Shell Model Far From Stability: IoI Mergers Fr ed eric Nowacki - - PowerPoint PPT Presentation

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Shell Model Far From Stability: IoI Mergers Fr ed eric Nowacki - - PowerPoint PPT Presentation

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Shell Model Far From Stability: IoI Mergers Fr ed eric Nowacki NUSPIN 2017, June 26 th -29 th 2017 The Archipelago of Islands of Inversion N=8 N=20 N=28 N=40 N=50 11 Li 32 Mg 42 Si 64 Cr 74 Cr Landscape of medium mass nuclei: Mergers

slide-1
SLIDE 1

Shell Model Far From Stability: IoI Mergers

Fr´ ed´ eric Nowacki

NUSPIN 2017, June 26th-29th 2017

slide-2
SLIDE 2

The Archipelago of Islands of Inversion

N=8 N=20 N=28 N=40 N=50

11Li 32Mg 42Si 64Cr 74Cr

slide-3
SLIDE 3

Landscape of medium mass nuclei: Mergers

  • 68 Ni

78 Ni 16 O 14 C 48 Ni 56 Ni 36 S 34 Si 32 Mg 52 Ca 48 Ca 40 Ca 22 O 42 Si 64 Cr

f7/2 g 9/2 f7/2 f5/2 g 9/2 f5/2 p 1/2 p 3/2 f7/2 p 3/2

90 Zr 80 Zr

p 1/2 g 9/2 d 5/2 p 1/2 f5/2 p 3/2

12 Be

f7/2

40 Mg 74 Cr 8 8 20 28 20 28 32 40

Z

28 28 20

N

40 8 20 14 Sn 100 50 50

slide-4
SLIDE 4

Evolution of nuclear shells due to Tensor force

42Si 91Zr 78Ni 132Sn

  • T. Otsuka et al.,
  • Phys. Rev. Lett. 95, 232502-1 (2005)

(2j> + 1)V T

j>,j′ + (2j< + 1)V T j<,j′ = 0,

reduction of spin-orbit partners splitting while filling j′ shell

slide-5
SLIDE 5

Spin-orbit shell closure far from stability

  • H. O.
  • H. O.

Π+ Π−

14 d5/2 28 f7/2

42 14Si28

sd-pf: 42Si deformed pf-sdg: 78Ni ??? sdg-phf: 132Sn doubly magic Evolution of Z=14 from N=20 to N=28 Evolution of Z=28 from N=40 to N=50 Evolution of N=50 from Z=40 to Z=28

slide-6
SLIDE 6

Spin-orbit shell closure far from stability

  • H. O.
  • H. O.

Π+ Π−

28 f7/2 50 g9/2

78 28Ni50

sd-pf: 42Si deformed pf-sdg: 78Ni ??? sdg-phf: 132Sn doubly magic Evolution of Z=14 from N=20 to N=28 Evolution of Z=28 from N=40 to N=50 Evolution of N=50 from Z=40 to Z=28

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SLIDE 7

Spin-orbit shell closure far from stability

  • H. O.
  • H. O.

Π+ Π−

50 g9/2 82 h11/2

132 50 Sn82

sd-pf: 42Si deformed

78Ni ???

pf-sdg: sdg-phf:

132Sn doubly magic

Evolution of Z=14 from N=20 to N=28 Evolution of Z=28 from N=40 to N=50 Evolution of N=50 from Z=40 to Z=28

slide-8
SLIDE 8

Physics around 78Ni

π υ sdg pf

60Ca PFSDG-U interaction: realistic TBME pf shell for protons and gds shell for neutrons monopole corrections ( 3N forces ) proton and neutrons gap 78Ni fixed to phenomenological derived values Calculations: excitations across Z=28 and N=50 gaps up to 5*1010 Slater Determinant basis states m-scheme code ANTOINE (non public version) J-scheme code NATHAN (parallelized version): 0.5*109 J basis states

slide-9
SLIDE 9

Physics around 78Ni

π pf υ sdg

60Ca PFSDG-U interaction: realistic TBME pf shell for protons and gds shell for neutrons monopole corrections ( 3N forces ) proton and neutrons gap 78Ni fixed to phenomenological derived values Calculations: excitations across Z=28 and N=50 gaps up to 5*1010 Slater Determinant basis states m-scheme code ANTOINE (non public version) J-scheme code NATHAN (parallelized version): 0.5*109 J basis states

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SLIDE 10

Neutron intruders constraints

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 38 40 42 44 46 48 50 52

Zn

S2n (MeV) Neutron number

PFSDG-U mix Exp.

slide-11
SLIDE 11

Neutron intruders constraints

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 38 40 42 44 46 48 50 52

Zn

S2n (MeV) Neutron number

PFSDG-U mix Exp.

g9/2 d5/2

50 Zn 82

N=50 Gap + Vd5d5

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SLIDE 12

Neutron intruders constraints

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 38 40 42 44 46 48 50 52

Zn

S2n (MeV) Neutron number

PFSDG-U mix Exp. 1 2 3 46 48 50 52 54

Zn

2+ 4+ E(2+) (MeV) Neutron number

PFSDG-U NNDC RIKEN

RIKEN MINOS experiment

  • C. Shand, Z. Podolyak, et al. to be published
slide-13
SLIDE 13

Neutron intruders constraints

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 38 40 42 44 46 48 50 52

Zn

S2n (MeV) Neutron number

PFSDG-U mix Exp. 1 2 3 46 48 50 52 54 56

Ge

2+ 4+ E(2+) (MeV) Neutron number

PFSDG-U NNDC RIKEN

RIKEN MINOS experiment

  • M. Lettman, V. Werner, N. Pietralla, accepted in Phys. Rev. C
slide-14
SLIDE 14

Neutron intruders constraints

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 38 40 42 44 46 48 50 52

Zn

S2n (MeV) Neutron number

PFSDG-U mix Exp. 1 2 3 46 48 50 52 54 56

Ge

2+ 4+ E(2+) (MeV) Neutron number

PFSDG-U NNDC RIKEN

RIKEN MINOS experiment

  • M. Lettman, V. Werner, N. Pietralla, accepted in Phys. Rev. C
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SLIDE 15

Neutron intruders constraints

9 10 11 12 13 14 42 44 46 48 50

Cu

S2n (MeV) Neutron number

JUN45 PFSDG-U AME2016 ISOLTRAP

data: AME2016 and ISOLTRAP Collaboration 2017

slide-16
SLIDE 16

NpNh excitations

9 10 11 12 13 14 42 44 46 48 50

Cu

S2n (MeV) Neutron number

0p0h AME2016 ISOLTRAP

theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

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SLIDE 17

NpNh excitations

9 10 11 12 13 14 42 44 46 48 50

Cu

S2n (MeV) Neutron number

2p2h AME2016 ISOLTRAP

theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

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SLIDE 18

NpNh excitations

9 10 11 12 13 14 42 44 46 48 50

Cu

S2n (MeV) Neutron number

4p4h AME2016 ISOLTRAP

theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

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SLIDE 19

NpNh excitations

9 10 11 12 13 14 42 44 46 48 50

Cu

S2n (MeV) Neutron number

6p6h AME2016 ISOLTRAP

theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

slide-20
SLIDE 20

NpNh excitations

9 10 11 12 13 14 42 44 46 48 50

Cu

S2n (MeV) Neutron number

8p8h AME2016 ISOLTRAP

theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

slide-21
SLIDE 21

NpNh excitations

9 10 11 12 13 14 42 44 46 48 50

Cu

S2n (MeV) Neutron number

8p8h AME2016 ISOLTRAP

theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

F . N

  • w

a c k i a n d I S O L T R A P C O L L A B O R A T I O N , t

  • b

e p u b l i s h e d

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SLIDE 22

NpNh excitations

9 10 11 12 13 14 42 44 46 48 50

Cu

S2n (MeV) Neutron number

8p8h AME2016 ISOLTRAP

theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

  • R. P. de Groote and the CRIS collaboration

in preparation

slide-23
SLIDE 23

Spherical structure of 78Ni

Ab-initio CC predictions for 78Ni

slide-24
SLIDE 24

Spherical structure of 78Ni

slide-25
SLIDE 25

Spherical structure of 78Ni

  • 370
  • 368
  • 366
  • 364
  • 362
  • 360

2 4 6 8 10 12 14 16 18

78Ni

E (MeV) ph excitations

0+1 2+1

GS and 2+

ph in 78Ni

slide-26
SLIDE 26

Spherical structure of 78Ni

  • 370
  • 368
  • 366
  • 364
  • 362
  • 360

2 4 6 8 10 12 14 16 18

78Ni

E (MeV) ph excitations

0+1 2+1

GS and 2+

ph in 78Ni

∼3.1

slide-27
SLIDE 27

Schematic SU3 predictions

20 22 24 26 28

Z

  • 5
  • 4
  • 3
  • 2
  • 1

1 2 3

MeV

0p-0h 2p-2h 4p-4h 78Ni 76Fe 74Cr

monopole + quadrupole model proton gap (5MeV) and neutron gap (5 MeV) estimates Quasi-SU3 (protons) and Pseudo-SU3 (neutrons) blocks Qs = (2q20 + 3.)b2)2/3.5 En = Gmp

n (50)−ωκ

Qm

0 (π)

15 b2

+ Qm

0 (ν)

23 b2

2 Gmp

n (50) = n ( 3.0 8 nπ f + 2.25) + ∆(n) + δp(n)

Prediction of Island of strong collectivity below 78Ni !!!

slide-28
SLIDE 28

Shape coexistence in 78Ni

At first approximation, 78Ni has a double closed shell structure for GS But very low-lying competing structures From the diagonalization, the first excited states in 78Ni are :

  • 0+

2 -2+ 1 predicted at 2.6-2.9 MeV and to be

deformed intruders of a rotationnal band !!! “1p1h” 2+

2 predicted at ∼ 3.1 MeV

Necessity to go beyond (fpg 9

2 d 5 2 ) LNPS

space and beyond ab-initio description Portal to a new Island of Inversion Constrained deformed HF in the SM basis (B. Bounthong, PhD Thesis, Strasbourg)

slide-29
SLIDE 29

Shape coexistence in 78Ni

At first approximation, 78Ni has a double closed shell structure for GS But very low-lying competing structures From the diagonalization, the first excited states in 78Ni are :

  • 0+

2 -2+ 1 predicted at 2.6-2.9 MeV and to be

deformed intruders of a rotationnal band !!! “1p1h” 2+

2 predicted at ∼ 3.1 MeV

Necessity to go beyond (fpg 9

2 d 5 2 ) LNPS

space and beyond ab-initio description Portal to a new Island of Inversion 78Ni

slide-30
SLIDE 30

Shape coexistence in 78Ni

At first approximation, 78Ni has a double closed shell structure for GS But very low-lying competing structures From the diagonalization, the first excited states in 78Ni are :

  • 0+

2 -2+ 1 predicted at 2.6-2.9 MeV and to be

deformed intruders of a rotationnal band !!! “1p1h” 2+

2 predicted at ∼ 3.1 MeV

Necessity to go beyond (fpg 9

2 d 5 2 ) LNPS

space and beyond ab-initio description Portal to a new Island of Inversion 78Ni

78Ni

2+

1

→ 0+

2

∆E∗ th. 0.229 Qs

  • 39

BE2↓ th. 516 Qi(e.fm2) 135 from Qs Qi(e.fm2) 195 from BE2 βe

2

∼ 0.3 prolate

slide-31
SLIDE 31

Shape coexistence in 78Ni

At first approximation, 78Ni has a double closed shell structure for GS But very low-lying competing structures From the diagonalization, the first excited states in 78Ni are :

  • 0+

2 -2+ 1 predicted at 2.6-2.9 MeV and to be

deformed intruders of a rotationnal band !!! “1p1h” 2+

2 predicted at ∼ 3.1 MeV

Necessity to go beyond (fpg 9

2 d 5 2 ) LNPS

space and beyond ab-initio description Portal to a new Island of Inversion 78Ni p f 7

2

f 5

2

p 3

2

p 1

2

5.4 1.0 1.0 0.5 n g 9

2

d 5

2

s 1

2

g 7

2

d 3

2

7.0 1.2 0.8 0.5 0.4

slide-32
SLIDE 32

Island of Deformation below 78Ni: PES’s

1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

72Fe

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

74Fe

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

76Fe

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

70Cr

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

72Cr

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

74Cr

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV

N=46 N=48 N=50

72Fe 74Fe 76Fe 70Cr 72Cr 74Cr

slide-33
SLIDE 33

Island of Deformation below 78Ni: PES’s

1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

72Fe

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

74Fe

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

76Fe

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

70Cr

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

72Cr

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

74Cr

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV

N=46 N=48 N=50

72Fe 74Fe 76Fe 70Cr 72Cr 74Cr

E*(2+

1 )

Qs BE2↓ Qm

i

βm (MeV) (e.fm2) (e2.fm4) (e.fm2)

70Cr

0.30

  • 41

420 340 0.26

72Cr

0.23

  • 48

549 407 0.30

74Cr

0.24

  • 51

630 552 0.39

72Fe

0.44

  • 36

316 289 0.21

74Fe

0.47

  • 39

330 308 0.22

76Fe

0.35

  • 39

346 320 0.25 Predicted New IoI centered at 74Cr

slide-34
SLIDE 34

Island of Deformation below 78Ni: PES’s

1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

72Fe

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

74Fe

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

76Fe

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

70Cr

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

72Cr

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV 1 2 3 4 5 6 7 8 9 10 10 20 30 40 50 60 γ β

74Cr

0.09 0.18 0.27 0.36 0.45 0.09 0.18 0.27 0.36 0.45 MeV

N=46 N=48 N=50

72Fe 74Fe 76Fe 70Cr 72Cr 74Cr

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SLIDE 35

The N=40 and N=50 IoI’s Merge

36 38 40 42 44 46 48 50 52

N

0.5 1 1.5 2 2.5 3

MeV

Ni (exp) Ni-Cr (lnps) Ni (pfsdg) Cr (exp) Cr (pfsdg)

64Cr 74Cr 68Ni 78Ni

slide-36
SLIDE 36

Like the N=20 and N=28 IoI’s did

18 20 22 24 26 28 30

N

1 2 3 4

2

+ excitation energy in MeV Si (exp) Si (th) Mg (exp) Mg (th) Ca (exp)

32Mg 40Mg 40Ca 48Ca

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SLIDE 37

Shell evolution and Tensor mechanism in mid-mass nuclei

−1 40 50 2 4 1h11/2 2d5/2 2d3/2 En ergy (MeV) (c) Neutron ESPE 2d5/2 1g7/2

  • 1

1 2 3 4 40 50 2d5/2 1g7/2 2d3/2 1h11/2 2 4 (c) neutron SPE at N=51 d3/2 d5/2 s 1/2 g7/2 h11/2 40 50 Z

  • T. Otsuka, et al.
  • K. Sieja, et al.
  • T. Otsuka, et al.
  • Phys. Rev. Lett. 95, 232502-1 (2005)
  • Phys. Rev. C79, 064310 (2009)
  • Phys. Rev. Lett. 104, 012501 (2010)
slide-38
SLIDE 38

Effective Single Particle Energies: Trends

34Si 42Si

7.5 5.1

  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10

14 16 20 28 32 34 40

ESPE (MeV) Neutron number

Silicium chain

d5/2 s1/2 d3/2

slide-39
SLIDE 39

Effective Single Particle Energies: Trends

34Si 42Si

7.5 5.1

  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10

14 16 20 28 32 34 40

ESPE (MeV) Neutron number

Silicium chain

d5/2 s1/2 d3/2

Spin-Tensor decomposition

V =

  • Vk =
  • Uk.Sk

k S S′ spin-tensor components C=Central 1 1 1 1 ALS=antisymmetric spin-orbit 1 1 1 LS=spin-orbit 2 1 1 T=Tensor

slide-40
SLIDE 40

Effective Single Particle Energies: Trends

34Si 42Si

7.5 5.1

  • 40
  • 35
  • 30
  • 25
  • 20
  • 15
  • 10

14 16 20 28 32 34 40

ESPE (MeV) Neutron number

Silicium chain

d5/2 s1/2 d3/2

∆ (d 5

2 -d 3 2 ) filling f 7 2 between 34Si and 42Si

G matrix SDPF-U diff. Tot

  • 3.15
  • 2.38

+0.77 Central +0.24

  • 0.11
  • 0.35

Vector

  • 0.27

+0.55 +0.82 LS

  • 0.11

+0.11 +0.22 ALS

  • 0.16

+0.44 +0.60 Tensor

  • 2.65
  • 2.77

+0.12

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SLIDE 41

Effective Single Particle Energies: Trends

68Ni 78Ni

8.6 4.9

  • 30
  • 20
  • 10

20 28 32 38 40 50

ESPE (MeV) Neutron number

f5/2 p3/2 p1/2 g9/2 f7/2

slide-42
SLIDE 42

Effective Single Particle Energies: Trends

68Ni 78Ni

8.6 4.9

  • 30
  • 20
  • 10

20 28 32 38 40 50

ESPE (MeV) Neutron number

f5/2 p3/2 p1/2 g9/2 f7/2

∆ (f 7

2 -f 5 2 ) filling g 9 2 between 68Ni and 78Ni

G matrix PFSDG-U diff. Tot

  • 3.21
  • 3.70
  • 0.49

Central

  • 0.28
  • 0.23

+0.05 Vector

  • 0.081
  • 1.09
  • 1.01

LS

  • 0.081
  • 0.65
  • 0.57

ALS 0.0

  • 0.44
  • 0.44

Tensor

  • 2.84
  • 2.38

+0.46

slide-43
SLIDE 43

Effective Single Particle Energies: Trends

68Ni 78Ni

8.6 4.9

  • 30
  • 20
  • 10

20 28 32 38 40 50

ESPE (MeV) Neutron number

f5/2 p3/2 p1/2 g9/2 f7/2

∆ (f 7

2 -f 5 2 ) filling g 9 2 between 68Ni and 78Ni

G matrix PFSDG-U diff. Tot

  • 3.21
  • 3.70
  • 0.49

Central

  • 0.28
  • 0.23

+0.05 Vector

  • 0.081
  • 1.09
  • 1.01

LS

  • 0.081
  • 0.65
  • 0.57

ALS 0.0

  • 0.44
  • 0.44

Tensor

  • 2.84
  • 2.38

+0.46

slide-44
SLIDE 44

Effective Single Particle Energies: Trends

120Sn 132Sn

5.2 5.9

  • 20
  • 10

50 56 64 66 70 82

ESPE (MeV) Neutron number

g9/2 d5/2 g7/2 s1/2 d3/2 h11/2

slide-45
SLIDE 45

Effective Single Particle Energies: Trends

120Sn 132Sn

5.2 5.9

  • 20
  • 10

50 56 64 66 70 82

ESPE (MeV) Neutron number

g9/2 d5/2 g7/2 s1/2 d3/2 h11/2

∆ (g 9

2 -g 7 2 ) filling h 11 2 between 120Sn and 132Sn

Vlowk NNSP diff. Tot

  • 2.15

+0.89 +3.04 Central

  • 0.034

+0.30 +0.33 Vector +0.12 +1.55 +1.43 LS

  • 0.038
  • 0.06
  • 0.022

ALS +0.49 +1.61 +1.12 Tensor

  • 2.30
  • 0.96

+1.34

slide-46
SLIDE 46

Effective Single Particle Energies: Trends

120Sn 132Sn

5.2 5.9

  • 20
  • 10

50 56 64 66 70 82

ESPE (MeV) Neutron number

g9/2 d5/2 g7/2 s1/2 d3/2 h11/2

∆ (g 9

2 -g 7 2 ) filling h 11 2 between 120Sn and 132Sn

Vlowk NNSP diff. Tot

  • 2.15

+0.89 +3.04 Central

  • 0.034

+0.30 +0.33 Vector +0.12 +1.55 +1.43 LS

  • 0.038
  • 0.06
  • 0.022

ALS +0.49 +1.61 +1.12 Tensor

  • 2.30
  • 0.96

+1.34

slide-47
SLIDE 47

Summary

The physics around magic or semi-magic closures depends of subtle balances between the spherical mean field and the (very large) correlation energies of the open shell configurations at play There is a common mechanism explaining the appearance of ”islands of inversion/deformation” (IoI’s) in nuclei with large neutron excess, and shape coexistence usually shows up as a its portal The IoI’s at N=20 and N=28 merge in the Magnesium isotopes. Shape coexistence in 78Ni is the portal to a new IoI at N=50 The IoI’s at N=40 and N=50 merge in the Chromium isotopes. Increasing role of spin-orbite force in intermediate mass region

slide-48
SLIDE 48

Summary

Special Thanks to:

  • B. Bounthong, E. Caurier, H. Naidja, A. Zuker
  • A. Poves
  • H. Grawe, S. Lenzi
  • J. Herzfeld