Jose Javier Valiente Dobón Laboratori Nazionali di Legnaro (INFN), Italia

1. Evidence of effective three-body forces in shell model calculations for neutron-rich lead isotopes Jose Javier Valiente Dobón Laboratori Nazionali di Legnaro (INFN), Italia

2. Overview • Experimental setup and challenges • Neutron-rich Pb nuclei beyond N=126 • Seniority 8+ isomers in Pb  the B(E2) probes • Effective 3-body forces • Summary

3. The Z=82 and beyond N=126 .Taking advantage of theseisomerswewant to study the developmet of nuclearstructure from 212Pb up to 218Pb and nearby nuclei 218Pb 216Pb 212Pb g9/2

4. Experimental challenges GSI • 5x106 pps • 2 HPGe detectors (Effγ=1%) • 350 ions implanted M. Pfutzner, PLB 444 (1998) 32 Difficult region to explore: only fragmentation possible, primary beam charge states!

5. Experimental setup 15 CLUSTERs x 7 crystals FRS-Rising at GSI: stopped beam campaign εγ = 11% at 1.3MeV 9 DSSSD, 1mm thick, 5x5 cm2 16x16 x-y strips Beam: 238U @ 1GevA S1 Target 2.5 g/cm2 Be S2 S3 S4 Deg. S1: Al 2.0 g/cm2 MONOCHROMATIC Deg S2: Al 758 mg/cm2

6. 213Tl 212Pb 206Hg 209Tl 215Bi 210Hg 218Pb 219Bi Nuclei populated in the fragmentation 1 GeVA238U beam from UNILAC-SIS at 109pps Z A/q

7. 212,214,216Pb: 8+ isomer

8. 214Pb: γγ coincidences

9. Ductu naturae The 8+ isomer is a seniority isomer, involving neutrons in the 2g9/2 216Pb 212Pb 214Pb 210Pb X 8+ 8+ X

10. Model space in LSSM calculations Kuo-Herling interaction j15/2 s1/2 4s d3/2 • 208Pb is the core (Z=82, N=126). • For neutron-rich Lead isotopes, the N=6 major shell is involved • No shells beyond the magic numbers for neutrons • Outside of the valencespace: 113/2orbitalis the quasi SU3 partner of the 1g9/2 3d g7/2 6ħw 2g d5/2 i11/2 1i g9/2 126 i13/2 ν E.K. Warburton and B.A. Brown PRC43, 602 (1991).

11. Shell Model calculations Kuo-Herling Calculations with Antoine and Nathan codes and K-H interaction E.K. Warburton and B.A. Brown PRC43, 602 (1991). K.-H:200ns 216Pb 218Pb 210Pb 212Pb 214Pb th. exp. th. exp. th. exp th. exp. th.

12. Wave functions from Kuo-Herling The neutron 2g9/2shellhas a dominantrolefor the 8+isomeric state. 1i11/2 , 1j15/2 and 3d5/2also play a role 8+ state wave functions: occupational numbers show quite pure wave functions Occupational numbers

13. Reduced transition prob. B(E2) B(E2) calculatedconsideringinternalconversioncoefficients, and a 20-90 keVenergyinterval for unknowntransitions. Upper limit 90 keV based on Kα X rays intensity (K electrons bound ~88 keV) Large discrepenciesfactor ~ 5 B(E2; 8+ -> 6+) B(E2) ~ Eγ-5 (1+α)-1τ-1 eν=0.8 A (Lead)

14. Effective 3 body interactions Usually neglected! One body Two body Three body • Effective 3-body termsappearnaturally in the renormalizationprocess, butthey are NOT included in shell-model codes (ANTOINE and NATHAN): • Two-body operators (H) becomeeffective 3-body operators • One-body transitionoperators (B(E2)) becomeeffective 2-body operators

15. Effective three-body forces The only way to include in a standard shell-model calculation (ANTOINE, NATHAN) the effective 3-body force and 2-body operators is to diagonalize usign the dressed wave function. Expectation value of the Hamiltonian and of the transition operators is calculated directly between the dressed wave functions, thus also including the many-body terms otherwise neglected. By allowingrelevantp-h excitations from the core to the g9/2shell to neutronshellsabove, we include the previuoslyneglectedterms . . . . . . ν shells above N=126 π shells above Z=82 2g9/2 2f7/2 quasi-SU3 Z=82 N=126 h11/2 i13/2 π ν In a perturbative approach, the bare g9/2 is «dressed» with p-h excitations from the 208Pb core

16. Effective 3-body interaction: Results Exp. data g9/2 g9/2(n-1)+ ν shells above g9/2(n-1) + ν shells above + core exc. Kahana Lee Scott (KLS) interaction S. Kahana, Scott, Lee Phys. Rev. 185 (1969). A. Abzouzi, E. Caurier, and A.P. Zuker, Phys. Rev. Lett. 66, 1134,(1991). M. Dufour and A.P. Zuker PRC54 1641 (1996) Standard eff. charges: eν = 0.5, eπ= 1.5 The explicitcoupling to the core restores the conjugationsymmetry

17. Conclusions • The neutron-rich Pb werepopulated, enabling to study the nuclearstructure in thisregion up to nowunknown due to experimentaldifficulties • The observedshellstructureseems to follow a seniorityscheme: However, a closer look reveals that the B(E2) values have an unexpected behaviour. B(E2) values might be a sensitive probe to understand in detail the features of the nuclear force  Seniority mixing; 3N forces, relevantvalencespace • Future: Measurement of B(E2) of the 2+0+ in Pb and Hg using transfer reactions and DSAM or RDDS (backing target) PRISMA BLF TLF Beam

18. Collaboration A. Gottardo, G. Benzoni, J.J.V.D., R. Nicolini, E. Maglione, A.P. Zuker, F. Nowacki A. Gadea, S.Lunardi, G. de Angelis, A. Bracco, D. Mengoni, A.I. Morales, F. Recchia, P. Boutachkov, L. Cortes, C. Domingo-Prado,F. Farinon, F.C.L. CrespiH. Geissel, , S. Leoni, B. Million, O. Wieland, D.R. Napoli, E. Sahin, R. Menegazzo,J. Gerl, N. Goel, M. Gorska, J. Grebosz, E. Gregor, T.Haberman,I. Kojouharov, N. Kurz, C. Nociforo, S. Pietri, A. Corsi, A. Prochazka, W.Prokopowicz, H. Schaffner,A. Sharma, F. Camera, H. Weick, H-J.Wollersheim, A.M. Bruce, A.M. Denis Bacelar, A. Algora, M. Pf¨utzner, Zs. Podolyak, N. Al-Dahan, N. Alkhomashi, M. Bowry, M. Bunce,A. Deo, G.F. Farrelly, M.W. Reed, P.H. Regan, T.P.D. Swan, P.M. Walker, K. Eppinger,S. Klupp, K. Steger, J. Alcantara Nunez, Y. Ayyad, J. Benlliure, Zs.Dombradi E. Casarejos,R. Janik,B. Sitar, P. Strmen, I. Szarka, M. Doncel, S.Mandal, D. Siwal, F. Naqvi,T. Pissulla,D. Rudolph,R. Hoischen, P.R.P. Allegro, R.V.Ribas, and the Rising collaboration Università di Padova e INFN sezione di Padova, Padova, I; INFN-LNL, Legnaro (Pd), I; Università degli Studi e INFN sezione di Milano, Milano, I; University of the West of Scotland, Paisley, UK; GSI, Darmstadt, D; Univ. Of Brighton, Brighton, UK; IFIC, Valencia, E; University of Warsaw, Warsaw, Pl; Universiy of Surrey, Guildford, UK; TU Munich, Munich, D; University of Santiago de Compostela, S. de Compostela, E; Univ. Of Salamanca, Salamanca, E; Univ. of Delhi, Delhi, IND; IKP Koeln, Koeln, D; Lund University, Lund, S; Univ. Of Sao Paulo, Sao Paulo, Br; ATOMKI, Debrecen, H.

19. Bi-isomer in 210Hg and217Bi

20. Origin of discrepancies • The results are roughlyindependent of the interactionused: KH, CD-Bonn, etc. • Onepossibilityis the mixing of states 6+ with differentseniorites, butrequirestoo large change of the realisticinteraction Isnot the case • Seniority mixing with g9/2seniorityisomersalso for the first g9/2 ( neutrons: 70Ni - 76Ni, protons: 92Mo - 98Cd)

21. Summary • Experiment with radioactivebeam, with the in-flighttechnique. Severalexperimentalchallengesovercome. • The neutron-richregionalongZ = 82 waspopulated, enabling to study the nuclearstructure in thisregion up to nowunknown due to experimentaldifficulties • The observedshellstructureseems to follow a seniorityscheme. However, a closer look reveals that the B(E2) values have an unexpected behaviour. B(E2) values are a sensitive probe to understand in detail the features of the nuclear force The mechanism of effective 3-body forcesis general, and could be relevantalso for otherparts of the nuclide chart. • Puzzle of the 210Hg  Need of furtherstudies • Many more isomers: 217Bi, 211-213Tl, 213Pb and remeasured: 208Hg

22. Seniority Mixing ν=2 ν=4 Calculations by P. Van Isacker

23. Origin of discrepancies • The results are roughly independent of the interaction used: KH, CD-Bonn, Delta, Gaussian • One possibility is the mixing of states 6+ with different seniorites, but requires too large change of the realistic interaction  Is not the case • Seniority mixing with g9/2 seniority isomers also for the first g9/2 ( neutrons: 70Ni - 76Ni, protons: 92Mo - 98Cd) • So ….. • Need to introduce state-dependent effective charges? • Caution when using renormalised interactions

24. Theory of effective interactions

25. Theory of effective interactions

26. Realistic collective nuclear H

27. Unified view

28. Reduced transition prob. B(E2)

29. 210Hg isomers (1) 208Hg PRC 80, 061302(R) Change in structure ? 210Hg Energy (keV)

30. Seniority mixing? ν=2 ν=4 Calculations by P. Van Isacker • Mixing between one ν=2 and two ν=4 states in 212,214Pb. The quadrupole matrix element to ν=4 states is more than five times the one to ν=2, and opposite in sign • Even a small mixing (few %) would be enough to correct the B(E2) value for 212Pb • One possibility is the mixing of states (6+) with seniority 4: need to modify the interaction

31. p3/2 f7/2 Cr40 d5/2 g9/2 32Mg20 20 40 sd pf Building up collectivity quasi-SU3 Quadrupole deformation can be generated by using a quadrupole force with the central field in the subspace spanned by a sequence of Dj = 2 orbits that come lowest by the spin-orbit splitting representing this relevant subspace a quasi-SU3. In the Cr region it happens something similarto what happens in the Island of inversion 32Mg.

32. Effective 3-body forces The only way to include in a standard shell-model calculation (ANTOINE, NATHAN) the effective 3-body forces and 2-body transitionoperatorsis to diagonalizeusing the dressedwavefunction N = 126 core break Z = 82 core break By allowing p-h excitations from the core to the g9/2shell, we include the previuoslyneglectedterms coupling to 2+ (and 3-) excitations from the core + GQR Constant eν = 0.5, eπ= 1.5

33. Effective 3-body interactions We «dress» the bare g9/2 with p-h excitations from the 208Pb core N = 126 core break Z = 82 core break Usuallyneglected! One body Two body Three body By allowing p-h excitations from the core to the g9/2shell to neutronshellsabove, we include the previuoslyneglectedterms The only way to include in a standard shell-model calculation (ANTOINE, NATHAN) the effective 3-body force and 2-body operatorsis to diagonalizeusign the dressedwavefunction

34. Conclusions • The neutron-rich Pb werepopulated, enabling to study the nuclearstructure in thisregion up to nowunknown due to experimentaldifficulties • The observedshellstructureseems to follow a seniorityscheme: However, a closer look reveals that the B(E2) values have an unexpected behaviour. B(E2) values might be a sensitive probe to understand in detail the features of the nuclear force  Seniority mixing; 3N forces, relevantvalencespace • Future: Measurement of B(E2) of the 2+0+ in Pb and Hg using transfer reactions and DSAM (backing target) 207Pb:TLF PRISMA BLF TLF Beam

35. The seniority scheme Nucleons in a valence jn configuration behave according to a seniority scheme: the states can be labelled by their seniority ν SENIORITY SCHEME 8+ 8+ 8+ 8+ 6+ 6+ 6+ ν = 2 6+ 4+ 4+ 4+ 4+ 2+ 2+ 2+ 2+ 0+ 0+ 0+ 0+ ν = 0 (2g9/2)2 (2g9/2)4 (2g9/2)6 (2g9/2)8 For even-even nuclei, the 0+ ground state has seniority ν = 0, while the 2+, 4+, 6+, 8+ states have ν = 2 In a pure seniority scheme, the relative level energies do not depend on the number of particles in the shell j

36. Core excitations below N=126 Anotherpossibilityis the inclusion of 2p-2h excitations from the N=126 core. Calculations in BCS, butunable to reproduceresults with shell-model codes Developing a new interaction with A. Zuker and F. Nowacki to break up the N=126 shell gap.

37. 3N forces in the 208Pb region

38. Puzzle 210Hg 3- calculated particle-vibration coupling models. 1+? s1/2 d3/2: SM: 1.5 MeV 208Hg interaction: Al-Dahan et al., PRC80, 061302(R) (2009).

39. Charge state selection • Formation of many charge states owing to interactions with materials • Isotope identification is more complicated • Need to disentangle nuclei that change their charge state after S2 deg. (Br)Ta-S2 – (Br)S2-S4 DQ=-1 217Pb_sett DQ=0 215Pb_sett DQ=-2 Z DQ=+1 Br1 - Br2 Br1 - Br2

40. Reduced transition prob. B(E2) B(E2) calculatedconsideringinternalconversioncoefficients, and a 20-90 keVenergyinterval for unknowntransitions. Pure seniorityscheme for g9/2 9 : 1 : 1 : 9 • Large discrepancies: • Seniorityscheme • Shell model KH eν = 0.8 PLB 606, 34 (2005) ?

41. Theory of effective interactions Instead of applying the perturbation theory to the operators involved in the problems, it is the wave function that is developed in a perturbative manner. The idea is to start from a bare many-body state and then dress it, giving origin to a quasiconguration.

42. Nuclear shell theory Amos-de-Shalit I. Talmi In una singola j-shell la seniorità si mescola solo se si mescolano le seniorità 1 e 3. Tuttavia nelle j-shell minori di 9/2 è impossibile avere due stati con lo stesso momento angolare e seniorità 1 e 3, per cui non ci può essere mescolamento fra queste due seniorità e quindi fra nessuna seniorità sotto j=9/2.

43. The Z=82 and beyond N=126 R-processpath Experimental β-decay data needed around 208Pb to validate theoretical models. I.N. Borzov PRC67, 025802 (2003)

44. Beta-decay spectroscopy • Background sources: δ-electrons, β-decay electroncs from other sources, “false” β decays/implantations • Standard exponential fits/novel numerical procedure [1] Uncorrelated events are determined from backward time-beta correlations [1] T. Kurtukian-Nieto et al., NIMA 67, 055802 (2008)

45. Beta-decay spectroscopy FRDM+QRPA and(selfconsistent) DF3 + QRPA models are in agreement with experimental data. New spectroscopic data on 219Po.

46. Experimental setup II ~70 m H. Geissel et al., Nucl. Instr. Meth. B70, 286 (1992) • Fragment position: TPC, MWPC, Scintillators • Time Of Flight TOF: Scintillators • Atomicnumber: MUSIC

47. Charge state problem S1 S2 92+ 238U 91+ 91+ 92+ 238U 90+ 90+ S2 212Pb 212Pb Mocadi simulations

48. Kuo-Herling interaction: Valence space • 208Pb is the core (Z=82, N=126). • For neutron-rich Lead isotopes, the N=6 major shell is involved • No shells beyond the magic numbers for neutrons S.p. energies (MeV) N=184 Shells -1.40 3d3/2 -1.45 2g7/2 4s1/2 -1.90 3d5/2 -2.37 -2.51 1j15/2 N=7 major shell -3.16 1i11/2 2g9/2 -3.94 N=126 E.K. Warburton and B.A. Brown PRC43, 602 (1991).