E0 transitions: where we have been, where we are … transitions: where we have been, where we are going, where we would like to go John L. Wood School of Physics Georgia Institute

E0 transitions: where we have been, where we are going,

where we would like to go

John L. Wood

School of Physics

Georgia Institute of Technology

E0: transition operator and matrix element--a model independent description

E0 transition strengths are a measure of theoff-diagonal matrix elements of themean-square charge radius operator.

Mixing of configurations with different mean-square charge radii producesE0 transition strength.

Ω values: http://bricc.anu.edu.au

τ: partial lifetime for E0 decay branch

J. Kantele et al. Z. Phys. A289 157 1979and seeJLW et al. Nucl. Phys. A651 323 1999

Comments on model-motivated research

• Research should be pursued to falsify models, not to promote them

• When a model fails, we have learned something—recall that failure of the Standard Model of particles and fields is being sought, avidly

• Models provide powerful schemes for organizing data

Wave functions must overlap for a transition to occur

Figure from JLW et al.,Nucl. Phys. A651 323 1999

solid line—schematic potential

dashed line—schematic wave function

In the earlier literature there are some serious misconceptions onthis point

E0 transition between states with very different deformations and mean-square charge radii

6.6 x 10-7

B(E1) W.u.

B(E2) W.u.

ρ2(E0) x 103

238 U

J. Kantele et al., Phys. Rev. Lett. 51, 91 (1983)


The E0 strength from the238U “fission” isomer isthe weakest known

T. Kibédi and R.H. Spear, ADNDT 89 77 2005

E0 transitions in the light Ni isotopes:the 02 01 strength in 58Ni is very small indicating near-pure neutron

configurations are involved (en = 0)

6.3 x 10-3

8030

1 < < 27

784266

> 0.43

T. Kibédi and R.H. Spear, ADNDT 89 77 2005


π2p-2h from 2-, 4-proton transfer RX

ρ2(E0) 103

E0 transitions associated with shape coexistence in 114-120Sn

.

0+

2+

0+

0+

2+

4+

1953

2240

2614

1:93

1300

2610

2156

0

4+

2530

2+

0+

0+

2+

0+ 0+ 0+

2+

0+

2+

4+

0+

4+

2+

0+

0+

2+

2113

1757

2027

1294

0

2489

2043

1758

2056

1230

0

2644

2097

1875

2160

1171

0

4.38 3.76 2.47

0.8718 >0.48

8719

1:100 1:75 1:37

J. Kantele et al., ZP A289, 157 (1979) T. Kibedi and R.H. Spear, ADNDT 89, 277 (2005)

114Sn 116Sn 118Sn 120Sn

ρ2(E0) 103

>36

Mixing of close lying configurations with different mean-square charge radii produces E0 strength

E2 transitions associated with shape coexistence in 114-120Sn

.

0+

2+

0+

0+

2+

4+

1953

2240

2614

1300

153

2156

0

4+

2530

2+

0+

0+

2+

0+ 0+ 0+

2+

0+

2+

4+

0+

4+

2+

0+

0+

2+

2113

1757

2027

1294

0

2489

2043

1758

2056

1230

0

2644

2097

1875

2160

1171

0

228

13030

12.44 12.15 11.42

445

397 5620

183 193 12.617

114Sn 116Sn 118Sn 120Sn

B(E2) W.u. Data from ENSDF

150

100

50

0

0 400 800 1200 1600

B(E

2)

(W.u

.)

E (keV)

Systematics of B(E2; 0+2 2+

1) vs. E (0+2 – 2+

1)

0+2 2+

1

2+1

0+1

0+2

strong

weak

B(E2; 02+ 21

+) vs. E(02+) – E(21

+): coexistence and mixing yields B(E2; 02

+21

+) ~ α2 β2 (ΔQ)2

Recall:B02 = 5 x B20

Deformed bands in 112-120Sn built on the first excited 0+ states

Figure from Rowe & Wood B(E2)’s in W.u. [100 = rel. value]

The nature of the shape coexisting state in 116Sn revealed by (3He,n) transfer reaction spectroscopy

Spectrum taken from H.W.Fielding et al., NP A281, 389 (1977)

Excited 0+ states at closed shells: intruder states in the Pb and Sn isotopes

neutron numbermid shell mid shell

green—yrast statesred—non-yrast states

Coexistence in even-Pb isotopes: multiple parabolas and spherical (seniority) structure

Figure: Heyde & Wood Heavy arrows indicate E0+M1+E2 transitions188Pb: G.D. Dracoulis et al., PR C67 R 051301 2003

Coexistence in the odd-Pb isotopes:Data for E0 transitions are from:J.C. Griffin et al., NP A530 (1991) 401—195Pb (UNISOR / LISOL);J. Vanhorenbeeck et al., NP A531 (1991) 63—197Pb (LISOL);K. Van de Vel et al., PR C65, 064301 (2002)—189,191Pb (KUL @ JYFL)

spin sequence in 195,197Pbimplies oblate deformation

Heavy downward vertical arrows indicate E0+M1+E2 transitions

Diagonal arrows indicateα-decay strength (from Po)

Shape coexistence in the even-Hg isotopes: NOTE characteristic parabolic energy trend

80Hgmid-shell

Figure from J. Elseviers et al.PR C84 034307 2011

Conversion electron spectroscopy:uniquely sensitive to E0 transitions, identifies shape coexistence

E0 E0 +

M1

+ E

2

E0 +

M1

+ E

2

E0 +

…

M.O. Kortelahti et al.,PR C43 484 1991 UNISOR

E0 transitions: αK > αK(M1)

M.O. Kortelahti et al., PR C43 484 1991

190Hg

21+-01

+ 41+-21

+ 61+-41

+

0+ 0+ decays are pure E0: no γ’s (190Hg)

M.O. Kortelahti et al. PR C43 484 1991 1279 keV pure E0evidence

The ground states of 178-186Pt and 177-187Ptare intruder states

Figure from: JLW et al.,Phys. Repts. 215, 101 (1992)

mid shellN = 104 See P.M. Davidson et al.,

NP A657 219 1999 (ANU)

Coexistence in the odd-Pt isotopesChapter 2. Background 19

Figur e 2.4: Systemat ics of yrast states in A = 168− 194 Pt isotopes as a funct ion of

the neutron number N . The even-A isotopes (open symbols) are plot ted with respect

to the 0+ ground state. Posit ive-signature states of odd-A isotopes (filled symbols) are

plot ted taking the 13/ 2+ state as a reference. Vert ical dashed lines highlight N = 95, 97

of 173,175Pt , respect ively. Around the neutron mid shell (N = 104) the excitat ion

energies of these yrast states have a pronounced staggering between the odd-A and

even-A nuclei. When moving away from the neut ron mid shell, the mot ion of the odd

neut ron is seen to become weakly coupled to the core deformat ion. This is seen from

the similarity of the excitat ion energy between even and odd-A Pt isotopes at N 97

and N ≥ 109. Data are taken from [Pii75, Jan88, Bes76, Nyb90, Bur67, De Voigt90,

Bag09, Dra86, Dra90, Dra91, Ced98, Jos05, GH09].

P. Peura, Ph.D. thesis, JYFL 2014mid shellN = 104

Coexistence in the even-Pt isotopes:mixing and E0 transition strength

From: J. von Schwarzenberg,PhD thesis, Ga Tech 1991

E (sph.gs) = 0

E (gs) = 0

ρ2(E0)

V = 50, 100, 400 keV

Coexistence in the even-Pt isotopes:coexistence of K = 0 and K = 2 bands in 184Pt

Y. Xu et al. PRL 68 3853 1992 UNISOR

E2 / M1 from low-temperaturenuclear orientation on-line

Coexistence in the even-Pt isotopes:K = 0 and K = 2 bands


Coexistence in the even-Pt isotopes:K = 0 and K = 2 bands


★

★

★

★

Pure E0’s in an odd-mass nucleus?

185Pt

J. von Schwarzenberg et al., PR C45 R896 1992 UNISOR

M1 + E2

Pure E0’s in an odd-mass nucleus

J. von Schwarzenberg et al., PR C45 R896 1992 UNISOR

185Au 185Pt

Isotope shifts: Pt, Au, Hg, Tl, Pb, Bi, Po, At

From: Barzakh INPC 2013

International Nuclear Physics Conference INPC2013: 2-7 June 2013, Firenze, Italy

Shape coexistence and charge radii in thallium, gold and astatine

isotopes studied by in-source laser spectroscopy at RILIS-ISOLDE

A. Barzakh

Petersburg Nuclear Physics Institute (PNPI), NRC Kurchatov Institute, 188300 Gatchina, Russia

On behalf of York-KU Leuven-Gatchina-Mainz-Bratislava-Liverpool-ISOLDE collaboration

Contact email: [email protected]

The competition between spherical and deformed nuclear shapes at low energy gives rise to

shape coexistence in the region of the neutron-deficient lead isotopes with Z~82 and N~104 [1]. In

order to determine to which extent the ground and/or isomeric states of those and neighboring nu-

clides are affected by this phenomenon, a campaign of investigation of changes in the mean-square

charge radii and electromagnetic moments is on-going at ISOLDE. By combining the high sensitiv-

ity of the in-source laser spectroscopy technique, ISOLDE mass separation and Windmill alpha-

decay spectroscopy setup [2], it has been possible to study long isotopic chains of lead [3] and po-

lonium [4], down to N=100 and N=107 respectively, and, recently, thallium isotopic chain down to

N=98.

In this contribution, we present the the preliminary results of the charge radii,

electromagnetic moments and spins measurements in thallium, gold and astatine isotopes. In the

gold and astatine cases, next to Faraday cup and Windmill measurements, also the Multi-Reflection

Time-of-Flight (MR-ToF) mass separation technique [5] involving the ISOLTRAP collaboration

was used.

100 105 110 115 120 125 130 135

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

177Au

179Tl

182Pb

197At

85At

78Pt

191Po

82Pb

N=133,

octu

po

le d

efo

rma

tio

n

N=104,

sh

ap

e c

oe

xis

ten

ce

84Po

83Bi

81Tl

80Hg

d<

r2>

N, N

0

Neutron number

79Au

N=126,

sh

ell

eff

ect

Figure 1: Charge radii for Pt-At isotopes. For the sake of clarity the data for different elements are

shifted relative to each other by a vertical off-set. Tl data for the light isotopes are from ISOLDE [5]

and Gatchina. Preliminary data for gold and astatine chains are from [6].

[1] K. Heyde and J. Wood. Rev. Mod. Phys., 83, 1467 (2011);

[2] A.N. Andreyev et al., Phys. Rev. Lett., 105, 252502,(2010);

[3] H. De Witte et al., Phys. Rev. Lett., 98, 112502 (2007);

[4] T.E. Cocolios et al., Phys. Rev. Lett., 106, 052503 (2011);

[5] R.N. Wolf et al., Nucl. Instr. and Meth. A 686, 82-90 (2012).

(fm

2)

Odd-mass Au systematics showingthe h9/2 intruder state

Figure from: M.O. Kortelahti et al., JP G14 1361 (1988)

E0 transitions between “single”and “double” intruder states in 185Au

9/2- state @ 9 keV: “double” intruder state:πh9/2 (1p) × 184Pt [π(2p-6h)] = π(3p-6h)

9/2- state @ 322 keV: “single” intruder state:πh9/2 (1p) × 184Pt [π(4h)] = π(1p-4h)

C.D. Papanicolopulos PhDthesis Ga Tech 1987 andZP A330 371 1988 UNISOR

Z = 79 427 keVmult αK

E1 0.010E2 0.027M1 0.11

expt. 0.33

E0 transitions between “spherical” states and “core” intruder states in 185Au

11/2- state @ 220 keV: “spherical” state:πh11/2 (1h) × 186Hg [π(2h)] = π(3h)

11/2- state @ 712 keV: “core” intruder state:πh11/2 (1h) × 186Hg [π(2p-4h)] = π(2p-5h)

C.D. PapanicolopulosPhD thesis Ga Tech 1987ZP A330 371 1988UNISOR

Z = 79 492 keVmult αK

E1 0.007E2 0.020M1 0.073

expt. 0.21


D. Rupnik et al. PR C51 R2867 1995 UNISOR

E2


D. Rupnik et al. PR C51 R2867 1995 UNISOR

WHEN STUDYING THE QUANTUM MECHANICAL MANY-BODY PROBEM, ALWAYS BE MINDFUL OF:

• "We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

Therefore, to the same natural effects we must, so far as

possible, assign the same causes.”--Isaac Newton

(From William of Ockham [near Guildford, UK], ca. 1320)

• “Everything should be made as simple as possible,

but not simpler.”-- Albert Einstein

Systematics of 02+ states in Zr isotopes, 50 ≤ N ≤ 62:

electric monopole transition strengths

0+ 0+ 0+ 0+ 0+ 0+

0+

0+

21+

0+

0+

0+

0+

0+

0+

3.5

8.0

7.6

11.2

90 92 94 96 98 100 102

0

1

2

E(MeV)

108

ρ2(E0)103

02+ is first excited state

in only 15 known nuclei:3 are here

large ρ2(E0)103 indicatescoexistence and strongmixing

Data are taken from T. Kibédi and R.H. Spear, ADNDT 89, 77 (2005)

11.5

Systematic of 21+ states in Zr isotopes, 50 ≤ N ≤ 62:

electric quadrupole transition strengths

0+ 0+ 0+ 0+ 0+ 0+

02+

0+

2+

2+ 2+

2+

2+

2+2+

5.4

6.4

2.3

>0.04

75 105

4.9

B(E2) W.u.

largest known change in 21

+ propertieson mass surface

90 92 94 96 98 100 102

0

1

2

E(MeV)

Systematic of E(21+) for N ≥ 50, Z ≤ 50

Ground-state properties are a direct signature of shell and deformation structures

R&W Fig. 1.41

R&W Fig. 1.42

Differences in mean-square charge radii (isotope shifts)determined by:

optical hyperfine spectroscopy using lasers

Two-neutron separation energies deduced from nuclear masses determined by:

direct mass measurements

21+ state properties are a strong signature of

shell and deformed structures

R&W Fig. 1.39

R&W Fig. 1.40

Energies of 21+ states determined by:

gamma-ray spectroscopy following β decayproblem—β-decaying parent is further from stability and yield will be (much)

lower than nucleus of interest

gamma-ray spectroscopy following Coulomb excitation

Reduced E2 transition rates, B(E2) from 21+ states

determined by:lifetime measurements using fast β-γ timing following β decay

problem--see above

gamma-ray yields following Coulomb excitation

Excited 0+ states at closed shells--mixing and repulsion of pair configurations in 90Zr

p1/22

0+

g9/22

0+

+0 0

1761

+0N=50: g9/2 seniority structure

j = ½ orbitals can only contributeto v = 0 states, at low energy

90Zr E(21+) is high: suggests a closed

subshell, BUT is due to depressionof the ground-state energy

Figure from Heyde & Wood

Shape coexistence at and near closed subshells: the nuclei 96Sr and 98Zr

Figure from K. Heyde and J.L. Wood, Rev. Mod. Phys. 83, 1467 (2011)

E0 transitions: ρ2(E0)103 values

are shown

96Sr5898Zr58

G. Lhersonneau et al., PR C49, 1379 (1994)

C.Y. Wu et al.,PR C70, 064312

(2004)

G. Lhersonneau et al., PR C49, 1379 (1994)

C.Y. Wu et al.,PR C70, 064312 (2004)

ρ2(E0)103 = 21031

in 96Sr is largest known for A > 56

21076

61

11

0.21031

Deformation in Zr isotopes, 50 ≤ N ≤ 62

0+ 0+ 0+ 0+ 0+ 0+

0+

0+

0+

0+

0+

0+

0+

0+

90 92 94 96 98 100 102

0

1

2

E(MeV)

2+

4+

deformedbands

0+

2+

4+

2+

4+

2+

4+

94Zr—A. Chakraborty et al.PRL 110 022504 2013

A deformed structure can intrude to become a ground state:

appears to produce a “collective phase change”

Proton particle-hole excitations across the Z = 64 gap may be the source of the coexisting shapes.

There is no a priori way to determine the nature of the unmixed configurations or the strength of the mixing.

En

erg

y

N90 92 9484 86 88

2+

0+

“p(2h)”

“p(2p-4h)”

2+

0+

2+

0+

normal

collectivity

suppressed

collectivity

N=90

2+

0+

2+

0+

mixedunmixed

E0

2+

2+

Less-deformed 2h and more-deformed 2p-4h structures coexist at low energy at N=90.

Strong mixing obscures the energy differences that are indicative of different shapes.

Strong E0 transitions are a key signature of the mixing of coexisting structures.

As observed, the K=2 bands will also mix strongly, resulting in E0 transitions.

24

Nuclei are manifestations of coexisting structuresthat may invert by addition of a few nucleons, and may mix.

52 54 56 58 60 62

N=58

Proton pair excitations with respect to the Z = 40 subshell

π(2p-2h)

π(0p-0h)

Ground state properties, S2n and δ<r2>, in the regions of N = 60, 90 are very similar

Figure from Heyde & WoodFigure from S. Naimi et al. Phys. Rev. Lett. 105 032502 (2010)

E(21+) systematics for N ~90 and Z ~64

Systematics of <r2> and S2n for the Eu isotopes

152Sm and the neighboring N = 90 isotones are a manifestation of shape coexistence

Shape coexistence in the N = 90 isotones:revealed by E0 transition strengths

Strong mixing of coexisting shapes produces strong electric monopole (E0) transitions and identical bands.

E0 strength is a function of mixing.

0 2 4 6 8

I(I+1)

En

erg

y

2

1

0

E(MeV)

Sm9062

152Gd

9064154

Dy9066

156

0+

2+

4+

6+

8+

10+

0+

4+

2+

6+

0+

2+

4+

6+

8+

10+

0+

2+

4+

6+

8+

10+

0+

2+

4+

6+

8+

10+

0+

2+

4+

6+

8+

10+

0+

2+

4+

6+

8+

10+

8917

749

8814

696

239

0.74

515

0+

2+

4+

1:9

r2•103

707

4214

7520

6310

6815

ρ2 ·103 = α2β2 ∆ r2 2·103 Z2

R40

≈ 356α2β2,

R0 = 1.2A1/3 fm

∆ r2 = 0.39fm2

ρ2 ·103 = α2β2 ∆ r2 2·103 Z2

R40

R0 = 1.2A1/3 fm

1

Thursday, 9 July 2009

Note: mixing produces “identical bands”

Data from Heyde and Wood (2011)

Strong mixing produces (near) identical bands

0 2 4 6 8 0 2 4 6 8

0

500

1000

1500

I(I+1)

E (

MeV

)

Mixing of coexisting structures in 152Sm

0.75690.70710.64330.57700.5334J

0.65360.70710.76560.81670.8458J

86420J

0+ 0

2+ 159

4+ 454

6+ 840

8+ 1290

0+ 296

2+ 378

4+ 563

6+ 840

8+ 1199

unmixed mixedV = 310 keV

4+

6+

8+

0+ 0

2+ 136

389

726

1127

8+ 1754

6+ 1346

0+ 687

2+ 793

4+ 1019

experimen

t

2+

0+

4+

6+

8+

685

810

1023

1311

1666

4+

6+

8+

366

706

1125

2+

0+ 0

122

(from Eu)

51570.8

69677.3

881484.4

87.0

85.2

exptcalc

148Ce 154Sm

Mixing of coexisting structures in 154Gd

0.53270.56860.61760.67020.7071J

0.84630.82260.78650.74220.7071J

86420J

0+ 0

2+ 159

4+ 454

6+ 840

8+ 1290

0+ 0

2+ 89

4+ 288

6+ 585

8+ 965

unmixed mixedV = 340 keV

4+

6+

8+

0+ 0

2+ 122

361

690

1091

8+ 1844

6+ 1416

0+ 680

2+ 806

4+ 1061

experimen

t

2+

0+

4+

6+

8+

681

815

1048

1366

1756

4+

6+

8+

371

718

1144

2+

0+ 0

123

(from Eu)

891791.0

74990.1

70785.9

79.6

74.0

exptcalc

148Ce 156Gd

152Sm: B(E2) values

Grodzins’ rule for quadrupole strength

Rotor matrix elements

e.g.,

*Grodzins +8%

Mottelson, Tokyo Conf., 1967: comment on breakdown of ΔK = 0 Alaga rules at N = 90

Multi-Coulex of 152Sm 02+(685 keV):

strongest response is to head of K=2+ band at 1769 keV(in-band response attenuated by 99.7% decay out @ 811 level)

The strongest response is from the band head of the

K=2+ structure at 1769 keV.

1084122

126

356

288

446

100

200

300

400

288

212

356

414

446

2+ 122

4+ 366

6+ 707

8+ 1125

10+ 1609

12+ 2149

14+ 2736

0+ 0

2+ 811

4+ 1023

6+ 1311

8+ 1666

10+ 2058

12+ 2526

0+ 685

2+ 1293

4+ 1613

6+ 2004

0+ 1083

2+ 1944

0+ 1755

2+ 1086

4+ 1371

6+ 1728

8+ 2140

10+ 2662

9+ 2376

3+ 1234

7+ 1946

5+ 1559

2+ 1769

4+ 2052

6+ 2417

3+ 1907

7+ 2623

5+ 2237

563

1084

414

200 600 1000 1400 E (keV)

Co

un

ts/c

ha

nn

el W.D. Kulp et al., Phys. Rev. C77 061301 2008152Sm

Gammasphere + CHICO@ 88” (Berkeley)

Multi-Coulex:152Sm beam + 208Pb target

1084

1084

563gate

Shape coexistence in the N = 90 isotones:coexisting K = 2 bands revealed by E0 transitions

Kulp, Wood, Garrett, Zganjar and others

E (MeV)

3+, K = 2 3+, K = 2: 631 keV transition in 158Er has no observable γ-ray strength, only ce’s[ 3K2 – I(I+1) = 0 ] are observed --accidental cancellation of E2; M1 is very weak.

152Sm: W.D. Kulp et al., Phys. Rev. C77 061301 2008

cf. 184Pt

Neutron-deficient Kr isotopes:puzzling collectivity

E. Clément et al.,PR C75 054313 2007

Multistep Coulomb excitation of 74,76Kr using radioactive beams of Kr on a 208Pb target

76Kr

74Kr 74Kr 76Kr


Quadrupole shape invariants constructed from E2 matrix elements for 74,76Kr

for the ground state


CONCLUSIONS: E0 TRANSITIONS

1). They give a unique perspective on shape coexistencein nuclei

2). They probe the proton and neutron configurations thatoccur in nuclei

3). They probe K quantum numbers through their ΔK = 0selection rule

We need more data for:T1/2(0+) [and T1/2(2+), T1/2(4+), T1/2(3+)] conversion electron intensitiesE2 / M1 mixing ratios—to extract E2 + M1 + E0

Electric monopole transition strengths: critical test of phase transition models

P. von Brentano et al., PRL 93, 152502 (2004)

Shape coexistence in the Hg and Cd isotopes

midshell midshellneutron number

E(M

eV)

--02+

-- intruder 0+,2+,4+,6+Z=48Z=80

Shape coexistence in the Cd isotopes

Fielding NP A281 389 1977

108Pd(3He,n)110Cd

110Pd(3He,n)112Cd

Pd targets π(4h)

Deformed bands in 110-116Cd

Figure from Rowe & Wood B(E2)’s in W.u. [100 = rel. value]

The spectroscopy of mixing in the Cd isotopes:ρ2 (E0) values in 114Cd

0

1

2

E(MeV)114Cd

ρ2(E0)103

ΔK=0τ(n,n’γ ) fs: >500

>800

0.655

1.8313

192

438

891

2

0+

2+ 558

0

1284

4+0+ 1306

0+ 1135

2+

1364

4+ 17320+

2+

2+

other

2+

1210

3+

4+

1864

19322+ 184

2

4+ 2152

3+ 2205

12020

<130<120

STRONG

Conv. Elec. ILL BILL/GAMSMheemeed NP A412 113 1984

Lifetimes n,n’γ Doppler U. KentuckyBandyopadhyay PR C76 054308 2007

Shape%coexistence%in%the%N%=%90%isotones:%%revealed%by%E0%transi6on%strengths%

Strong mixing of coexisting shapes produces strong electric monopole (E0) transitions and identical bands.

E0 strength is a function of mixing.

0 2 4 6 8

I(I+1)

En

erg

y

2

1

0

E(MeV)

Sm9062

152Gd

9064

154Dy

9066

156

0+

2+

4+

6+

8+

10+

0+

4+

2+

6+

0+

2+

4+

6+

8+

10+

0+

2+

4+

6+

8+

10+

0+

2+

4+

6+

8+

10+

0+

2+

4+

6+

8+

10+

0+

2+

4+

6+

8+

10+

8917

749

8814

696

239

0.74

515

0+

2+

4+

1:9

r2•103

707

4214

7520

6310

6815

ρ2 ·103 = α2β2 ∆ r2 2·103 Z2

R40

≈ 356α2β2,

R0 = 1.2A1/ 3 fm

∆ r2 = 0.39fm2

ρ2 ·103 = α2β2 ∆ r2 2·103 Z2

R40

R0 = 1.2A1/3 fm

1

Thursday, 9 July 2009

Note:%mixing%produces%“iden6cal%bands”%

Data%from%Heyde%and%Wood%(2011)%

Based on a figure in WoodNP A651 323 1999

E0 transition strengths in 114Cd support the existence of good K quantum numbers

STRONG Δ K=2 E0 Δ K=2 MIXING

0

1

2

E(MeV)114Cd

ρ2(E0)103

ΔK=2τ(n,n’γ ) fs: >500>450

Bke: 0.00003640

0+

2+ 558

0

1284

4+0+ 1306

0+ 1135

2+

1364

4+ 17320+

2+

2+

other

255

2+

1210

3+

4+

1864

19322+ 184

2

4+ 2152

3+ 2205

2020

<0.1 nil

nil

<1.5 nil

nil

<300

WEAK

Spectroscopy of mixing in the Cd isotopes:ρ2 (E0)103 values in 114Cd

0

1

2

E(MeV)114Cdρ2(E0)103

0.655

1.8313

192

438

891

2

0+

2+ 558

0

1284

4+0+ 1306

0+ 1135

2+

1364

4+ 1732

2+

1210

3+

4+

1864

19322+ 184

2

4+ 2152

3+ 2205

12020

<130<120

Conv. Elec. ILL BILL/GAMS Mheemeed NP A412 113 1984

Lifetimesn,n’γ Doppler U. Kentucky Bandyopadhyay PR C76 054308 2007Coulex yield multiple ions Fahlander NP A485 327 1988p-e(t) (d,pe) Julin ZP A296 315 1980Coulex yield 16-O Julin thesis Univ. Jyvaskyla 1979

255

NOTE:despite the proximity of these two 2+ states, the ρ2 (E0) value is not large

ρJ J2 (E0) 103 ~ 400 αJ

2 βJ2

ρ2(E0)103 max ~ 100 (obs.)

Δ<r2 > ~ 0.45 fm2 [2nd est.]

β0 / α0 ~ 0.23

Spectroscopy of mixing in the Cd isotopes:116Cd (p,t) 114Cd and ρ2 (E0) 103

Fortune PR C35 2318 1987

VJ=0 330 keV

β0 / α0 0.28

ρ0 02 (E0) 103 = 19 = 482 [Δ<r2 >]2 103 [0.28 x 0.96]2

[1.2 x 1141/3]4

ρJ J2 (E0) 103 ~ 300 αJ

2 βJ2

Δ<r2 > ~ 0.4 fm2 [first estimate]

. 02+

01+ 01

+

114Cd 116Cd(p,t)

σpt(02+)

σpt(01+)

0def+

0sph+

Ed

Es

02+

01+

1135

0

~

~

114Cd(expt)

ρ0 02 (E0) ~ [Δ<r2 >]2 α0

2 β02

Δ<r2 > = <r2 >def - <r2 >sph [unknown] E0

Wood et al.NP A651 323 1999

α02 + β0

2 = 1

The spectroscopy of mixing in the Cd isotopes:114Cd unmixed energies

The spectroscopy of mixing in the Cd isotopes:114Cd energies

The spectroscopy of mixing in the Cd isotopes:ρ2 (E0) values in 114Cd

The spectroscopy of mixing in the Cd isotopes:M(E2) and B(E2) values in 114Cd

Electric monopole transition strengths in the N = 60 isotones

98Sr6038

100Zr6040

102Mo6042

104Ru6044

Systematics of low-lying collective states in N=60 isotones

0+ 0 0+ 0 0+ 0 0+ 0

2+ 144

4+ 434

6+ 867

8+ 1432

0+ 215

2+ 871

2+ 212

4+ 564

6+ 1063

8+ 1687

0+ 829

2+ 878

4+ 1415

6+ 1856

0+ 331

2+ 1196

2+ 297

4+ 744

6+ 1328

8+ 2019

0+ 1334

2+ 1250

0+ 698

3+ 1246

4+ 1398

2+ 848

6+ 2009

2+ 358

4+ 889

6+ 1556

0+ 1335

2+ 1515

0+ 988

3+ 1242

4+ 1502

2+ 893

5+ 1872

4+ 2081

6+ 2196

8+ 2320

96

127

57515 82

101

67

10819 74

89 7030

12050

60

81 25

36

23

B(E2) W.u.

2(E0)•103

Spectroscopy of mixing in the Cd isotopes:ρ2 (E0)103 values in 114Cd

0

1

2

E(MeV)114Cdρ2(E0)103

0.655

1.8313

192

438

891

2

0+

2+ 558

0

1284

4+0+ 1306

0+ 1135

2+

1364

4+ 1732

2+

1210

3+

4+

1864

19322+ 184

2

4+ 2152

3+ 2205

12020

<130<120

255

αJ2 βJ

2

0102 0.95 0.052123 0.88 0.124142 0.67 0.332224 0.50 0.502223 0.93 0.07mixing is 2-state

αJ2 βJ

2

0102 0.99 0.012123 0.97 0.024142 0.94 0.052224 0.87 0.042223 0.87 0.09

Garrett, Green, Wood PR C78 044307 2008To fit B(E2)’s

IBM2-MIXmixing is multi-state

expt

th

Excited 0+ decays in the Cd isotopes

TRIUM F EEC Update on Research Proposal Update of Proposed Research for Experiment # :1288

7.9

40

1680

27.0

0.051

80

30.2 31.1 33.5

0.730

27.40.0

127

0 0

2 658

2 1476 01473

0 1731

0 0

2 618

012242 1313

0 1433

0 0

2 558

2 12100 1306

01135

0 0

2 513

212130 1283

01380

110Cd 112Cd 114Cd 116Cd

<

(8) (3) (19) (12)

<< (12)

99(14)(14)

(16)

26(4)(17)

(6)9(22)

3.0(8) 104

Figure 2: Port ion of the level schemes for 110,112,114,116Cd showing the decays from the low-lying 0+

states. The observed transit ions between levels are indicated by arrows with widths proport ional to

the B(E2) values and are labeled with the absolute B(E2) values or limits, with the uncertaint ies

in parentheses.

The result of our studies with the 8π spectrometer have been extremely successful. Very recent ly,

we have published our first results from the 110In decay to 110Cd from S984 [9]. Combining level

lifet imes from the (n, n γ) react ion, and the branching rat ios or limits from the β-decay data, we

could, for the first t ime, extract B(E2) values or limits for every possible decay from the previously-

purported mult i-phonon states. What we found was remarkable – aside from the 0+ int ruder band

head and 6+ state in the ground state band, there was a lack of enhancement in any of the tran-

sitions between the intruder configuration and the non-intruder states. Comparison with theoret ical

calculat ions indicated that this scenario could only occur if the mixing were weak [9].

The reject ion of the strong-mixing scenario in 110Cd immediately raised the quest ion of the

explanat ion of the decay of the excited 0+ states. In the previous vibrat ional picture, the 0+3 level

was a two-phonon state and the 0+2 level the intruder band head; maximal mixing of these two levels

was required to account for the enhancement of the B(E2; 0+2 → 0+

gs) value and the cancellat ion of

the matrix elements contribut ing to the B(E2; 0+3 → 0+

gs). However, since this st rong-mixing scenario

was rejected, a new interpretat ion was required. From the decay pat terns, the underlying structure of

the non-intruder has the appearance that is associated with a γ-soft potent ial, or Wilets-Jean model,

whose key signature is an enhanced decay of the excited 0+ state to the second excited 2+ state, as

observed in the Cd isotopes as shown in Fig. 2.

In addit ion to this paradigm shift in the 110Cd structure, it was also suggested that the propert ies

of the 0+4 level, previously assigned as a three-phonon 0+ , was actually the head of a deformed proton

4p − 6h int ruder band. This suggest ion was based on its strongly favored decay to the 2+ int ruder

band level, which has theproton 2p− 4h assignment. Figure3 displays a port ion of theγ-ray spectrum

of coincidences with a 1397-keV γ ray from the 3475-keV I = 1 → 2079-keV 0+4 level, clearly showing

the dominance of the 295-keV 0+4 → 2+

3 (i ) γ ray feeding the 2+ int ruder level. Also noted is the

locat ion of a potent ial 603-keV 0+4 → 2+

2 t ransit ion (the expected enhanced transit ion if the 0+4 level

were a three-phonon state); the extracted upper limit for the branch is < 0.18. With a sensit ivity

to individual branches at the 10− 4 level, the β-decay data provides an unprecedented view into the

collect ive nature of low-lying states.

2

Deformed band head 0+ states: strong E2 decay to “one-phonon” 2+ states

“Two-phonon” 0+ states: very weak E2 decay to “one-phonon” 2+ states;but strong E2 decay to “two-phonon” 2+ states

Introduction to mid-shell collectivityin Z = 48, 52 (N = 66) isotones

0+

2+

4+

0+2+

2+

3+

(4)+

4+6+

8+

(5)+

6+

0+

0+

2+

2+

2+

4+

4+

4+

3+

6+

5+ 6+

8+

0

1

2

3

118Te 114Cd

MIX

E(MeV)

0+

2+

0+3-

other states

.

otherstates

3356

691115

801014

312

624

11936

π (4p-2h) ?

π (2p-4h)

0+

Differences exist for 03+ and higher-lying states

Demise of quadrupole vibrations in 110-116Cd: low-energy 0+ states are shell and subshell excitations

0

1

2

0d+

2d+

4d+

6d+

01+

21+

22+

41+

0+,3+,4+,6+

02+

23+

trans. 110Cd 112Cd 114Cd 116Cd harm.vib.

π 2p-4h

π 2h g9/2-2

π 2h p1/2-

2

P.E. Garrett and J.L. Wood, J.Phys. G37, 064028 (2010) J.L. Wood, J.Phys. Conf. Ser. 403, 012011 (2012)

E(MeV)

2302 242 278 175 3510 42

2341 < 5 < 0.4 < 0.3 < 7 31

2322 < 0.76 < 2 2.84 2.06 17

0221 < 7.9 0.009944 0.00264 0.554 60

2101 27 30 31 34 30 (norm)

B(E2)’s (W.u.) from lifetime measurements @ Univ. of Kentucky using (n,n’γ).

High-lying, low-energy transitions are difficult to observe: used 8Pi array @TRIUMF-ISAC and ultrahigh statistics β-decay scheme studies.

4d2d 11535 11912

Coexisting deformed bands in the even-mass Pb isotopes

Figure from Heyde & Wood Heavy arrows indicate E0+M1+E2 transitions:G.D. Dracoulis et al., PR C67 R 051301 2003

Shape coexistence in 184Pt:revealed by E0 transitions


Figure: Heyde & Wood

Figure from A. Saha et al. PL B82 208 1979

Zirconium isotopes have excited 0+ states that are strongly populated in two- and four-nucleon transfer reactions

(6Li,8B)--a)

(14C,16O)--b)

(d,6Li)

(t,p)

gs 02+ %

gs gs 100%

gs = 01+

Documents

E0 transitions: where we have been, where we are … transitions: where we have been, where we are going, where we would like to go John L. Wood School of Physics Georgia Institute