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

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 100 Sn �� �� 50 �� �� �� �� �� �� �� �� 80 Zr 90 Zr 40 �� �� �� �� �� �� �� �� g p 9/2 �� �� 1/2 �� �� �� �� �� �� �� �� p 3/2 f5/2 Z 20 28 40 48 Ni 56 Ni 68 Ni 78 Ni f7/2 p g p f5/2 3/2 1/2 9/2 28 28 ��� ��� �� �� �� �� ��� ��� �� �� �� �� ��� ��� �� �� �� �� ��� ��� �� �� �� �� 64 Cr 74 Cr f7/2 f7/2 40 Ca 48 Ca 52 Ca 20 20 f7/2 p p f5/2 g 50 3/2 1/2 9/2 32 36 S ��� ��� ��� ��� N ��� ��� ��� ��� 34 Si 42 Si ��� ��� ��� ��� ��� ��� ��� ��� ��� ��� 40 Mg 32 Mg 16 O 22 O 8 8 14 C d 5/2 12 Be 14 20 28 8

Evolution of nuclear shells due to Tensor force 78 Ni 42 Si 91 Zr T. Otsuka et al., Phys. Rev. Lett. 95 , 232502-1 (2005) ( 2 j > + 1 ) V T j >, j ′ + ( 2 j < + 1 ) V T j <, j ′ = 0 , reduction of spin-orbit partners splitting while filling j ′ shell 132 Sn

Spin-orbit shell closure far from stability Π− sd-pf: 42 Si deformed H. O. 28 pf-sdg: 78 Ni ??? Π+ f 7 / 2 sdg-phf: 132 Sn 42 14 Si 28 H. O. 14 doubly magic d 5 / 2 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

Spin-orbit shell closure far from stability Π− sd-pf: 42 Si deformed H. O. 50 pf-sdg: 78 Ni ??? Π+ g 9 / 2 sdg-phf: 132 Sn 78 28 Ni 50 H. O. 28 doubly magic f 7 / 2 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

Spin-orbit shell closure far from stability Π− sd-pf: 42 Si deformed H. O. 82 78 Ni ??? Π+ h 11 / 2 pf-sdg: sdg-phf: 132 50 Sn 82 H. O. 50 132 Sn doubly magic g 9 / 2 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

Physics around 78 Ni PFSDG-U interaction: realistic TBME pf shell for protons and gds shell υ for neutrons monopole corrections ( 3N forces ) proton and neutrons gap 78 Ni sdg fixed to phenomenological derived values π Calculations: pf excitations across Z=28 and N=50 gaps up to 5*10 10 Slater Determinant basis states m-scheme code ANTOINE (non public version) 60 Ca J-scheme code NATHAN (parallelized version): 0.5*10 9 J basis states

Physics around 78 Ni PFSDG-U interaction: realistic TBME pf shell for protons and gds shell υ for neutrons monopole corrections ( 3N forces ) proton and neutrons gap 78 Ni sdg fixed to phenomenological derived values π Calculations: pf excitations across Z=28 and N=50 gaps up to 5*10 10 Slater Determinant basis states m-scheme code ANTOINE (non public version) 60 Ca J-scheme code NATHAN (parallelized version): 0.5*10 9 J basis states

Neutron intruders constraints 24 PFSDG-U mix 23 Exp. 22 21 20 19 18 S2n (MeV) 17 16 15 Zn 14 13 12 11 10 9 8 7 6 38 40 42 44 46 48 50 52 Neutron number

Neutron intruders constraints 24 PFSDG-U mix 23 Exp. 22 82 Zn 21 d5/2 20 50 19 g9/2 18 S2n (MeV) 17 16 15 Zn 14 13 N=50 Gap + V d 5 d 5 12 11 10 9 8 7 6 38 40 42 44 46 48 50 52 Neutron number

Neutron intruders constraints 3 24 PFSDG-U Zn PFSDG-U mix 23 E(2+) (MeV) NNDC Exp. RIKEN 22 2 21 4+ 20 19 1 18 S2n (MeV) 2+ 17 16 15 0 Zn 14 46 48 50 52 54 13 Neutron number 12 11 10 RIKEN MINOS experiment 9 8 C. Shand, Z. Podolyak, et al. to be published 7 6 38 40 42 44 46 48 50 52 Neutron number

Neutron intruders constraints 3 24 PFSDG-U Ge PFSDG-U mix 23 E(2+) (MeV) NNDC Exp. RIKEN 22 2 21 4+ 20 19 1 18 S2n (MeV) 2+ 17 16 15 0 Zn 14 46 48 50 52 54 56 13 Neutron number 12 11 10 RIKEN MINOS experiment 9 8 M. Lettman, V. Werner, N. Pietralla, accepted in Phys. Rev. C 7 6 38 40 42 44 46 48 50 52 Neutron number

Neutron intruders constraints 3 24 PFSDG-U Ge PFSDG-U mix 23 E(2+) (MeV) NNDC Exp. RIKEN 22 2 21 4+ 20 19 1 18 S2n (MeV) 2+ 17 16 15 0 Zn 14 46 48 50 52 54 56 13 Neutron number 12 11 10 RIKEN MINOS experiment 9 8 M. Lettman, V. Werner, N. Pietralla, accepted in Phys. Rev. C 7 6 38 40 42 44 46 48 50 52 Neutron number

Neutron intruders constraints 14 JUN45 PFSDG-U S2n (MeV) 13 AME2016 ISOLTRAP 12 11 10 Cu 9 42 44 46 48 50 Neutron number data: AME2016 and ISOLTRAP Collaboration 2017

NpNh excitations 14 0p0h AME2016 S2n (MeV) 13 ISOLTRAP 12 11 10 Cu 9 42 44 46 48 50 Neutron number theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

NpNh excitations 14 2p2h AME2016 S2n (MeV) 13 ISOLTRAP 12 11 10 Cu 9 42 44 46 48 50 Neutron number theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

NpNh excitations 14 4p4h AME2016 S2n (MeV) 13 ISOLTRAP 12 11 10 Cu 9 42 44 46 48 50 Neutron number theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

NpNh excitations 14 6p6h AME2016 S2n (MeV) 13 ISOLTRAP 12 11 10 Cu 9 42 44 46 48 50 Neutron number theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

NpNh excitations 14 8p8h AME2016 S2n (MeV) 13 ISOLTRAP 12 11 10 Cu 9 42 44 46 48 50 Neutron number theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

NpNh excitations 14 8p8h AME2016 d S2n (MeV) 13 e h s ISOLTRAP i l b u p e b 12 o t , N O I T A R 11 O B A L L O C 10 P A R T L O Cu S I d 9 n a i k c a 42 44 46 48 50 w o N F . Neutron number theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017

NpNh excitations 14 8p8h AME2016 S2n (MeV) 13 ISOLTRAP 12 11 10 Cu 9 42 44 46 48 50 Neutron number theory PFSDG-U data: AME2016 and ISOLTRAP Collaboration 2017 R. P. de Groote and the CRIS collaboration in preparation

Spherical structure of 78 Ni Ab-initio CC predictions for 78 Ni

Spherical structure of 78 Ni

Spherical structure of 78 Ni -360 0+ 1 2+ 1 -362 78 Ni -364 E (MeV) -366 -368 -370 0 2 4 6 8 10 12 14 16 18 ph excitations GS and 2 + ph in 78 Ni

Spherical structure of 78 Ni -360 0+ 1 2+ 1 -362 78 Ni -364 E (MeV) -366 -368 ∼ 3.1 -370 0 2 4 6 8 10 12 14 16 18 ph excitations GS and 2 + ph in 78 Ni

Schematic SU3 predictions monopole + quadrupole model 3 0p-0h proton gap (5MeV) and neutron gap (5 2p-2h 2 4p-4h MeV) estimates 1 78 Ni Quasi-SU3 (protons) and Pseudo-SU3 0 (neutrons) blocks MeV -1 Q s = ( � 2 q 20 � + 3 . ) b 2 ) 2 / 3 . 5 76 Fe � � Q m -2 � 2 + � Q m 0 ( π ) � 0 ( ν ) � E n = G mp n ( 50 ) − � ωκ 15 b 2 23 b 2 -3 G mp n ( 50 ) = n ( 3 . 0 8 n π f + 2 . 25 ) + ∆( n ) + δ p ( n ) -4 74 Cr -5 28 26 24 22 20 Prediction of Island of strong collectivity Z below 78 Ni !!!

Shape coexistence in 78 Ni At first approximation, 78 Ni has a double closed shell structure for GS But very low-lying competing structures From the diagonalization, the first excited states in 78 Ni are : • 0 + 2 -2 + 1 predicted at 2.6-2.9 MeV and to be deformed intruders of a rotationnal band !!! “1 p 1 h ” 2 + 2 predicted at ∼ 3.1 MeV Necessity to go beyond ( fpg 9 2 d 5 2 ) LNPS Constrained deformed HF in the space and beyond ab-initio description SM basis (B. Bounthong, PhD Thesis, Portal to a new I sland o f I nversion Strasbourg)

Shape coexistence in 78 Ni At first approximation, 78 Ni has a double closed shell structure for GS But very low-lying competing structures From the diagonalization, the first excited states in 78 Ni are : • 0 + 2 -2 + 1 predicted at 2.6-2.9 MeV and to be deformed intruders of a rotationnal band !!! “1 p 1 h ” 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 I sland o f I nversion 78 Ni

Shape coexistence in 78 Ni At first approximation, 78 Ni has a double closed shell structure for GS But very low-lying competing structures From the diagonalization, the first excited states in 78 Ni are : • 0 + 2 -2 + 1 predicted at 2.6-2.9 MeV and to be deformed intruders of a rotationnal band !!! “1 p 1 h ” 2 + 2 predicted at ∼ 3.1 MeV 78 Ni 2 + → 0 + 1 2 ∆ E ∗ th. 0.229 Necessity to go beyond ( fpg 9 2 d 5 2 ) LNPS Q s -39 BE2 ↓ th. 516 space and beyond ab-initio description Q i (e.fm 2 ) 135 from Q s Q i (e.fm 2 ) 195 Portal to a new I sland o f I nversion from BE2 78 Ni β e ∼ 0.3 2 prolate