 132

A = 128

A = 126

126Sn

1141 keV

128Sn

1169 keV

132Te974 keV

134Te1279

keV

136Te606 keV

126Te666 keV

128Te743 keV

134Ba605 keV

136Ba819 keV

Note multiple beam components

RIB Coulex Analysis

Measure =-HyBall coincidences

HyBall singlesC

R

Calculate for Coulex and Rutherford as a function of B(E2)dd

Integrate over the first three rings of HyBall

Compare calculated with observed to get B(E2)C

R

HH

Correct for isobaric content of the beam

- determined from Coulex of stable contaminants, decay counting and X-ray spectra

Inverse Kinematics for Coulomb excitation

C.O.M. frame

SnC

Lab frame

SnC

10 30 50 70

C(LAB)

20

60

100

140

C(C

OM

)

20

60

100

140

EC(L

AB

) (

MeV

)

Energy

10 30 50 70

C(LAB)

0.001

0.01

0.1

1

10

100

1000

d/d

(b/

Sr)

0+ (elastic)

2+ (Coulex)

7

44

128Sn on C 3 MeV/u

Angle-integrated:

0+ = 1460 mb

2+ = 5 mb [for B(E2) = 0.1e2b2]

Beam Composition from X-rays

Sn

Sb

Te

SnSb

Te

A = 126 RIB in Mo foil

A = 128 RIB in Mo foil

SIB calibrations

12 16 20 24 28 32 36EX (keV)

Te, I, Ba in Au foil

Te, I, Ba in Pd foil

Au L

Pd K Pd K

Te

TeI

I

Ba

Ba

MCP

Metal foil

X-raydetector

Tellurium Results

Beam

A=132 RIB

A=134 RIB

A=136 RIB

128Te SIB

136Ba SIB

aCalculated from observed excitation, using adopted values for the B(E2; 0+ 2+) (0.66 e2b2 for 134Ba, 0.41 e2b2 for 136Ba)

Nuclide

132Te132Sb132Sn132I

134Te134I134Ba134Sb

136Te136Ba136I

128Te

136Ba

fraction (%)

86(4)11(3)1.3(3)1.3(6)

87(4)11(3)1.0(2)a

0.9(3)

59(5)29(3)a

12(3)

100

100

-C

790(10)

377(22)

119(15)

224(15)

1790(44)

280(17)

C

1.7 107

1.6 107

3 106

5.5 106

1.4 106

B(E2; 0+ 2+) (e2b2)

0.172(17)

0.096(12)

0.103(15)

0.346(26)

0.46(4)

[0.383(6)]

[0.410(8)]

[Adopted values]

B(E2) Results and Systematics

70 80 90Neutron Number

0.2

0.6

1.0

1.4

1.8

B(E

2; 0

+

2+)

(e2 b

2 )

Sn

Te

Xe

Ba

Ce

New Results

Shell Model

136Te: Low B(E2) Value

The low value for the B(E2) in 136Te is very surprising

- Energy of 2+levels is also low

N = 80 N = 82 N = 84

0 0 0

0 0 0

2

2

2

2

2

2

40411221

725

9741279

606

130Sn 132Sn 134Sn

132Te 134Te 136Te0.17e2b2 0.10e2b2 0.10e2b2

Submitted to Phys. Rev. C, 0208042

Quasiparticle RPA Calculations - J. Terasaki et al.

- Used separable quadrupole-plus-pairing Hamiltonian

- Single-particle energies taken from experiment whenever possible

- Two-body interaction: isQQ + ivQQ + Q-pairing forces

- Monopole pairing gaps taken from renormalized experimental odd-even mass differences where possible

- Large configuration space; B(E2)s calculated with bare charges

0

1

2

3

4

5

62 64 66 68 70 72 74 76 78 80 82 84 86

E2+

[MeV

]

Sn

calexp

0

0.1

0.2

0.3

0.4

0.5

0.6

62 64 66 68 70 72 74 76 78 80 82 84 86

B(E

2) [e

2 b2 ]

Sn

calexp

0

1

2

80 82 84

E2+

[MeV

] Teexpcal

0

0.1

0.2

0.3

0.4

0.5

0.6

80 82 84

B(E

2) [e

2 b2 ]

Te

calexp

0

1

2

80 82 84

E2+

[MeV

] Xeexpcal

0

0.1

0.2

0.3

0.4

0.5

0.6

80 82 84

B(E

2) [e

2 b2 ]

Xe

calexp

0

1

2

80 82 84

E2+

[MeV

]

N

Baexpcal

0

0.1

0.2

0.3

0.4

0.5

0.6

80 82 84

B(E

2) [e

2b2]

N

Ba

Quasiparticle RPA Calculations - J. Terasaki et al.

Energy and B(E2) both decreasefor small values of neutron pairing gap

Neutron pairing strength from odd-even mass differences:

0

0.4

0.8

1.2

1.6

E2+

[MeV

]

Te136Te

132Te

0

0.05

0.1

0.15

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

B(E

2) [e

2 b2 ]

∆n [MeV]

Te

136Te

132Te

74 78 82 86 90N

0.2

0.6

1.0

1.4

n (

MeV

)

Sn

Te Ba

Future Plans: Coulex

B(E2) in 130Sn using pure Sn beam

Q2+ in 126Sn by reorientation

Odd-even and odd-odd nuclei

Could populate many levels not observed in beta decay

B(E2) of 2+ in 132Sn using pure Sn beam

Ex > 4 MeV

Analog to 208Pb?

Use BaF array for high efficiency (~60%)

Use 48Ti target and "slightly unsafe" energyBaF 37-crystal stack

(1 of 4)

Lead B(E2) Systematics

208Pb B(E2) = 8.5 W.u.; 19% of Isoscalar E2 EWSR

204 206 208 210Mass Number

0.1

0.2

0.3

B(E

2; 0

+

2+)

(e2 b

2 )

2

4

6

8

10

W.u

.

500

1500

2500

3500

4500

E2+

(ke

V)

208Pb

Conclusions

Nuclear structure experiments with heavy post-accelerated RIBs are:

Exciting Challenging Feasible!

Need a good clean trigger - combine detection of , light-ion, recoil, etc.

Have already shown that we can do fusion-evaporation and Coulex

Transfer reactions are harder

Will need high-efficiency -detection to select populated levels

Waiting for RIA with much anticipation!