Shell Model A Unified View of Nuclear Structure

Transcription

1 Shell Model A Unified View of Nuclear Structure Frédéric Nowacki 1 18 th STFC UK Postgraduate Summer School Lancaster, August 4 th -September 5 th Strasbourg-Madrid Shell-Model collaboration

2 Bibliography Basic ideas and concepts in nuclear physics an introductory approach Heyde K. IOP Publishing 1994 Shell model applications in nuclear spectroscopy Brussaard P.J., Glaudemans P.W.M. North-Holland 1977 The nuclear shell model Heyde K. Springer-Verlag 1994 The nuclear shell model A. Poves and F. Nowacki Lecture Notes in Physics 581 (1) 7ff The shell model as a unified view of nuclear structure E. Caurier, G. Martinez-Pinedo, F. Nowacki, A. Poves, A. P. Zuker Rev. Mod. Phys. 77, 47 (5) Shell structure evolution and effective in-medium NN interaction N. Smirnova Ecole Joliot-Curie 9

3 Outline Lecture 1: Introduction, basic notions, shell model codes and calculations Lecture : Lanczos structure functions, Effective Interactions Lecture 3: Shell model applications to nuclear spectroscopy

4 monopole and Multipole Hamiltonians H monopole : spherical mean-field ( saturation and evolution of the spherical single particle levels). H multipole : correlator (pairing, quadrupole, octupole...) Important property: CS ± 1 H CS ± 1 = CS ± 1 H monopole CS ± 1 Adjust monopole part only on CS±1 particle nuclei E exc ( + ) (MeV) ESPE (MeV) O, Z=8 THE EXP Neutron number ds d5/ 1s1/ Ca, Z= THE EXP 8 3 Neutron number f7/ 1p3/ fp 8 3 All realistic NN interactions provide similar monopole and multipole parts The link to the phase shifts is independent on the details of the potential and renormalization procedures. They all share the same problems, in particular, the lack of spin-orbit shell closures. Phys. Rev. C85 (11) 5131

5 Shell evolution mechanism H monopole = i n i ǫ i + i j n i.n j V ij Π ν Π ν

6 Shell gap Definition The shell gap is defined as the difference of binding energies (positively defined) = [BE(N) BE(N 1)] [BE(N + 1) BE(N)] = BE(N) BE(N + 1) BE(N 1) The uncorrelated shell gap is therefore equal to the difference of the corresponding ESPE and fully given by H monopole.

7 Landscape of medium mass nuclei 1 Sn 5 8 Zr g 9/ 9 Zr 4 p 1/ p 3/ Z 8 4 f 5/ 48 Ni f 7/ 56 Ni p p 68 Ni g 3/ f 5/ 1/ 9/ 78 Ni 8 8 f 7/ 64 Cr f 7/ 74 Cr 4 Ca 48 Ca 5 Ca 36 S 34 Si f 7/ p 3/ p 1/ f 5/ 3 4 Si g 9/ 5 N 3 Mg 4 Mg 16 O O d C 5/ 8 1 Be 14 8

8 Landscape of medium mass nuclei 1 Sn 5 8 Zr UNDERSTANDING REGULARITIES for both SPHERICAL and DEFORMED systems g 9/ 9 Zr 4 p 1/ Z Magic Numbers: 4 O, 48 Ni, 54 Ca, 78 Ni, 1 Sn 8 Islands of Deformation: 1 Be, 3 Mg, 4 Si, 64 Cr, 8 Zr... p 3/ f 5/ 48 Ni f 7/ 56 Ni p p 68 Ni g 3/ f 5/ 1/ 9/ 78 Ni Variety of phenomena dictated by shell structure 4 Ca shell structure f 7/ 48 Ca 16 O O d C 5/ 5 Ca 64 Cr f 7/ p 3/ p 1/ f 5/ g 9/ 3 74 f 7/ Cr Close connection between collective behaviour and underlying 5 36 S H = H m +H M 34 4 N Si Monopole Si field (spherical mean field) Interplay between 3 4 Mg Multipole Mg correlations (pairing, Q.Q,...) 8 1 Be 14 8

9 Effective Single Particle Energies: Trends ESPE (MeV) d5/ s1/ d3/ f7/ p3/ p1/ f5/ 8 O At the neutron drip line, the ESPE s of 8 O are completely at variance with Magic numbers are associated to enegy gaps in the spherical mean those of 4 Ca at the stability valley. The field. Therefore, 34 Si to promote particles above change thefrom Fermi the standard levels ESPE s costs of energy 16 O to the anomalous ones in 8 O is 4 Ca totally due to the interactions of sd shell However some intruders configurations can neutrons overwhelm among themselves their loss of monopole energy with their huge gain in correlation energy Several examples of this phenomenon exist in stable magic nuclei Notice that the sd shell orbits remain (as in 4 Ca nucleus) in the form of coexisting alwaysspherical, below th pf shell deformed with the νf 7 and superdeformed states in a very narrow and νp energy 3 orbitals range DO get inverted At the very neutron rich or very proton rich edges, the T= and T=1 The monopole part of the channels of the effective nuclear interaction weight very differently than they do at the stability line. Therefore N= the shell effective gap whensingle the valley of particle structure may suffer important changes, stability is approached leading in some cases to the vanishing of established shell closures or to the appearance Proton number of new ones neutron-proton interaction restores the Spin-Tensor decomposition shows it is mainly a Central and Tensor effect

10 Effective Single Particle Energies: Trends ESPE (MeV) d5/ s1/ d3/ f7/ p3/ p1/ f5/ 8 O 34 Si 4 Ca At the neutron drip line, the ESPE s of 8 O are completely at variance with those of 4 Ca at the stability valley. The change from the standard ESPE s of 16 O to the anomalous ones in 8 O is totally due to the interactions of sd shell neutrons among themselves Notice that the sd shell orbits remain always below th pf shell with the νf 7 and νp 3 orbitals DO get inverted The monopole part of the neutron-proton interaction restores the N= shell gap when the valley of stability is approached Proton number Spin-Tensor decomposition shows it is mainly a Central and Tensor effect

11 Effective Single Particle Energies: Trends ESPE (MeV) d5/ s1/ d3/ f7/ p3/ p1/ f5/ 8 O 34 Si 4 Ca 1i13/ (14) At the neutron drip line, 3p1/the ESPE s () of 8 3p O are completely atf5/ 3p3/ (4) variance with(6) f those of 4 f7/ (8) N=5 Ca at the stability 1h9/ valley. (1) The change from the standard ESPE s of 16 1h O to the anomalous ones in 8 1h11/ O(1) is 3s 3s1/ () totally due to the interactions d3/of sd(4) shell d N=4 neutrons among themselves d5/ N=3 1g p 1f Notice that the sd shell orbits remain 1f7/ (8) always below th pf shell with the νf 7 s N= 1d3/ and νp1d3 orbitals DOs get inverted N=1 1p 1g9/ 1f5/ 1p1/ 1g7/ p1/ p3/ 1d5/ 1p3/ N= The monopole part of 1sthe () neutron-proton interaction restores the N= shell gap when the valley of stability is approached 1s () (6) (8) (1) () (6) (4) (4) () (6) () (4) (16) (8) (64) (5) (4) (38) () (14) (8) (6) (8) Proton number Spin-Tensor decomposition shows it is mainly a Central and Tensor effect

12 Effective Single Particle Energies: Trends ESPE (MeV) O d5/ s1/ d3/ f7/ p3/ p1/ f5/ Mg Si N= Ca At the neutron drip line, the ESPE s of 8 O are completely at variance with those of 4 Ca at the stability valley. The change from the standard ESPE s of 16 O to the anomalous ones in 8 O is totally due to the interactions of sd shell neutrons among themselves Notice that the sd shell orbits remain always below th pf shell with the νf 7 and νp 3 orbitals DO get inverted The monopole part of the neutron-proton interaction restores the N= shell gap when the valley of stability is approached Proton number Spin-Tensor decomposition shows it is mainly a Central and Tensor effect

13 Effective Single Particle Energies: Trends ESPE (MeV) O d5/ s1/ d3/ f7/ p3/ p1/ f5/ Mg Si N= Ca At the neutron drip line, the ESPE s of 8 O are completely at variance with those of 4 Ca at the stability valley. The change from the standard ESPE s of 16 O to the anomalous ones in 8 O is totally due to the interactions of sd shell neutrons among themselves Notice that the sd shell orbits remain always below th pf shell with the νf 7 and νp 3 orbitals DO get inverted The monopole part of the neutron-proton interaction restores the N= shell gap when the valley of stability is approached Proton number Spin-Tensor decomposition shows it is mainly a Central and Tensor effect

14 Effective Single Particle Energies: Trends ESPE (MeV) O d5/ s1/ d3/ f7/ p3/ p1/ f5/ Spin-Tensor decomposition Mg V = 34 SiV k = U k.s k Ca k S S spin-tensor components N= C=Central ALS=antisymmetric spin-orbit LS=spin-orbit 1 1 T=Tensor At the neutron drip line, the ESPE s of 8 O are completely at variance with those of 4 Ca at the stability valley. The change from the standard ESPE s of 16 O to the anomalous ones in 8 O is totally due to the interactions of sd shell neutrons among themselves Notice that the sd shell orbits remain always below th pf shell with the νf 7 and νp 3 orbitals DO get inverted The monopole part of the neutron-proton interaction restores the N= shell gap when the valley of stability is approached Proton number Spin-Tensor decomposition shows it is mainly a Central and Tensor effect

15 Effective Single Particle Energies: Trends ESPE (MeV) O (f 7 -d 3 ) filling d 5 3 Mg 34 Si G matrix SDPF-U 4 Ca diff. 1.9Tot Central Vector N= LS ALS Tensor d5/ s1/ Nuclear d3/ shell evolution and in-medium NN interaction f7/ N. Smirnova, K. Heyde, B. Bailly, F. Nowacki, K. Sieja p3/ Phys. p1/ Rev. C86, (1) f5/ between 3 Mg and 34 Si At the neutron drip line, the ESPE s of 8 O are completely at variance with those of 4 Ca at the stability valley. The change from the standard ESPE s of 16 O to the anomalous ones in 8 O is totally due to the interactions of sd shell neutrons among themselves Notice that the sd shell orbits remain always below th pf shell with the νf 7 and νp 3 orbitals DO get inverted The monopole part of the neutron-proton interaction restores the N= shell gap when the valley of stability is approached Proton number Spin-Tensor decomposition shows it is mainly a Central and Tensor effect

16 Effective Single Particle Energies: Trends ESPE (MeV) O (f 7 -d 3 ) filling d 5 3 Mg 34 Si G matrix SDPF-U 4 Ca diff. 1.9Tot Central Vector N= LS ALS Tensor d5/ s1/ Nuclear d3/ shell evolution and in-medium NN interaction f7/ N. Smirnova, K. Heyde, B. Bailly, F. Nowacki, K. Sieja p3/ Phys. p1/ Rev. C86, (1) f5/ between 3 Mg and 34 Si At the neutron drip line, the ESPE s of 8 O are completely at variance with those of 4 Ca at the stability valley. The change from the standard ESPE s of 16 O to the anomalous ones in 8 O is totally due to the interactions of sd shell neutrons among themselves Notice that the sd shell orbits remain always below th pf shell with the νf 7 and νp 3 orbitals DO get inverted The monopole part of the neutron-proton interaction restores the N= shell gap when the valley of stability is approached Proton number Spin-Tensor decomposition shows it is mainly a Central and Tensor effect

17 Effective Single Particle Energies: Trends Π ν p3/ 1f7/ 1d3/ s1/ 1d5/ 35 Si (p 3 -p 1 ) filling s 1 between 34 Si and 36 S KLS N3LO N3LO (bare) (4 ω) Tot Central... Vector Tensor... G. Burgunder, PhD Thesis GANIL, December 11

18 Effective Single Particle Energies: Trends Π ν p3/ 1f7/ 1d3/ s1/ 1d5/ 35 Si (p 3 -p 1 ) filling s 1 between 34 Si and 36 S KLS N3LO N3LO (bare) (4 ω) Tot Central... Vector Tensor... G. Burgunder, PhD Thesis GANIL, December 11

19 Effective Single Particle Energies: Trends Π ν p3/ 1f7/ 1d3/ s1/ 1d5/ 37 S (p 3 -p 1 ) filling s 1 between 34 Si and 36 S KLS N3LO N3LO (bare) (4 ω) Tot Central... Vector Tensor... G. Burgunder, PhD Thesis GANIL, December 11

20 Effective Single Particle Energies: Trends Π ν p3/ 1f7/ 1d3/ s1/ 1d5/ 37 S (p 3 -p 1 ) filling s 1 between 34 Si and 36 S KLS N3LO N3LO (bare) (4 ω) Tot Central... Vector Tensor... G. Burgunder, PhD Thesis GANIL, December 11

21 Correlation Energies Let us consider the configurations with closed N= [sd] 1,Z (normal filling) and the ones with two neutrons blocked in the pf shell [sd] 1,Z [pf], (intruder) And calculate the energy of the ground states at fixed configuration, with and without correlations

22 Correlations energies: normal vs p-h intruder p-h p-h Z F. Nowacki and A. Poves Phys. Rev. C9, 143 (14)

23 Correlations energies: normal vs p-h intruder p-h p-h - 8 O Z F. Nowacki and A. Poves Phys. Rev. C9, 143 (14)

24 Correlations energies: normal vs p-h intruder p-h p-h - 8 O Ne Z F. Nowacki and A. Poves Phys. Rev. C9, 143 (14)

25 Correlations energies: normal vs p-h intruder p-h p-h - 8 O Ne -1 3 Mg Z F. Nowacki and A. Poves Phys. Rev. C9, 143 (14)

26 Correlations energies: normal vs p-h intruder p-h p-h - 8 O Ne Mg 34 Si Z F. Nowacki and A. Poves Phys. Rev. C9, 143 (14)

27 Gaps: normal vs p-h intruder 14 E(p-h)-E(p-h) : without correlations E(p-h)-E(p-h) : with correlations MeV Si - ISLAND OF INVERSION 3 Mg 3 Ne Z F. Nowacki and A. Poves Phys. Rev. C9, 143 (14)

28 Merging of the islands of inversion at N= and N=8 + excitation energy in MeV Si EXP TH + excitation energy in MeV Mg EXP TH N N 1 8 BE,SM EXP 15 BE(e.fm 4 ) 6 4 Si e fm B(E) exp B(E) th

29 Merging of the islands of inversion at N= and N=8 + excitation energy in MeV Si EXP TH + excitation energy in MeV Mg EXP TH N N 1 8 BE,SM EXP 15 BE(e.fm 4 ) 6 4 Si e fm B(E) exp B(E) th

30 Merging of the islands of inversion at N= and N=8 + excitation energy in MeV Si EXP TH + excitation energy in MeV Mg EXP TH N N 1 8 BE,SM EXP 15 BE(e.fm 4 ) 6 4 Si e fm B(E) exp B(E) th

31 Merging of the islands of inversion at N= and N=8 + excitation energy in MeV Si EXP TH + excitation energy in MeV Mg EXP TH N N 1 8 BE,SM EXP 15 BE(e.fm 4 ) 6 4 Si e fm B(E) exp B(E) th

32 Island of inversion at N=4, an old story: 1996 A. Poves

33 Island of inversion at N=4, an old story: 3 GANIL N= N=4 5 6 effective SPE (MeV) d3/ p3/ 1f7/ effective SPE (MeV) 4 1f5/ d5/ 1g9/ Proton number Proton number

34 More recent experimental information MSU RAPID COMMUNICATIONS PHYSICAL REVIEW C 81, 5134(R) (1) Collectivity at N = 4 in neutron-rich 64 Cr A. Gade, 1, R. V. F. Janssens, 3 T. Baugher, 1, D. Bazin, 1 B. A. Brown, 1, 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, K. Meierbachtol, 1,7 A. Ratkiewicz, 1, S. R. Stroberg, 1, K. A. Walsh, 1, D. Weisshaar, 1 R. Winkler, 1 and S. Zhu 3 1 National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 4884, USA Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 4884, USA 3 Physics Division, Argonne National Laboratory, Argonne, Illinois 6439, USA 4 Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 74, USA GANIL PHYSICAL REVIEW C 81, 6131(R) (1) RAPID COMMUNICATIONS Onset of collectivity in neutron-rich Fe isotopes: Toward a new island of inversion? J. Ljungvall, 1,,3 A. Görgen, 1 A. Obertelli, 1 W. Korten, 1 E. Clément, G. de France, A. Bürger, 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, 1 T. Pissulla, 6 A. Poves, 11 F. Recchia, 1 M. Rejmund, W. Rother, 6 E. Sahin, 1 C. Schmitt, A. Shrivastava, K. Sieja, 1 J. J. Valiente-Dobón, 1 K. O. Zell, 6 and M. Zielińska 13 1 CEA Saclay, IRFU, Service de Physique Nucléaire, F Gif-sur-Yvette, France GANIL, CEA/DSM-CNRS/INP3, Bd Henri Becquerel, BP 557, F-1476 Caen, France 3 CSNSM, CNRS/INP3, F-9145 Orsay, France

35 SM framework Island of inversion around 64 Cr S. Lenzi, F. Nowacki, A. Poves and K. Sieja Phys. Rev. C 8, 5431, 1. Π ν LNPS interaction: based on realistic TBME new fit of the pf shell (KB3GR, E. Caurier) monopole corrections g 9/ -d 5/ gap set to 1.5 Mev in 68 Ni d5/ g9/ Calculations: p1/ f5/ p3/ f7/ up to 14p-14h excitations across Z=8 and N=4 gaps up to 1 1 m-scheme code ANTOINE (non public version) 48 Ca

36 Shape transition at N=4 E( + ) (MeV) SM EXP N=4 (a) 68 Ni B(E; + -> + ) (e fm 4 ) Z Nucleus νg 9/ νd 5/ configuration 68 Ni.98.1 ph(51%) 66 Fe p4h(6%) 64 Cr p6h(3%) 6 Ti p4h(48%) SM EXP 68 Ni Z (b)

37 Shape transition at N=4 E( + ) (MeV) SM EXP N=4 66 Fe (a) 68 Ni B(E; + -> + ) (e fm 4 ) Z Nucleus νg 9/ νd 5/ configuration 68 Ni.98.1 ph(51%) 66 Fe p4h(6%) 64 Cr p6h(3%) 6 Ti p4h(48%) SM EXP 66 Fe 68 Ni Z (b)

38 Shape transition at N=4 E( + ) (MeV) SM EXP N=4 64 Cr 66 Fe (a) 68 Ni B(E; + -> + ) (e fm 4 ) Z Nucleus νg 9/ νd 5/ configuration 68 Ni.98.1 ph(51%) 66 Fe p4h(6%) 64 Cr p6h(3%) 6 Ti p4h(48%) SM EXP 64 Cr 66 Fe 68 Ni Z (b)

39 Neutron effective single particle energies O 6 Ca (a) 3 Mg 64 Cr 68 Ni 34 Si (b) ESPE (MeV) f7/ p3/ f5/ p1/ g9/ d5/ 8 3 Z N=4 ESPE (MeV) d5/ s1/ d3/ f7/ p3/ Z N= reduction of the νf 5/ -g 9/ gap with removing f 7/ protons proximity of the quasi-su3 partner d 5/ inversion of d 5/ and g 9/ orbitals same ordering as CC calculations reduction of the νd 3/ -f 7/ gap with removing d 5/ protons proximity of the quasi-su3 partner p 3/ inversion of p 3/ and f 7/ orbitals

40 Neutron effective single particle energies O 6 Ca (a) 3 Mg 64 Cr 68 Ni 34 Si (b) ESPE (MeV) f7/ p3/ f5/ p1/ g9/ d5/ G. Hagen et al. 8 3 Z N=4 ESPE (MeV) d5/ s1/ d3/ f7/ p3/ Z N= Phys. Rev. Lett. 19, 35 (1) reduction of the νf 5/ -g 9/ gap with removing f 7/ protons proximity of the quasi-su3 partner d 5/ inversion of d 5/ and g 9/ orbitals same ordering as CC calculations reduction of the νd 3/ -f 7/ gap with removing d 5/ protons proximity of the quasi-su3 partner p 3/ inversion of p 3/ and f 7/ orbitals

41 Extension of collectivity N=4 towards N=5 Energy (MeV) R4=E(4+)/E(+) 1 LNPS-m Literature This work Neutron number LNPS-m Literature This work Neutron number Energy (MeV) R4=E(4+)/E(+) 1 LNPS-m Literature This work Neutron number LNPS-m Literature This work Neutron number

42 Extension of collectivity N=4 towards N=5 Energy (MeV) R4=E(4+)/E(+) 1 LNPS-m Literature This work Neutron number LNPS-m Literature This work Neutron number Energy (MeV) R4=E(4+)/E(+) 1 LNPS-m Literature This work Neutron number LNPS-m Literature This work Neutron number

43 Extension of collectivity N=4 towards N=5 Energy (MeV) R4=E(4+)/E(+) 1 LNPS-m Literature This work Neutron number LNPS-m Literature This work Neutron number Energy (MeV) R4=E(4+)/E(+) 1 LNPS-m Literature This work Neutron number LNPS-m Literature This work Neutron number

44 Extension of collectivity N=4 towards N=5 Energy (MeV) R4=E(4+)/E(+) 1 LNPS-m Literature This work Neutron number LNPS-m Literature This work Neutron number Energy (MeV) 1 LNPS-m Literature This work Neutron number C. Santamaria et al., submitted for publication in Phys. Rev. Lett. R4=E(4+)/E(+) LNPS-m Literature This work Neutron number

45 Spin-orbit shell closure far from stability Π H. O. sd-pf: 4 Si deformed Π+ pf-sdg: 78 Ni??? H. O. sdg-phf: 13 Sn doubly magic Evolution of Z=8 from N=4 to N=5 Evolution of N=5 from Z=4 to Z=8

46 Three-body forces in medium mass nuclei 5 16 O 4 O ds 5 4 Ca 48 Ca 5 68 Ni 78 Ni -5-1 d5/ 1s1/ f7/ 1p3/ fp g9/ 1d5/ gd 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 78 Ni K. Sieja, F. Nowacki Phys. Rev. C85, 5131(R) (1)

47 Physics around 78 Ni H. O. Π+/ Π /+ H. O. PFSDG-U interaction: based on realistic TBME pf shell for protons and gds shell for neutrons monopole corrections proton and neutrons gap 78 Ni fixed to phenomenological derived values Calculations: excitations across Z=8 and N=5 gaps up to 1 1 Slater Determinant basis states m-scheme code ANTOINE (non public version)

48 Physics around 78 Ni Π /+ 1 1 H. O. PFSDG-U interaction: based on realistic TBME pf shell for protons and gds shell for neutrons monopole corrections proton and neutrons gap 78 Ni fixed to phenomenological derived values Π+/ Calculations: H. O excitations across Z=8 and N=5 gaps up to 1 1 Slater Determinant basis states m-scheme code ANTOINE (non public version)

49 Shape coexistence in 78 Ni At first approximation, 78 Ni has a double closed shell structure for GS But very low-lying 4p4h structures The first excited state + 1 in 78 Ni predicted at.8 MeV and to be a deformed intruder!!! Necessity to go beyond (fpg 9 d 5 ) LNPS space Constrained deformed HF in the SM basis (B. Bounthong, Ph D Thesis, Strasbourg)

50 Island of Deformation below 78 Ni Schematic SU3 predictions: arxiv Nilsson-SU3 selfconsistency: Quadrupole dominance in heavy N=Z nuclei monopole + quadrupole model Energies in MeV realtive to the ph states p-h p-h 4p-4h Ni78 Fe76 Cr74 proton gap (5MeV) and neutron gap (5 MeV) estimates Quasi-SU3 (protons) and Pseudo-SU3 (neutrons) estimates Q s = ( q +3.)b ) /3.5 E = ǫ i n i ωκ( q (3) 15 + q (4) 3 ) Prediction of Island of strong collectivity below 78 Ni!!!

51 Island of Deformation below 78 Ni Schematic SU3 predictions: arxiv Nilsson-SU3 selfconsistency: Quadrupole dominance in heavy N=Z nuclei Energies in MeV realtive to the ph states E*( + 1 ) (MeV) Q s (e.fm ) BE (e.fm 4 ) monopole Q i from+ quadrupole Q i frommodel β proton Q s gap (5MeV) fromand BE neutron gap (5 7 MeV) estimates Cr Quasi-SU3 (protons) and Pseudo-SU3 Cr (neutrons) 16 estimates Cr Fe Q s = 135 ( q +3.)b 13 ) /3.5.6 p-h p-h 4p-4h Ni78 Fe76 Cr74 E = ǫ i n i ωκ( q (3) 15 + q (4) 3 ) Prediction of Island of strong collectivity below 78 Ni!!!

52 Island of Deformation below 78 Ni Schematic SU3 predictions: arxiv Energies in MeV realtive to the ph states p-h p-h 4p-4h Energy (MeV) Nilsson-SU3 selfconsistency: Quadrupole dominance PFSDG-U in heavy N=Z nuclei Literature This work 1 Ni78 Fe76 Cr74 4+ monopole + quadrupole model proton gap (5MeV) and neutron gap (5 MeV) estimates Quasi-SU3 (protons) and Pseudo-SU3 (neutrons) + estimates Q s = ( q +3.)b ) /3.5 Neutron number E = ǫ i n i ωκ( q (3) + q (4) ) 15 3 Prediction of Island of strong collectivity below 78 Ni!!! Extension of Island of deformation to N=5!!!

53 Spin-orbit shell closure far from stability Π H. O. sd-pf: 4 Si deformed Π+ pf-sdg: 78 Ni??? H. O. sdg-phf: 13 Sn doubly magic Evolution of Z=8 from N=4 to N=5 Evolution of N=5 from Z=4 to Z=8

54 Effective Single Particle Energies: Trends Silicium chain Si d5/ s1/ d3/ ESPE (MeV) Si Neutron number

55 Effective Single Particle Energies: Trends Silicium chain Si d5/ s1/ d3/ ESPE (MeV) (d 5 -d 3 ) filling f 7 between 34 Si and 4 Si 4 Si G matrix SDPF-U diff. 7.5 Tot Central Vector LS ALS Tensor Neutron number

56 Effective Single Particle Energies: Trends Silicium chain Si d5/ s1/ d3/ ESPE (MeV) (d 5 -d 3 ) filling f 7 between 34 Si and 4 Si 4 Si G matrix SDPF-U diff. 7.5 Tot Central Vector LS ALS Tensor Neutron number

57 Effective Single Particle Energies: Trends ESPE (MeV) Ni 78 Ni -3 f5/ p3/ p1/ g9/ f7/ Neutron number 5.

58 Effective Single Particle Energies: Trends ESPE (MeV) f5/ p3/ p1/ g9/ f7/ (f 7 -f 5 ) filling g 9 68 Ni between 68 Ni and 78 Ni G matrix PFSDG-U diff. Tot Central Vector LS ALS Tensor Neutron number 78 Ni 5.

59 Effective Single Particle Energies: Trends ESPE (MeV) f5/ p3/ p1/ g9/ f7/ (f 7 -f 5 ) filling g 9 68 Ni between 68 Ni and 78 Ni G matrix PFSDG-U diff. Tot Central Vector LS ALS Tensor Neutron number 78 Ni 5.

60 Effective Single Particle Energies: Trends ESPE (MeV) -1 - g9/ d5/ g7/ s1/ d3/ h11/ 1 Sn Neutron number 13 Sn 5.9

61 Effective Single Particle Energies: Trends ESPE (MeV) -1 - g9/ d5/ g7/ s1/ d3/ h11/ (g 9 -g 7 ) filling h 11 1 Sn between 1 Sn and 13 Sn V lowk NNSP diff. Tot Central Vector LS ALS Tensor Neutron number 13 Sn 5.9

62 Effective Single Particle Energies: Trends ESPE (MeV) -1 - g9/ d5/ g7/ s1/ d3/ h11/ (g 9 -g 7 ) filling h 11 1 Sn between 1 Sn and 13 Sn V lowk NNSP diff. Tot Central Vector LS ALS Tensor Neutron number 13 Sn 5.9

63 Summary Monopole drift develops in all regions but the Interplay between correlations (pairing + quadrupole) and spherical mean-field (monopole field) determines the physics. It can vary from : - island of inversion at N= and N=4 - deformation at Z=14, N=8 for 4 Si and shell weakening at Z=8, N=5 for 78 Ni - deformation extending from N=4 to N=5 for Z=4-6 for 74 Cr and 76 Fe The islands of inversion appear due to the effect of the correlations, hence they could also be called islands of enhanced collectivity. As quadrupole correlations are dominant in 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 of symmetries Spin-Tensor Analysis show competing trends but varying significantly from light to middle mass nuclei

64 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