model stability from shell...
TRANSCRIPT
![Page 1: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/1.jpg)
Model Stability from Shell far
Frederic Nowacki1
International Collaborations in nuclear theory:
Theory for open-shell nuclei near the limits of stability
1Strasbourg-Madrid Shell-Model collaboration
![Page 2: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/2.jpg)
Landscape of medium mass nuclei
���������������
���������������
���������������
���������������
������������
������������
��������
��������
��������
��������
���������������
���������������
����������
����������
����������
����������
68 Ni 78 Ni
16 O
14 C
48 Ni 56 Ni
36 S34 Si32 Mg
52 Ca48 Ca40 Ca
22 O
42 Si
64 Cr
f7/2 g 9/2
f7/2
f5/2
g 9/2f5/2p 1/2p 3/2f7/2
p 3/2
90 Zr80 Zr
p 1/2g 9/2
d5/2
p 1/2f5/2p 3/2
12 Be
f7/2
40 Mg
74 Cr
8 8
20
28
20
28
32
40Z
28
2820
N
40
82014
Sn100 50
50
![Page 3: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/3.jpg)
Landscape of medium mass nuclei
���������������
���������������
���������������
���������������
������������
������������
��������
��������
��������
��������
���������������
���������������
����������
����������
����������
����������
68 Ni 78 Ni
16 O
14 C
48 Ni 56 Ni
36 S34 Si32 Mg
52 Ca48 Ca40 Ca
22 O
42 Si
64 Cr
f7/2 g 9/2
f7/2
f5/2
g 9/2f5/2p 1/2p 3/2f7/2
p 3/2
90 Zr80 Zr
p 1/2g 9/2
d5/2
p 1/2f5/2p 3/2
12 Be
f7/2
40 Mg
74 Cr
8 8
20
28
20
28
32
40Z
28
2820
N
40
82014
Sn100 50
50
UNDERSTANDING REGULARITIESfor both SPHERICAL and DEFORMED systems
Magic Numbers: 24O, 48Ni, 54Ca, 78Ni, 100Sn
Islands of Deformation: 12Be, 32Mg, 42Si, 64Cr, 80Zr ...
Variety of phenomena dictated by shell structure
Close connection between collective behaviour and underlyingshell structure
H = Hm +HM
Interplay between• Monopole field (spherical mean field)• Multipole correlations (pairing, Q.Q, ...)
![Page 4: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/4.jpg)
Effective Single Particle Energies: Trends
28O
34Si
40Ca
-20
-10
0
10
8 14 16 20
ES
PE
(M
eV
)
Proton number
d5/2s1/2d3/2f7/2
p3/2
p1/2f5/2
At the neutron drip line, the ESPE’s of28O are completely at variance with
those of 40Ca at the stability valley. Thechange from the standard ESPE’s of16O to the anomalous ones in 28O istotally due to the interactions of sd shellneutrons among themselves
Notice that the sd shell orbits remainalways below th pf shell with the ν0f 7
2
and ν0p 3
2
orbitals DO get inverted
The monopole part of theneutron-proton interaction restores theN=20 shell gap when the valley ofstability is approached
Spin-Tensor decomposition shows it ismainly a Central and Tensor effect
Magic numbers are associated to enegy gaps in the spherical meanfield. Therefore, to promote particles above the Fermi levels costsenergy
However some intruders configurations can overwhelm their loss ofmonopole energy with their huge gain in correlation energy
Several examples of this phenomenon exist in stable magic nuclei(as in 40Ca nucleus) in the form of coexisting spherical, deformedand superdeformed states in a very narrow energy range
At the very neutron rich or very proton rich edges, the T=0 and T=1channels of the effective nuclear interaction weight very differentlythan they do at the stability line. Therefore the effective singleparticle structure may suffer important changes, leading in somecases to the vanishing of established shell closures or to theappearance of new ones
![Page 5: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/5.jpg)
Effective Single Particle Energies: Trends
28O
34Si
40Ca
-20
-10
0
10
8 14 16 20
ES
PE
(M
eV
)
Proton number
d5/2s1/2d3/2f7/2
p3/2
p1/2f5/2
At the neutron drip line, the ESPE’s of28O are completely at variance with
those of 40Ca at the stability valley. Thechange from the standard ESPE’s of16O to the anomalous ones in 28O istotally due to the interactions of sd shellneutrons among themselves
Notice that the sd shell orbits remainalways below th pf shell with the ν0f 7
2
and ν0p 3
2
orbitals DO get inverted
The monopole part of theneutron-proton interaction restores theN=20 shell gap when the valley ofstability is approached
Spin-Tensor decomposition shows it ismainly a Central and Tensor effect
![Page 6: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/6.jpg)
Effective Single Particle Energies: Trends
28O
34Si
40Ca
-20
-10
0
10
8 14 16 20
ES
PE
(M
eV
)
Proton number
d5/2s1/2d3/2f7/2
p3/2
p1/2f5/2
At the neutron drip line, the ESPE’s of28O are completely at variance with
those of 40Ca at the stability valley. Thechange from the standard ESPE’s of16O to the anomalous ones in 28O istotally due to the interactions of sd shellneutrons among themselves
Notice that the sd shell orbits remainalways below th pf shell with the ν0f 7
2
and ν0p 3
2
orbitals DO get inverted
The monopole part of theneutron-proton interaction restores theN=20 shell gap when the valley ofstability is approached
Spin-Tensor decomposition shows it ismainly a Central and Tensor effect
0
1s (2) 2
1p(8)(6)
8
1g7/2
1f2p
1d2s 2
3s
(38)(40)(50)
1g
1h
1h11/2
2d
3p
2d3/2
2p1/2
2s
1p3/21p1/2
1s
2p3/2
1h9/2
3s1/2
2d5/2
2f7/22f5/2 3p3/23p1/2
(64)
(82)
2f
1g9/2
1f5/2
1f7/2
1d3/2
1d5/2
(8)
(6)(4)(2)
(10)
(8)(6)
(4)(2)
(12)
(2)(6)(4)
(12)
(8)
(6)(2)(4)
(2)
(2)
(4)
(126)
(20)(14)
1i13/2 (14)
N=5
N=4
N=3
N=2
N=1
N=0
(28) 28
82
126
50
![Page 7: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/7.jpg)
Effective Single Particle Energies: Trends
28O
32Mg
34Si
40Ca
1.9
5.1
7.3
N=20
-20
-10
0
10
8 14 16 20
ES
PE
(M
eV
)
Proton number
d5/2
s1/2
d3/2f7/2
p3/2p1/2
f5/2
At the neutron drip line, the ESPE’s of28O are completely at variance with
those of 40Ca at the stability valley. Thechange from the standard ESPE’s of16O to the anomalous ones in 28O istotally due to the interactions of sd shellneutrons among themselves
Notice that the sd shell orbits remainalways below th pf shell with the ν0f 7
2
and ν0p 3
2
orbitals DO get inverted
The monopole part of theneutron-proton interaction restores theN=20 shell gap when the valley ofstability is approached
Spin-Tensor decomposition shows it ismainly a Central and Tensor effect
![Page 8: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/8.jpg)
Effective Single Particle Energies: Trends
28O
32Mg
34Si
40Ca
1.9
5.1
7.3
N=20
-20
-10
0
10
8 14 16 20
ES
PE
(M
eV
)
Proton number
d5/2s1/2d3/2f7/2
p3/2
p1/2f5/2
At the neutron drip line, the ESPE’s of28O are completely at variance with
those of 40Ca at the stability valley. Thechange from the standard ESPE’s of16O to the anomalous ones in 28O istotally due to the interactions of sd shellneutrons among themselves
Notice that the sd shell orbits remainalways below th pf shell with the ν0f 7
2
and ν0p 3
2
orbitals DO get inverted
The monopole part of theneutron-proton interaction restores theN=20 shell gap when the valley ofstability is approached
Spin-Tensor decomposition shows it ismainly a Central and Tensor effect
![Page 9: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/9.jpg)
Effective Single Particle Energies: Trends
28O
32Mg
34Si
40Ca
1.9
5.1
7.3
N=20
-20
-10
0
10
8 14 16 20
ES
PE
(M
eV
)
Proton number
d5/2s1/2d3/2f7/2
p3/2
p1/2f5/2
At the neutron drip line, the ESPE’s of28O are completely at variance with
those of 40Ca at the stability valley. Thechange from the standard ESPE’s of16O to the anomalous ones in 28O istotally due to the interactions of sd shellneutrons among themselves
Notice that the sd shell orbits remainalways below th pf shell with the ν0f 7
2
and ν0p 3
2
orbitals DO get inverted
The monopole part of theneutron-proton interaction restores theN=20 shell gap when the valley ofstability is approached
Spin-Tensor decomposition shows it ismainly a Central and Tensor effect
Spin-Tensor decomposition
V =∑
Vk =∑
Uk .Sk
k S S′ spin-tensor components
0 0 0 C=Central1 1
1 0 1 ALS=antisymmetric spin-orbit1 01 1 LS=spin-orbit
2 1 1 T=Tensor
![Page 10: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/10.jpg)
Effective Single Particle Energies: Trends
28O
32Mg
34Si
40Ca
1.9
5.1
7.3
N=20
-20
-10
0
10
8 14 16 20
ES
PE
(M
eV
)
Proton number
d5/2s1/2d3/2f7/2
p3/2
p1/2f5/2
At the neutron drip line, the ESPE’s of28O are completely at variance with
those of 40Ca at the stability valley. Thechange from the standard ESPE’s of16O to the anomalous ones in 28O istotally due to the interactions of sd shellneutrons among themselves
Notice that the sd shell orbits remainalways below th pf shell with the ν0f 7
2
and ν0p 3
2
orbitals DO get inverted
The monopole part of theneutron-proton interaction restores theN=20 shell gap when the valley ofstability is approached
Spin-Tensor decomposition shows it ismainly a Central and Tensor effect
∆ (f 72-d 3
2) filling d 5
2between 32Mg and 34Si
G matrix SDPF-U diff.Tot 1.57 1.17 -0.40
Central 1.11 0.70 -0.41Vector -0.159 -0.155 0.004
LS -0.049 -0.12 -0.071ALS -0.11 -0.035 0.075
Tensor 0.61 0.63 0.02Nuclear shell evolution and in-medium NN interaction
N. Smirnova, K. Heyde, B. Bailly, F. Nowacki, K. Sieja
Phys. Rev. C86, 034314 (2012)
![Page 11: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/11.jpg)
Effective Single Particle Energies: Trends
28O
32Mg
34Si
40Ca
1.9
5.1
7.3
N=20
-20
-10
0
10
8 14 16 20
ES
PE
(M
eV
)
Proton number
d5/2s1/2d3/2f7/2
p3/2
p1/2f5/2
At the neutron drip line, the ESPE’s of28O are completely at variance with
those of 40Ca at the stability valley. Thechange from the standard ESPE’s of16O to the anomalous ones in 28O istotally due to the interactions of sd shellneutrons among themselves
Notice that the sd shell orbits remainalways below th pf shell with the ν0f 7
2
and ν0p 3
2
orbitals DO get inverted
The monopole part of theneutron-proton interaction restores theN=20 shell gap when the valley ofstability is approached
Spin-Tensor decomposition shows it ismainly a Central and Tensor effect
∆ (f 72-d 3
2) filling d 5
2between 32Mg and 34Si
G matrix SDPF-U diff.Tot 1.57 1.17 -0.40
Central 1.11 0.70 -0.41Vector -0.159 -0.155 0.004
LS -0.049 -0.12 -0.071ALS -0.11 -0.035 0.075
Tensor 0.61 0.63 0.02Nuclear shell evolution and in-medium NN interaction
N. Smirnova, K. Heyde, B. Bailly, F. Nowacki, K. Sieja
Phys. Rev. C86, 034314 (2012)
![Page 12: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/12.jpg)
Effective Single Particle Energies: Trends
1d3/2
νΠ
1f7/22p3/2
Si35
2s1/2
1d5/2
∆ (p 3
2
-p 1
2
) filling s 1
2
between 34Si and 36S
KLS N3LO N3LO(bare) (4~ω)
Tot 0.58 0.58 0.60
Central 0.00 0.00 0.00Vector 0.58 0.58 0.60Tensor 0.00 0.00 0.00
G. Burgunder, PhD ThesisGANIL, December 2011
![Page 13: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/13.jpg)
Effective Single Particle Energies: Trends
1d3/2
νΠ
1f7/22p3/2
Si35
2s1/2
1d5/2
∆ (p 3
2
-p 1
2
) filling s 1
2
between 34Si and 36S
KLS N3LO N3LO(bare) (4~ω)
Tot 0.58 0.58 0.60
Central 0.00 0.00 0.00Vector 0.58 0.58 0.60Tensor 0.00 0.00 0.00
G. Burgunder, PhD ThesisGANIL, December 2011
![Page 14: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/14.jpg)
Effective Single Particle Energies: Trends
1d3/2
νΠ
1f7/22p3/2
2s1/2
1d5/2
37 S
∆ (p 3
2
-p 1
2
) filling s 1
2
between 34Si and 36S
KLS N3LO N3LO(bare) (4~ω)
Tot 0.58 0.58 0.60
Central 0.00 0.00 0.00Vector 0.58 0.58 0.60Tensor 0.00 0.00 0.00
G. Burgunder, PhD ThesisGANIL, December 2011
![Page 15: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/15.jpg)
Effective Single Particle Energies: Trends
1d3/2
νΠ
1f7/22p3/2
2s1/2
1d5/2
37 S
∆ (p 3
2
-p 1
2
) filling s 1
2
between 34Si and 36S
KLS N3LO N3LO(bare) (4~ω)
Tot 0.58 0.58 0.60
Central 0.00 0.00 0.00Vector 0.58 0.58 0.60Tensor 0.00 0.00 0.00
G. Burgunder, PhD ThesisGANIL, December 2011
![Page 16: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/16.jpg)
Correlation Energies
Let us consider the configurations with closed N=20
[sd ]12,Z (normal filling) and the ones with two neutrons
blocked in the pf shell [sd ]10,Z [pf ]2,0 (intruder)
And calculate the energy of the ground states at fixed
configuration, with and without correlations
![Page 17: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/17.jpg)
Correlations energies: normal vs 2p-2h intruder
8 9 10 11 12 13 14 15 16 17 18
Z-14
-12
-10
-8
-6
-4
-2
0
0p-0h 2p-2h
F. Nowacki and A. PovesPhys. Rev. C90, 014302 (2014)
![Page 18: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/18.jpg)
Correlations energies: normal vs 2p-2h intruder
8 9 10 11 12 13 14 15 16 17 18
Z-14
-12
-10
-8
-6
-4
-2
0
0p-0h 2p-2h
28O
F. Nowacki and A. PovesPhys. Rev. C90, 014302 (2014)
![Page 19: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/19.jpg)
Correlations energies: normal vs 2p-2h intruder
8 9 10 11 12 13 14 15 16 17 18
Z-14
-12
-10
-8
-6
-4
-2
0
0p-0h 2p-2h
28O
30Ne
F. Nowacki and A. PovesPhys. Rev. C90, 014302 (2014)
![Page 20: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/20.jpg)
Correlations energies: normal vs 2p-2h intruder
8 9 10 11 12 13 14 15 16 17 18
Z-14
-12
-10
-8
-6
-4
-2
0
0p-0h 2p-2h
28O
30Ne
32Mg
F. Nowacki and A. PovesPhys. Rev. C90, 014302 (2014)
![Page 21: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/21.jpg)
Correlations energies: normal vs 2p-2h intruder
8 9 10 11 12 13 14 15 16 17 18
Z-14
-12
-10
-8
-6
-4
-2
0
0p-0h 2p-2h
28O
30Ne
32Mg34Si
F. Nowacki and A. PovesPhys. Rev. C90, 014302 (2014)
![Page 22: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/22.jpg)
Gaps: normal vs 2p-2h intruder
8 9 10 11 12 13 14 15 16 17 18
Z
-2
0
2
4
6
8
10
12
14M
eVE(2p-2h)-E(0p-0h) : without correlationsE(2p-2h)-E(0p-0h) : with correlations
ISLAND OF INVERSION
30Ne
32Mg
34Si
F. Nowacki and A. PovesPhys. Rev. C90, 014302 (2014)
![Page 23: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/23.jpg)
Merging of the islands of inversion at N=20 and N=28
8 10 12 14 16 18 20 22 24 26 28 30 32
N0
1
2
3
4
2+ e
xcita
tion
ener
gy in
MeV
EXPTH
0
20
40
60
80
100
34 36 38 40 42 44
BE
2(e2 .fm
4 )
A
Si
BE2,SMEXP
8 10 12 14 16 18 20 22 24 26 28 30 32
N
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2+ e
xcita
tion
ener
gy in
MeV
EXPTH
30 32 34 36 38 40A
0
50
100
150
e2 fm4
B(E2) expB(E2) th
Si
Mg
![Page 24: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/24.jpg)
Merging of the islands of inversion at N=20 and N=28
8 10 12 14 16 18 20 22 24 26 28 30 32
N0
1
2
3
4
2+ e
xcita
tion
ener
gy in
MeV
EXPTH
0
20
40
60
80
100
34 36 38 40 42 44
BE
2(e2 .fm
4 )
A
Si
BE2,SMEXP
8 10 12 14 16 18 20 22 24 26 28 30 32
N
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2+ e
xcita
tion
ener
gy in
MeV
EXPTH
30 32 34 36 38 40A
0
50
100
150
e2 fm4
B(E2) expB(E2) th
Si
Mg
![Page 25: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/25.jpg)
Merging of the islands of inversion at N=20 and N=28
8 10 12 14 16 18 20 22 24 26 28 30 32
N0
1
2
3
4
2+ e
xcita
tion
ener
gy in
MeV
EXPTH
0
20
40
60
80
100
34 36 38 40 42 44
BE
2(e2 .fm
4 )
A
Si
BE2,SMEXP
8 10 12 14 16 18 20 22 24 26 28 30 32
N
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2+ e
xcita
tion
ener
gy in
MeV
EXPTH
30 32 34 36 38 40A
0
50
100
150
e2 fm4
B(E2) expB(E2) th
Si
Mg
![Page 26: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/26.jpg)
Merging of the islands of inversion at N=20 and N=28
8 10 12 14 16 18 20 22 24 26 28 30 32
N0
1
2
3
4
2+ e
xcita
tion
ener
gy in
MeV
EXPTH
0
20
40
60
80
100
34 36 38 40 42 44
BE
2(e2 .fm
4 )
A
Si
BE2,SMEXP
8 10 12 14 16 18 20 22 24 26 28 30 32
N
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2+ e
xcita
tion
ener
gy in
MeV
EXPTH
30 32 34 36 38 40A
0
50
100
150
e2 fm4
B(E2) expB(E2) th
Si
Mg
![Page 27: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/27.jpg)
Island of inversion at N=40, an old story: 1996
A. Poves
![Page 28: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/28.jpg)
Island of inversion at N=40, an old story: 2003
8 10 12 14 16 18 20
Proton number
−20
−15
−10
−5
0
5
effe
ctiv
e S
PE
(M
eV)
N=20
1f7/2
1d3/2
2p3/2
20 22 24 26 28
Proton number
−2
0
2
4
6
effe
ctiv
e S
PE
(M
eV)
N=40
1g9/2
1f5/2
2d5/2
GANIL
![Page 29: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/29.jpg)
More recent experimental information
RAPID COMMUNICATIONS
PHYSICAL REVIEW C 81, 051304(R) (2010)
Collectivity at N = 40 in neutron-rich 64Cr
A. Gade,1,2 R. V. F. Janssens,3 T. Baugher,1,2 D. Bazin,1 B. A. Brown,1,2 M. P. Carpenter,3 C. J. Chiara,3,4 A. N. Deacon,5
S. J. Freeman,5 G. F. Grinyer,1 C. R. Hoffman,3 B. P. Kay,3 F. G. Kondev,6 T. Lauritsen,3 S. McDaniel,1,2 K. Meierbachtol,1,7
A. Ratkiewicz,1,2 S. R. Stroberg,1,2 K. A. Walsh,1,2 D. Weisshaar,1 R. Winkler,1 and S. Zhu3
1National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA2Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
3Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA4Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
RAPID COMMUNICATIONS
PHYSICAL REVIEW C 81, 061301(R) (2010)
Onset of collectivity in neutron-rich Fe isotopes: Toward a new island of inversion?
J. Ljungvall,1,2,3 A. Gorgen,1 A. Obertelli,1 W. Korten,1 E. Clement,2 G. de France,2 A. Burger,4 J.-P. Delaroche,5 A. Dewald,6
A. Gadea,7 L. Gaudefroy,5 M. Girod,5 M. Hackstein,6 J. Libert,8 D. Mengoni,9 F. Nowacki,10 T. Pissulla,6 A. Poves,11
F. Recchia,12 M. Rejmund,2 W. Rother,6 E. Sahin,12 C. Schmitt,2 A. Shrivastava,2 K. Sieja,10 J. J. Valiente-Dobon,12
K. O. Zell,6 and M. Zielinska13
1CEA Saclay, IRFU, Service de Physique Nucleaire, F-91191 Gif-sur-Yvette, France2GANIL, CEA/DSM-CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen, France
3CSNSM, CNRS/IN2P3, F-91405 Orsay, France
MSU
GANIL
![Page 30: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/30.jpg)
SM framework
Island of inversion around 64Cr
S. Lenzi, F. Nowacki, A. Poves and K. Sieja
Phys. Rev. C 82, 054301, 2010.
f7/2
p1/2
f5/2
p3/2
Π
g9/2d5/2
Ca
ν
48
LNPS interaction:
based on realistic TBMEnew fit of the pf shell (KB3GR, E. Caurier)
monopole corrections
g9/2-d5/2 gap set to 1.5 Mev in 68Ni
Calculations:
up to 14p-14h excitations across Z=28and N=40 gaps
up to 1010
m-scheme code ANTOINE (non publicversion)
![Page 31: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/31.jpg)
Shape transition at N=40
68Ni
68Ni
0
0.5
1
1.5
2
2.5
3
20 22 24 26 28
E(2
+)
(MeV
)
Z
N=40
(a)SMEXP
0
100
200
300
400
500
20 22 24 26 28
B(E
2;2+
->
0+)
(e2 fm
4 )
Z
(b)
SMEXP
Nucleus νg9/2 νd5/2 configuration68Ni 0.98 0.10 0p0h(51%)66Fe 3.17 0.46 4p4h(26%)64Cr 3.41 0.76 6p6h(23%)62Ti 3.17 1.09 4p4h(48%)
![Page 32: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/32.jpg)
Shape transition at N=40
66Fe
66Fe
68Ni
68Ni
0
0.5
1
1.5
2
2.5
3
20 22 24 26 28
E(2
+)
(MeV
)
Z
N=40
(a)SMEXP
0
100
200
300
400
500
20 22 24 26 28
B(E
2;2+
->
0+)
(e2 fm
4 )
Z
(b)
SMEXP
Nucleus νg9/2 νd5/2 configuration68Ni 0.98 0.10 0p0h(51%)66Fe 3.17 0.46 4p4h(26%)64Cr 3.41 0.76 6p6h(23%)62Ti 3.17 1.09 4p4h(48%)
![Page 33: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/33.jpg)
Shape transition at N=40
64Cr
64Cr
66Fe
66Fe
68Ni
68Ni
0
0.5
1
1.5
2
2.5
3
20 22 24 26 28
E(2
+)
(MeV
)
Z
N=40
(a)SMEXP
0
100
200
300
400
500
20 22 24 26 28
B(E
2;2+
->
0+)
(e2 fm
4 )
Z
(b)
SMEXP
Nucleus νg9/2 νd5/2 configuration68Ni 0.98 0.10 0p0h(51%)66Fe 3.17 0.46 4p4h(26%)64Cr 3.41 0.76 6p6h(23%)62Ti 3.17 1.09 4p4h(48%)
![Page 34: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/34.jpg)
Neutron effective single particle energies
-25
-20
-15
-10
-5
0
5
20 28 32
ES
PE
(M
eV)
Z
(a)
N=40
f7/2p3/2f5/2p1/2g9/2d5/2
reduction of the νf5/2-g9/2 gap withremoving f7/2 protons
proximity of the quasi-SU3 partnerd5/2
inversion of d5/2 and g9/2 orbitalssame ordering as CC calculations
60Ca 64Cr 68Ni
-25
-20
-15
-10
-5
0
5
8 14 16
ES
PE
(M
eV)
Z
(b)
N=20
d5/2s1/2d3/2f7/2p3/2
reduction of the νd3/2-f7/2 gap withremoving d5/2 protons
proximity of the quasi-SU3 partnerp3/2
inversion of p3/2 and f7/2 orbitals
28O32Mg
34Si
![Page 35: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/35.jpg)
Neutron effective single particle energies
-25
-20
-15
-10
-5
0
5
20 28 32
ES
PE
(M
eV)
Z
(a)
N=40
f7/2p3/2f5/2p1/2g9/2d5/2
reduction of the νf5/2-g9/2 gap withremoving f7/2 protons
proximity of the quasi-SU3 partnerd5/2
inversion of d5/2 and g9/2 orbitalssame ordering as CC calculations
60Ca 64Cr 68Ni
-25
-20
-15
-10
-5
0
5
8 14 16
ES
PE
(M
eV)
Z
(b)
N=20
d5/2s1/2d3/2f7/2p3/2
reduction of the νd3/2-f7/2 gap withremoving d5/2 protons
proximity of the quasi-SU3 partnerp3/2
inversion of p3/2 and f7/2 orbitals
28O32Mg
34Si
G. Hagen et al.
Phys. Rev. Lett. 109, 032502 (2012)
![Page 36: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/36.jpg)
Extension of collectivity N=40 towards N=50
0
1
2
34 36 38 40 42 44 46 48
En
erg
y (
MeV
)
Neutron number
2+
4+
LNPS-mLiteratureThis work
0
1
2
34 36 38 40 42 44 46 48
En
erg
y (
MeV
)
Neutron number
2+
4+
LNPS-mLiteratureThis work
2
3
34 36 38 40 42 44 46 48R4
2=
E(4
+)/
E(2
+)
Neutron number
LNPS-mLiteratureThis work
2
3
34 36 38 40 42 44 46 48R4
2=
E(4
+)/
E(2
+)
Neutron number
LNPS-mLiteratureThis work
![Page 37: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/37.jpg)
Extension of collectivity N=40 towards N=50
0
1
2
34 36 38 40 42 44 46 48
En
erg
y (
MeV
)
Neutron number
2+
4+
LNPS-mLiteratureThis work
0
1
2
34 36 38 40 42 44 46 48
En
erg
y (
MeV
)
Neutron number
2+
4+
LNPS-mLiteratureThis work
2
3
34 36 38 40 42 44 46 48R4
2=
E(4
+)/
E(2
+)
Neutron number
LNPS-mLiteratureThis work
2
3
34 36 38 40 42 44 46 48R4
2=
E(4
+)/
E(2
+)
Neutron number
LNPS-mLiteratureThis work
![Page 38: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/38.jpg)
Extension of collectivity N=40 towards N=50
0
1
2
34 36 38 40 42 44 46 48
En
erg
y (
MeV
)
Neutron number
2+
4+
LNPS-mLiteratureThis work
0
1
2
34 36 38 40 42 44 46 48
En
erg
y (
MeV
)
Neutron number
2+
4+
LNPS-mLiteratureThis work
2
3
34 36 38 40 42 44 46 48R4
2=
E(4
+)/
E(2
+)
Neutron number
LNPS-mLiteratureThis work
2
3
34 36 38 40 42 44 46 48R4
2=
E(4
+)/
E(2
+)
Neutron number
LNPS-mLiteratureThis work
![Page 39: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/39.jpg)
Extension of collectivity N=40 towards N=50
0
1
2
34 36 38 40 42 44 46 48
En
erg
y (
MeV
)
Neutron number
2+
4+
LNPS-mLiteratureThis work
0
1
2
34 36 38 40 42 44 46 48
En
erg
y (
MeV
)
Neutron number
2+
4+
LNPS-mLiteratureThis work
2
3
34 36 38 40 42 44 46 48R4
2=
E(4
+)/
E(2
+)
Neutron number
LNPS-mLiteratureThis work
2
3
34 36 38 40 42 44 46 48R4
2=
E(4
+)/
E(2
+)
Neutron number
LNPS-mLiteratureThis work
C. Santamaria et al., submitted for publication in Phys. Rev. Lett.
![Page 40: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/40.jpg)
Spin-orbit shell closure far from stability
H. O.
H. O.
Π+
Π−
sd-pf: 42Si deformed
pf-sdg: 78Ni ???
sdg-phf: 132Sn
doubly magic
Evolution of Z=28 from N=40 to N=50
Evolution of N=50 from Z=40 to Z=28
![Page 41: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/41.jpg)
Three-body forces in medium mass nuclei
16O 24O 40Ca 48Ca 68Ni 78Ni
-10
-5
0
5
8 14 16
ds
0d5/21s1/2
-10
-5
0
5
20 28 32
fp0f7/21p3/2
-10
-5
0
5
40 50 56
gd0g9/21d5/2
Evolution of the neutron effective single-particle energies
with neutron filling in ds, fp, and gd shells
“Universal” mechanism for the generation of T=1 spin-orbit
shell closures
Connection with 3N forces and ab-initio calculations:
• “works” for Coupled-Cluster and to be checked in nickels
• problems for “ab-initio” core shell-model
Three body forces and persistence of spin-orbit shell gaps in medium-mass nuclei: Towards the doubly magic 78NiK. Sieja, F. NowackiPhys. Rev. C85, 051301(R) (2012)
![Page 42: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/42.jpg)
Physics around 78Ni
H. O.
H. O.
Π+/−
Π−/+
PFSDG-U interaction:
based on realistic TBMEpf shell for protons and gds shell forneutronsmonopole corrections
proton and neutrons gap 78Ni fixed tophenomenological derived values
Calculations:
excitations across Z=28 and N=50gaps
up to 1010 Slater Determinant basisstatesm-scheme code ANTOINE (nonpublic version)
![Page 43: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/43.jpg)
Physics around 78Ni
������������
������������
������������
������������
������������
������������
������������
������������
���������������
���������������
���������������
���������������
H. O.
H. O.
Π+/−
Π−/+
PFSDG-U interaction:
based on realistic TBMEpf shell for protons and gds shell forneutronsmonopole corrections
proton and neutrons gap 78Ni fixed tophenomenological derived values
Calculations:
excitations across Z=28 and N=50gaps
up to 1010 Slater Determinant basisstatesm-scheme code ANTOINE (nonpublic version)
![Page 44: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/44.jpg)
Island of Deformation below 78Ni
Schematic SU3 predictions: arXiv 1404.0224
Nilsson-SU3 selfconsistency:
Quadrupole dominance in heavy N=Z nuclei
Ni78 Fe76 Cr74-5
-4
-3
-2
-1
0
1
2
Ene
rgie
s in
MeV
rea
ltive
to th
e 0p
0h s
tate
s
0p-0h2p-2h4p-4h
monopole + quadrupole model
proton gap (5MeV) and neutron gap (5MeV) estimates
Quasi-SU3 (protons) and Pseudo-SU3(neutrons) blocks
Qs = (〈2q20〉 + 3.)b2)2/3.5
E = ǫi〈ni〉 − ~ωκ(〈2q20(3)〉
15+
〈2q20(4)〉
23)
Prediction of Island of strong collectivity
below 78Ni !!!
![Page 45: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/45.jpg)
Shape coexistence in 78Ni
At first approximation, 78Nihas a double closed shellstructure for GS
But very low-lying 4p4hstructures
The first excited state 2+1 in
78Ni predicted at 2.8 MeVand to be a deformedintruder !!!
Necessity to go beyond(fpg 9
2d 5
2) LNPS space
Constrained deformed HF in the SM basis
(B. Bounthong, Ph D Thesis, Strasbourg)
![Page 46: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/46.jpg)
Island of Deformation below 78Ni
Schematic SU3 predictions: arXiv 1404.0224
Nilsson-SU3 selfconsistency:
Quadrupole dominance in heavy N=Z nuclei
Ni78 Fe76 Cr74-5
-4
-3
-2
-1
0
1
2
Ene
rgie
s in
MeV
rea
ltive
to th
e 0p
0h s
tate
s
0p-0h2p-2h4p-4h
monopole + quadrupole model
proton gap (5MeV) and neutron gap (5MeV) estimates
Quasi-SU3 (protons) and Pseudo-SU3(neutrons) estimates
Qs = (〈2q20〉 + 3.)b2)2/3.5
E = ǫi〈ni〉 − ~ωκ(〈2q20(3)〉
15+
〈2q20(4)〉
23)
Prediction of Island of strong collectivity
below 78Ni !!!
![Page 47: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/47.jpg)
Island of Deformation below 78Ni
Schematic SU3 predictions: arXiv 1404.0224
Nilsson-SU3 selfconsistency:
Quadrupole dominance in heavy N=Z nuclei
Ni78 Fe76 Cr74-5
-4
-3
-2
-1
0
1
2
Ene
rgie
s in
MeV
rea
ltive
to th
e 0p
0h s
tate
s
0p-0h2p-2h4p-4h
monopole + quadrupole model
proton gap (5MeV) and neutron gap (5MeV) estimates
Quasi-SU3 (protons) and Pseudo-SU3(neutrons) estimates
Qs = (〈2q20〉 + 3.)b2)2/3.5
E = ǫi〈ni〉 − ~ωκ(〈2q20(3)〉
15+
〈2q20(4)〉
23)
Prediction of Island of strong collectivity
below 78Ni !!!
E*(2+1 ) Qs BE2↓ Qi from Qi from β
(MeV) (e.fm2) (e2.fm4) Qs from BE2
72Cr 0.24 -48 551 167 166 0.3774Cr 0.29 -46 515 162 161 0.3676Cr 0.41 -29 239 100 108 0.22
76Fe 0.35 -39 346 135 132 0.26
![Page 48: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/48.jpg)
Island of Deformation below 78Ni
Schematic SU3 predictions: arXiv 1404.0224
Nilsson-SU3 selfconsistency:
Quadrupole dominance in heavy N=Z nuclei
Ni78 Fe76 Cr74-5
-4
-3
-2
-1
0
1
2
Ene
rgie
s in
MeV
rea
ltive
to th
e 0p
0h s
tate
s
0p-0h2p-2h4p-4h
monopole + quadrupole model
proton gap (5MeV) and neutron gap (5MeV) estimates
Quasi-SU3 (protons) and Pseudo-SU3(neutrons) estimates
Qs = (〈2q20〉 + 3.)b2)2/3.5
E = ǫi〈ni〉 − ~ωκ(〈2q20(3)〉
15+
〈2q20(4)〉
23)
Prediction of Island of strong collectivity
below 78Ni !!!
0
1
2
34 36 38 40 42 44 46 48 50
En
erg
y (
MeV
)
Neutron number
2+
4+
PFSDG-ULiteratureThis work
Extension of Island of deformation to N=50 !!!
![Page 49: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/49.jpg)
Spin-orbit shell closure far from stability
H. O.
H. O.
Π+
Π−
sd-pf: 42Si deformed
pf-sdg: 78Ni ???
sdg-phf: 132Sn
doubly magic
Evolution of Z=28 from N=40 to N=50
Evolution of N=50 from Z=40 to Z=28
![Page 50: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/50.jpg)
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
ES
PE
(M
eV
)
Neutron number
Silicium chain
d5/2s1/2d3/2
![Page 51: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/51.jpg)
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
ES
PE
(M
eV
)
Neutron number
Silicium chain
d5/2s1/2d3/2
∆ (d 52-d 3
2) filling f 7
2between 34Si and 42Si
G matrix SDPF-U diff.Tot -3.15 -2.38 +0.77
Central 0.24 -0.11 -0.35Vector -0.27 0.55 0.82
LS -0.11 0.11 0.22ALS -0.16 0.44 0.60
Tensor -2.65 -2.77 0.12
![Page 52: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/52.jpg)
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
ES
PE
(M
eV
)
Neutron number
Silicium chain
d5/2s1/2d3/2
∆ (d 52-d 3
2) filling f 7
2between 34Si and 42Si
G matrix SDPF-U diff.Tot -3.15 -2.38 +0.77
Central 0.24 -0.11 -0.35Vector -0.27 0.55 0.82
LS -0.11 0.11 0.22ALS -0.16 0.44 0.60
Tensor -2.65 -2.77 0.12
![Page 53: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/53.jpg)
Effective Single Particle Energies: Trends
68Ni
78Ni
8.8
5.2
-30
-20
-10
0
20 28 32 38 40 50
ES
PE
(M
eV
)
Neutron number
f5/2p3/2
p1/2g9/2f7/2
![Page 54: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/54.jpg)
Effective Single Particle Energies: Trends
68Ni
78Ni
8.8
5.2
-30
-20
-10
0
20 28 32 38 40 50
ES
PE
(M
eV
)
Neutron number
f5/2p3/2
p1/2g9/2f7/2
∆ (f 72-f 5
2) filling g 9
2between 68Ni and 78Ni
G matrix PFSDG-U diff.Tot -3.21 -3.64 -0.43
Central -0.28 -0.12 +0.16Vector -0.081 -1.70 -1.62
LS -0.081 -1.12 -1.04ALS 0.0 -0.58 -0.58
Tensor -2.84 -1.82 +1.02
![Page 55: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/55.jpg)
Effective Single Particle Energies: Trends
68Ni
78Ni
8.8
5.2
-30
-20
-10
0
20 28 32 38 40 50
ES
PE
(M
eV
)
Neutron number
f5/2p3/2
p1/2g9/2f7/2
∆ (f 72-f 5
2) filling g 9
2between 68Ni and 78Ni
G matrix PFSDG-U diff.Tot -3.21 -3.64 -0.43
Central -0.28 -0.12 +0.16Vector -0.081 -1.70 -1.62
LS -0.081 -1.12 -1.04ALS 0.0 -0.58 -0.58
Tensor -2.84 -1.82 +1.02
![Page 56: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/56.jpg)
Effective Single Particle Energies: Trends
120Sn
132Sn
5.2
5.9
-20
-10
0
50 56 64 66 70 82
ES
PE
(M
eV
)
Neutron number
g9/2
d5/2g7/2
s1/2d3/2
h11/2
![Page 57: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/57.jpg)
Effective Single Particle Energies: Trends
120Sn
132Sn
5.2
5.9
-20
-10
0
50 56 64 66 70 82
ES
PE
(M
eV
)
Neutron number
g9/2
d5/2g7/2
s1/2d3/2
h11/2
∆ (g 92-g 7
2) filling h 11
2between 120Sn and 132Sn
Vlowk NNSP diff.Tot -2.15 +0.89 +3.04
Central -0.034 +0.30 +0.33Vector +0.12 +1.55 +1.43
LS -0.038 -0.06 -0.022ALS +0.49 +1.61 +1.12
Tensor -2.30 -0.96 +1.34
![Page 58: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/58.jpg)
Effective Single Particle Energies: Trends
120Sn
132Sn
5.2
5.9
-20
-10
0
50 56 64 66 70 82
ES
PE
(M
eV
)
Neutron number
g9/2
d5/2g7/2
s1/2d3/2
h11/2
∆ (g 92-g 7
2) filling h 11
2between 120Sn and 132Sn
Vlowk NNSP diff.Tot -2.15 +0.89 +3.04
Central -0.034 +0.30 +0.33Vector +0.12 +1.55 +1.43
LS -0.038 -0.06 -0.022ALS +0.49 +1.61 +1.12
Tensor -2.30 -0.96 +1.34
![Page 59: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/59.jpg)
Summary
Monopole drift develops in all regions but the Interplay betweencorrelations (pairing + quadrupole) and spherical mean-field(monopole field) determines the physics.It can vary from :- island of inversion at N=20 and N=40- deformation at Z=14, N=28 for 42Si and shell weakening atZ=28, N=50 for 78Ni- deformation extending from N=40 to N=50 for Z=24-26 for 74Crand 76FeThe “islands of inversion” appear due to the effect of thecorrelations, hence they could also be called “islands ofenhanced collectivity”. As quadrupole correlations are dominantin this region, most of thei inhabitants are deformed rotors.Shape transitions and coexistence show up everywhere
Quadrupole energies can be huge and understood in terms ofsymmetries
Spin-Tensor Analysis show competing trends but varyingsignificantly from light to middle mass nuclei
![Page 60: Model Stability from Shell farnuclearphysicsworkshops.github.io/ICNTatMichiganStateUniversity/d… · Model Stability from Shell far Fred´ eric Nowacki´ 1 International Collaborations](https://reader034.vdocuments.site/reader034/viewer/2022050103/5f423249fa052851355d4057/html5/thumbnails/60.jpg)
Summary
Special Thanks to:
B. Bounthong, E. Caurier, H. Naidja, K. Sieja, A. Zuker
A. Poves
M. Hjorth-Jensen
H. Grawe, S. Lenzi, O. Sorlin
J. Herzfeld