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Shell-model progress in the investigation of 132 Sn mass region Houda NAÏDJA In Collaboration with Frédéric NOWACKI IPHC Strasbourg, France LPMS, Université Constantine 1, Algeria. 20 th Colloque GANIL 2017 Amboise October 15-20, 2017 Houda Naïdja ([email protected]) GANIL 2017 October 15-20 2017 1 / 29

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Page 1: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Shell-model progressin the investigation of 132Sn mass region

Houda NAÏDJA

In Collaboration with Frédéric NOWACKI

IPHC Strasbourg, FranceLPMS, Université Constantine 1, Algeria.

20th Colloque GANIL 2017Amboise October 15-20, 2017

Houda Naïdja ([email protected]) GANIL 2017 October 15-20 2017 1 / 29

Page 2: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Introduction

G. S. Simpson et al., PRL 113, 132502 (2014)H. Naïdja et al., J. Phys. Conf. Series 580, 012030 (2015)

H. Naïdja et al., Acta. Phys. Pol B 46, 669 (2015)R. Lozeva et al., PRC 93,014316 (2016)

R. Lozeva et al., PRC 93,014316 (2016)U. Urban et al., PRC 93, 034326 (2016)H. Naïdja et al., PRC 95, 064303 (2017)H. Naïdja et al.,PRC 96, 034312 (2017)

132Sn

2/29

Page 3: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Introduction

☞ G. S. Simpson et al., PRL 113, 132502 (2014)H. Naïdja et al., J. Phys. Conf. Series 580, 012030 (2015)

H. Naïdja et al., Acta. Phys. Pol B 46, 669 (2015)R. Lozeva et al., PRC 93,014316 (2016)

R. Lozeva et al., PRC 93,014316 (2016)U. Urban et al., PRC 93, 034326 (2016)H. Naïdja et al., PRC 95, 064303 (2017)H. Naïdja et al.,PRC 96, 034312 (2017)

Low-lying state energies and isomeric transitions in 134,136,138Sn

seniority-mixing

3/29

Page 4: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Introduction

G. S. Simpson et al., PRL 113, 132502 (2014)☞ H. Naïdja et al., J. Phys. Conf. Series 580, 012030 (2015)

☞ H. Naïdja et al., Acta. Phys. Pol B 46, 669 (2015)R. Lozeva et al., PRC 93,014316 (2016)

R. Lozeva et al., PRC 93,014316 (2016)U. Urban et al., PRC 93, 034326 (2016)H. Naïdja et al., PRC 95, 064303 (2017)H. Naïdja et al.,PRC 96, 034312 (2017)

Non sub-shell closure at N=90, and the tins masses

4/29

Page 5: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Introduction

G. S. Simpson et al., PRL 113, 132502 (2014)H. Naïdja et al., J. Phys. Conf. Series 580, 012030 (2015)

H. Naïdja et al., Acta. Phys. Pol B 46, 669 (2015)☞ R. Lozeva et al., PRC 93,014316 (2016)

☞ R. Lozeva et al., PRC 93,014316 (2016)U. Urban et al., PRC 93, 034326 (2016)H. Naïdja et al., PRC 95, 064303 (2017)H. Naïdja et al.,PRC 96, 034312 (2017)

Revised level scheme of 136Sb, and the first spectroscopic information on 140Sb

5/29

Page 6: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Introduction

G. S. Simpson et al., PRL 113, 132502 (2014)H. Naïdja et al., J. Phys. Conf. Series 580, 012030 (2015)

H. Naïdja et al., Acta. Phys. Pol B 46, 669 (2015)R. Lozeva et al., PRC 93,014316 (2016)

R. Lozeva et al., PRC 93,014316 (2016)☞ U. Urban et al., PRC 93, 034326 (2016)☞ H. Naïdja et al., PRC 95, 064303 (2017)

H. Naïdja et al.,PRC 96, 034312 (2017)

142Ba 144Ce

High spin states and collectivity in 142Ba and 144Ce

6/29

Page 7: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Introduction

G. S. Simpson et al., PRL 113, 132502 (2014)H. Naïdja et al., J. Phys. Conf. Series 580, 012030 (2015)

H. Naïdja et al., Acta. Phys. Pol B 46, 669 (2015)R. Lozeva et al., PRC 93,014316 (2016)

R. Lozeva et al., PRC 93,014316 (2016)U. Urban et al., PRC 93, 034326 (2016)H. Naïdja et al., PRC 95, 064303 (2017)

☞ H. Naïdja et al.,PRC 96, 034312 (2017)

spectroscopy and collectivity in Xe, Te, Ba, Ce, Nd nuclei, N=82,84,86

7/29

Page 8: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Shell-model overview

Model space

☞Diagonalization with Antoine and Nathan

Strasbourg SM codes.

Effective interaction

1 derived from realistic interaction

N3LO

2 renormalised by Vlow−k to exclude

the repulsive short range (cutoff

Λ = 2.2fm−1).

3 adapted to the model space by many

body perturbation theory,

Veff =

Vlow +VlowQ

E −H0

Vlow

︸ ︷︷ ︸

second order

+VlowQ

E−H0Vlow

QE−H0

Vlow

4 Monopole and Multipole adjutments

to N3LO interaction

⇓N3LOP interaction

r5i r4h

8/29

Page 9: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Part I : Spectroscopy and collectivity in even-even nuclei

Te, Xe, Ba, Ce, Nd with 82 ≤ N ≤ 88

9/29

Page 10: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Energy levels of Te,Xe,Ba,Ce,Nd 82 ≤ N ≤ 86

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

0

500

1000

1500

2000

E (

keV

)

134Te 136Te 138Te

Exp SM Exp SM Exp SM0+

2+

4+6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0

500

1000

1500

2000

E (

keV

)

136Xe 138Xe 140XeExp SM Exp SM Exp SM

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0

500

1000

1500

2000

E (

keV

)138Ba 140Ba 142Ba

Exp SM Exp SM Exp SM0+

2+

4+

6+

0+

2+

4+6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0

500

1000

1500

2000

E (

keV

)

140Ce 142Ce 144CeExp SM Exp SM Exp SM

6+

4+

2+

0+

6+

4+

2+

0+ 0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+ 0

500

1000

1500

2000

E (

keV

)

142Nd 144Nd 146NdExp SM Exp SM Exp SM

6+

4+

2+

0+0+

2+

4+6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

0+

2+

4+

6+

A compression in the level schemes from N=82 to N=86 isotones⇓

sign of collectivity

10/29

Page 11: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

E2 Transitions

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

100

200

300

400

500

600

700

800

900

1000

134Te 136Xe 138Ba 140Ce 142Nd

BE

2(2+ ->

0+ ) [e

.fm]

N=82

600

800

1000

1200

1400

1600

1800

2000

138Te 140Xe 142Ba 144Ce 146Nd

BE

2(2+ ->

0+ ) [e

.fm]

N=86

200

400

600

800

1000

1200

136Te 138Xe 140Ba 142Ce 144Nd

B(E

2;2+ ->

0+ ) (e

2 fm4 )

N=84

600

800

1000

1200

1400

1600

1800

2000

2200

2400

140Te 142Xe 144Ba 146Ce

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

N=88

✓ The overestimated 136Te

strength is now consistent with

the new measurement

J. M. Allmond et al. PRL. 118, 092503 (2017)

✓ small B(E2) in N=82 isotones,

due to spherical character

✓ strong B(E2) in N=86 and 88

isotones, reflecting the

presence of collective

character

(eeff (ν),eeff (π)) = (0.6e,1.6e)

11/29

Page 12: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

M1 Moments

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

FREE g−FACTORS

(gsπ ,g

lπ) = (5.5857,1.0)

(gsν ,g

lν) = (−3.8263,0.0)

☞ overall bad agreement with the data

EFFECTIVE g-FACTORS

(gsπ ,g

lπ) = (3.250,1.069)

(gsν ,g

lν) = (−1.506,0.019)

☞ overall good agreement with the data

µ(2+,4+,6+)

-1

0

1

2

3

4

5

6

7

8

134Te136Xe136Xe138Ba138Ba138Ba142Ba140Ce140Ce142Ce146Ce142Nd144Nd146Nd

µ [µ N

]

expg free

12/29

Page 13: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

M1 Moments

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

FREE g−FACTORS

(gsπ ,g

lπ) = (5.5857,1.0)

(gsν ,g

lν) = (−3.8263,0.0)

☞ overall bad agreement with the data

EFFECTIVE g-FACTORS

(gsπ ,g

lπ) = (3.250,1.069)

(gsν ,g

lν) = (−1.506,0.019)

☞ overall good agreement with the data

µ(2+,4+,6+)

-1

0

1

2

3

4

5

6

7

8

134Te136Xe136Xe138Ba138Ba138Ba142Ba140Ce140Ce142Ce146Ce142Nd144Nd146Nd

µ (µ N

)

gfreegeffExp

13/29

Page 14: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Signs of Collectivity in N=86, 88 isotones

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

0

500

1000

1500

2000

2500

52 54 56 58 60 52 54 56 58 60 52 54 56 58 60 52 54 56 58

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

Z

N=82N=84N=86N=88

-100

-80

-60

-40

-20

0

20

40

60

80

100

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q [e

.fm2 ]

21+

22+

-100

-50

0

50

100138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q(3+ )[

e.fm

2 ]

0

500

1000

1500

2000

2500

3000

3500

4000

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

BE

2(3+ ->

2 2+ )[e2 .fm

4 ]

14/29

Page 15: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Signs of Collectivity in N=86, 88 isotones

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

0

500

1000

1500

2000

2500

52 54 56 58 60 52 54 56 58 60 52 54 56 58 60 52 54 56 58

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

Z

N=82N=84N=86N=88

-100

-80

-60

-40

-20

0

20

40

60

80

100

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q [e

.fm2 ]

21+

22+

-100

-50

0

50

100138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q(3+ )[

e.fm

2 ]

0

500

1000

1500

2000

2500

3000

3500

4000

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

BE

2(3+ ->

2 2+ )[e2 .fm

4 ]

0

500

1000

1500

2000

2500

52 54 56 58 60 52 54 56 58 60 52 54 56 58 60 52 54 56 58

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

Z

N=82N=84N=86N=88

Strong BE2 tarnsitions

15/29

Page 16: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Signs of Collectivity in N=86, 88 isotones

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

0

500

1000

1500

2000

2500

52 54 56 58 60 52 54 56 58 60 52 54 56 58 60 52 54 56 58

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

Z

N=82N=84N=86N=88

-100

-80

-60

-40

-20

0

20

40

60

80

100

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q [e

.fm2 ]

21+

22+

-100

-50

0

50

100138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q(3+ )[

e.fm

2 ]

0

500

1000

1500

2000

2500

3000

3500

4000

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

BE

2(3+ ->

2 2+ )[e2 .fm

4 ]

0

500

1000

1500

2000

2500

3000

3500

Te Xe Ba Ce Nd

E(2

2+ ) [k

eV]

N=82N=84N=86N=88

Very low-lying 2+2 energy state

16/29

Page 17: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Signs of Collectivity in N=86, 88 isotones

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

0

500

1000

1500

2000

2500

52 54 56 58 60 52 54 56 58 60 52 54 56 58 60 52 54 56 58

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

Z

N=82N=84N=86N=88

-100

-80

-60

-40

-20

0

20

40

60

80

100

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q [e

.fm2 ]

21+

22+

-100

-50

0

50

100138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q(3+ )[

e.fm

2 ]

0

500

1000

1500

2000

2500

3000

3500

4000

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

BE

2(3+ ->

2 2+ )[e2 .fm

4 ]

-100

-80

-60

-40

-20

0

20

40

60

80

100

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q [e

.fm2 ]

21+

22+

Q(2+γ ) =−Q(2+

yrast )

17/29

Page 18: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Signs of Collectivity in N=86, 88 isotones

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

0

500

1000

1500

2000

2500

52 54 56 58 60 52 54 56 58 60 52 54 56 58 60 52 54 56 58

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

Z

N=82N=84N=86N=88

-100

-80

-60

-40

-20

0

20

40

60

80

100

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q [e

.fm2 ]

21+

22+

-100

-50

0

50

100138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q(3+ )[

e.fm

2 ]

0

500

1000

1500

2000

2500

3000

3500

4000

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

BE

2(3+ ->

2 2+ )[e2 .fm

4 ]

-100

-50

0

50

100138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q(3+ )[

e.fm

2 ]Q(3+) = 0

18/29

Page 19: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Signs of Collectivity in N=86, 88 isotones

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

0

500

1000

1500

2000

2500

52 54 56 58 60 52 54 56 58 60 52 54 56 58 60 52 54 56 58

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

Z

N=82N=84N=86N=88

-100

-80

-60

-40

-20

0

20

40

60

80

100

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q [e

.fm2 ]

21+

22+

-100

-50

0

50

100138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q(3+ )[

e.fm

2 ]

0

500

1000

1500

2000

2500

3000

3500

4000

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

BE

2(3+ ->

2 2+ )[e2 .fm

4 ]

0

500

1000

1500

2000

2500

3000

3500

4000

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

BE

2(3+ ->

2 2+ )[e2 .fm

4 ]strong B(E2,3+ → 2+

2 )

19/29

Page 20: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Signs of Collectivity in N=86, 88 isotones

H. Naïdja, F. Nowacki and B. Bounthong, PRC 96, 034312 (2017).

0

500

1000

1500

2000

2500

52 54 56 58 60 52 54 56 58 60 52 54 56 58 60 52 54 56 58

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

Z

N=82N=84N=86N=88

-100

-80

-60

-40

-20

0

20

40

60

80

100

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q [e

.fm2 ]

21+

22+

-100

-50

0

50

100138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

Q(3+ )[

e.fm

2 ]

0

500

1000

1500

2000

2500

3000

3500

4000

138Te140Te140Xe142Xe142Ba144Ba144Ce146Ce146Nd

BE

2(3+ ->

2 2+ )[e2 .fm

4 ]

Features of K=2 triaxial γ-band

20/29

Page 21: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Deformation parametersβ deformation parameter and γ angle∗

0

5

10

15

20

25

30

0.1 0.12 0.14 0.16 0.18 0.2

γ an

gle

[°]

β

140Te

142Xe

144Ba146Ce

138Te

140Xe142Ba

144Ce

146Nd

Mild deformation in 138Te and 140Te.

Increase in deformation with non-axiality from 140Xe to 146Nd.

The maximum of the collectivity in 144Ba and 146Ce

(*) K. Kumar, PRL 28, 249 (1972) 21/29

Page 22: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

SU(3) symmetries vs collectivity

500

1000

1500

2000

2500

138Te 140Xe 142Ba 144Ce 146Nd

BE

2(2+ ->

0+ ) [e2 .fm

4 ]

Expr4h-r5i

qp-SU(3)

minor impact of pseudo-SU(3) / quasi-SU(3)

Excitations to πh11/2 reduce the collectivity due to the pairing effect,

which confirms our previous conclusion in 140Sm analysis with 100Sn core

M.Klintefjord, et al, PRC 93, 054303 (2016)

qu

asi-

SU

(3)

pse

ud

o-S

U(3

)

22/29

Page 23: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

PES with CHFSM

012345678910

0

10

20

30

40

5060

(deg)γ

β

138Te

0 0.03 0.06 0.09 0.12 0.15

0

0.03

0.06

0.09

0.12

0.15 (MeV)

012345678910

0

10

20

30

40

5060

(deg)γ

β

140Xe

0 0.04 0.08 0.12 0.16

0

0.04

0.08

0.12

0.16 (MeV)

012345678910

5

3

3 1

0

10

20

30

40

5060

(deg)γ

β

144Ce

0 0.06 0.12 0.18 0.24

0

0.06

0.12

0.18

0.24 (MeV)

012345678910

97

53

3 1

0

10

20

30

40

5060

(deg)γ

β

142Ba

0 0.06 0.12 0.18 0.24

0

0.06

0.12

0.18

0.24 (MeV)

012345678910

0

10

20

30

40

5060

(deg)γ

β

146Nd

0 0.06 0.12 0.18 0.24

0

0.06

0.12

0.18

0.24 (MeV)

Presence of triaxial minima

CHFSM is an approach developped by Strasbourg SM group :B. Bounthong, PhD Thesis, Université de Strasbourg (2016)

The same SM Hamiltonian (N3LOP) and the same model space (r4h-r5i) are used

(β ,γ) are consistent with Kumar23/29

Page 24: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Part II : Even-odd and odd-even nuclei

24/29

Page 25: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

odd-even nuclei : Sb, I, Cs, La

0

200

400

600

800

1000

1200

E(k

eV)

Exp VlowN3LOP

135Sb

(7/2+)

(5/2+)

(3/2+)

(9/2+)

(11/2+)

(1/2+)

7/2+

5/2+

3/2+

9/2+

11/2+

1/2+

7/2+

5/2+

3/2+

9/2+

11/2+

1/2+

0

500

1000

1500

2000

E(k

eV)

Exp Exp SMSM

135I 137I

(7/2+)

(5/2)+

(11/2+)(9/2+)

7/2+

5/2+

11/2+9/2+

(7/2+)

5/2+

9/2+11/2+

13/2+

7/2+

5/2+

9/2+11/2+

(13/2+)

0

500

1000

1500

2000

E(k

eV)

Exp Exp SMSM

137Cs 139Cs

7/2+

5/2+

(11/2+)

1/2+

(15/2+)

7/2+

5/2+

11/2+

1/2+

15/2+

7/2+

5/2+,7/2+3/2+,5/2+,7/2+

(9/2+)(11/2+)

(13/2+)(15/2+)

7/2+

5/2+3/2+

9/2+1/2+

13/2+15/2+

0

500

1000

1500

2000

E(k

eV)

Exp Exp SMSM

139La 141La

7/2+

5/2+

9/2+

(13/2+)

1/2+

7/2+

5/2+

9/2+

13/2+

1/2+

(7/2+)

(5/2+)

(3/2+)(1/2+)

7/2+

5/2+

3/2+

1/2+

25/29

Page 26: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

odd-even nuclei : Sb, I, Cs, La

0

200

400

600

800

1000

1200

E(k

eV)

Exp VlowN3LOP

135Sb

(7/2+)

(5/2+)

(3/2+)

(9/2+)

(11/2+)

(1/2+)

7/2+

5/2+

3/2+

9/2+

11/2+

1/2+

7/2+

5/2+

3/2+

9/2+

11/2+

1/2+

0

500

1000

1500

2000

E(k

eV)

Exp Exp SMSM

135I 137I

(7/2+)

(5/2)+

(11/2+)(9/2+)

7/2+

5/2+

11/2+9/2+

(7/2+)

5/2+

9/2+11/2+

13/2+

7/2+

5/2+

9/2+11/2+

(13/2+)

0

500

1000

1500

2000

E(k

eV)

Exp Exp SMSM

137Cs 139Cs

7/2+

5/2+

(11/2+)

1/2+

(15/2+)

7/2+

5/2+

11/2+

1/2+

15/2+

7/2+

5/2+,7/2+3/2+,5/2+,7/2+

(9/2+)(11/2+)

(13/2+)(15/2+)

7/2+

5/2+3/2+

9/2+1/2+

13/2+15/2+

0

500

1000

1500

2000

E(k

eV)

Exp Exp SMSM

139La 141La

7/2+

5/2+

9/2+

(13/2+)

1/2+

7/2+

5/2+

9/2+

13/2+

1/2+

(7/2+)

(5/2+)

(3/2+)(1/2+)

7/2+

5/2+

3/2+

1/2+

0

200

400

600

800

1000

1200

E(k

eV)

Exp VlowN3LOP

135Sb

(7/2+)

(5/2+)

(3/2+)

(9/2+)

(11/2+)

(1/2+)

7/2+

5/2+

3/2+

9/2+

11/2+

1/2+

7/2+

5/2+

3/2+

9/2+

11/2+

1/2+

26/29

Page 27: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

even-odd nuclei : Te, Xe, Ba, Ce

0

200

400

600

800

1000

1200

1400

1600

E(k

eV)

Exp Exp SMSM137Te 139Te

(7/2-)

(3/2-)

(1/2-)(5/2-)(11/2-)(9/2-)

7/2-

3/2-

1/2-

5/2-

11/2-

9/2-

(7/2-)

(11/2-)

(13/2-)(15/2-)

7/2-

11/2-

13/2-15/2-

0

200

400

600

800

1000

1200

1400

1600

E(k

eV)

Exp Exp SMSM137Xe 139Xe

7/2-

3/2-

(1/2)-

9/2-5/2-

7/2-

3/2-

1/2-

9/2-5/2-

3/2-(7/2-)(5/2-)

(9/2-)

3/2-

7/2-

5/2-

9/2-

0

200

400

600

800

1000

1200

1400

1600

1800

E(k

eV)

Exp Exp SMSM139Ba 141Ba

7/2-

3/2-

(1/2)-

9/2-

5/2-

7/2-

3/2-

1/2-

9/2-

5/2-

3/2-(5/2-)(7/2-)

(9/2-)(11/2-)

(13/2-)

3/2-5/2-7/2-

9/2-11/2-

13/2-

0

200

400

600

800

1000

1200

1400

1600

1800

E(k

eV)

Exp Exp SMSM141Ce 143Ce

7/2-

3/2-

1/2-

9/2-13/2+

5/2-

7/2-

3/2-

1/2-9/2-13/2+

5/2-

3/2-7/2-5/2-

9/2-

3/2-5/2-7/2-

9/2-

27/29

Page 28: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Magnetic dipole momentµGS(7/2+,7/2−,3/2−)

-4

-2

0

2

4

135I 137Cs139Cs139La135Te137Xe139Xe139Ba141Ba141Ce143Ce

µ [µ N

]

Expgeff

gfree

using the effective g factors the agreement with the data is far more

satisfying than using the free g factors.

a disagreement in µ(7/2−) of 141Ce remains unexplained.

28/29

Page 29: Shell-model progressganilcolloque.sciencesconf.org/data/N._Houda.pdf134Te 136Xe 138Ba 140Ce 142Nd BE2(2 + -> 0 + ) [e .fm ] N=82 600 800 1000 1200 1400 1600 1800 2000 138Te 140Xe 142Ba

Conclusions and Perspectives

✓ Our results achieved using N3LOP are in good agreement compared tothe data.

✓ First signs of the collectivity in the N=86,88 isotones was shown, with the

signature of triaxial γ band.

✓ Evolution of the collectivity is sensitive to SU(3) symmetries of neutrons

and protons orbits sequence and to the excitations to h11/2

✓ These applications constitute a stringent test of N3LOP interaction, and

our predictions are a benchmark for future experimental measurements.

☞ Extension of the calculations to higher mass number along isotopic and

isotonic chains☞ Explore the octupole correlations

29/29