1. Neutron-rich lead isotopes provide hints on the role of the effective three-body forces Jose Javier Valiente Dobón Laboratori Nazionali di Legnaro (INFN), Italia

2. Overview Neutron-rich Pb nuclei beyond N=126 Experimental setup and challenges Seniority Pb isomers  the B(E2) probes Effective 3-body forces A puzzle: 210 Hg Summary

3. The Z=82 and beyond N=126 216 Pb 212 Pb 218 Pb g 9/2.Taking advantage of these isomers we want to study the developmet of nuclear structure from 212 Pb up to 218 Pb and nearby nuclei

4. 5x10 6 pps 2 HPGe detectors (Eff γ =1%) 350 ions implanted GSI M. Pfutzner, PLB 444 (1998) 32 Difficult region to explore: only fragmentation possible, primary beam charge states! Experimental challenges

5. FRS-Rising at GSI: stopped beam campaign Target 2.5 g/cm 2 Be Deg. S1: Al 2.0 g/cm 2 MONOCHROMATIC Deg S2: Al 758 mg/cm 2 S1 S2 S3 S4 15 CLUSTERs x 7 crystals ε γ = 11% at 1.3MeV Beam: 238 U @ 1GevA 9 DSSSD, 1mm thick, 5x5 cm 2 16x16 x-y strips Experimental setup

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

7. 90+ 91+ 92+ 212 Pb 238 U 212 Pb S1S1 S1S1 S2 92+ 91+ 90+ Charge state problem Mocadi simulations

8. 1 GeVA 238 U beam from UNILAC-SIS at 10 9 pps 206 Hg 210 Hg 209 Tl 213 Tl 212 Pb 218 Pb 215 Bi 219 Bi A/q Z Nuclei populated in the fragmentation

9. 212,214,216 Pb: 8 + isomer

10. 214 Pb: γγ coincidences

11. 210 Pb The 8 + isomer is a seniority isomer, involving neutrons in the 2g 9/2 214 Pb 212 Pb 216 Pb 8+8+ X 8+8+ X Ductu naturae

12. 2g 9/2 1i 11/2 1j 15/2 3d 5/2 3d 3/2 4s 1/2 2g 7/2 -3.94 -2.37 -2.51 -3.16 -1.45 -1.90 -1.40 S.p. energies (MeV) Shells 208 Pb 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 N=126 N=184 N=7 major shell Kuo-Herling interaction: Valence space E.K. Warburton and B.A. Brown PRC43, 602 (1991).

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

14. The neutron 2g 9/2 shell has a dominant role for the 8 + isomeric state. 1i 11/2, 1j 15/2 and 3d 5/2 also play a role 210 Pb n = 2 212 Pb n = 4 214 Pb n = 6 216 Pb n = 8 218 Pb n = 10 2g 9/2 1.993.394.786.216.96 1i 11/2 0.0050.330.681.042.16 1j 15/2 0.0020.160.320.430.59 3d 5/2 0.00080.040.080.110.14 8 + state wave functions: occupational numbers show quite pure wave functions The ground state wave functions are in general more fragmented, with the 1i 11/2 shell around 25 - 30 % Occupational numbers Wave functions from Kuo-Herling

15. B(E2) calculated considering internal conversion coefficients, and a 20- 90 keV energy interval for unknown transitions. Reduced transition prob. B(E2) B(E2; 8+ -> 6+) A (Lead) e ν =0.8 Large discrepencies factor ~ 5 210 Pb 212 Pb 214 Pb 216 Pb Isomer t 1/2 (μs)0.20 (2)6.0 (8)6.2 (3)0.40 (4) B(E2) e 2 fm 4 Exp.47(4)1.8(3)1.4-1.924.7-30.5 B(E2) e 2 fm 4 KH4180.2616.4 Upper limit 90 keV based on K α X rays intensity (K electrons bound ~88 keV) B(E2) ~ E γ -5 (1+α) -1 τ -1

16. The results are roughly independent of the interaction used: KH, CD-Bonn, etc. 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 g 9/2 seniority isomers also for the first g 9/2 ( neutrons: 70 Ni - 76 Ni, protons: 92 Mo - 98 Cd) Origin of discrepancies

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

18. 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 g 9/2 seniority isomers also for the first g 9/2 ( neutrons: 70 Ni - 76 Ni, protons: 92 Mo - 98 Cd) So ….. Need to introduce state-dependent effective charges? Caution when using renormalised interactions Origin of discrepancies

19. Theory of effective interactions

21. Realistic collective nuclear H

22. Unified view

23. Effective 3 body interactions Two bodyThree body Usually neglected! One body Effective 3-body terms appear naturally in the renormalization process, but they are NOT included in shell-model codes (ANTOINE and NATHAN): Two-body operators (H) become effective 3-body operators One-body transition operators (B(E2)) become effective 2-body operators

24. Effective three-body forces Z=82N=126 h 11/2 i 13/2 2f 7/2 2g 9/2 πν In a perturbative approach, the bare g 9/2 is «dressed» with p-h excitations from the 208 Pb core............ ν shells above N=126 π shells above Z=82 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 allowing relevant p-h excitations from the core to the g 9/2 shell to neutron shells above, we include the previuosly neglected terms quasi-SU3

25. Exp. data g 9/2 (n-1) + ν shells above + core exc. g 9/2 (n-1) + ν shells above g 9/2 Standard eff. charges: e ν = 0.5, e π = 1.5 Standard eff. charges: e ν = 0.5, e π = 1.5 Effective 3-body interaction: Results The explicit coupling to the core restores the conjugation symmetry 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)

26. Bi-isomer in 210 Hg 643 0 1196 663 E3 (663keV) and E1 (20 keV) 10 6 suppression in the E1 643 553 663 (0 + ) (2 + ) (6 + ) (4 + ) 1366 (8 + ) ? T 1/2 ~1 μs

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

28. Experiment with radioactive beam, with the in-flight technique. Several experimental challenges overcome. The neutron-rich region along Z = 82 was populated, enabling to study the nuclear structure in this region up to now unknown due to experimental difficulties The observed shell structure seems to follow a seniority scheme. 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 forces is general, and could be relevant also for other parts of the nuclide chart. Puzzle of the 210 Hg  Need of further studies Many more isomers: 217 Bi, 211-213 Tl, 213 Pb and remeasured: 208 Hg Summary

29. 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. Collaboration

30. Reduced transition prob. B(E2)

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

32. Mixing between one ν=2 and two ν=4 states in 212,214 Pb. 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 212 Pb One possibility is the mixing of states (6+) with seniority 4: need to modify the interaction Seniority mixing? ν=2 ν=4 Calculations by P. Van Isacker

33. Building up collectivity Quadrupole deformation can be generated by using a quadrupole force with the central field in the subspace spanned by a sequence of  j = 2 orbits that come lowest by the spin-orbit splitting representing this relevant subspace a quasi-SU3. In the Cr region it happens something similar to what happens in the Island of inversion 32 Mg. 32 Mg 20 sd p 3/2 f 7/2 20 Cr 40 pf d 5/2 g 9/2 40 quasi-SU3

34. 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 transition operators is to diagonalize using the dressed wave function By allowing p-h excitations from the core to the g 9/2 shell, we include the previuosly neglected terms N = 126 core break Z = 82 core break GQR + coupling to 2 + (and 3 - ) excitations from the core Constant e ν = 0.5, e π = 1.5

35. Effective 3-body interactions We «dress» the bare g 9/2 with p-h excitations from the 208 Pb core N = 126 core break Z = 82 core break 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 By allowing p-h excitations from the core to the g 9/2 shell to neutron shells above, we include the previuosly neglected terms Two body Three body Usually neglected! One body

36. The neutron-rich Pb were populated, enabling to study the nuclear structure in this region up to now unknown due to experimental difficulties The observed shell structure seems to follow a seniority scheme: 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, relevant valence space Future: Measurement of B(E2) of the 2+  0+ in Pb and Hg using transfer reactions and DSAM (backing target) Conclusions BLF TLF PRISMA 207 Pb:TLF Beam

37. Nucleons in a valence j n configuration behave according to a seniority scheme: the states can be labelled by their seniority ν 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 0+0+ 2+2+ 6+6+ 8+8+ 4+4+ (2g 9/2 ) 2 0+0+ 2+2+ (2g 9/2 ) 4 0+0+ 2+2+ (2g 9/2 ) 6 0+0+ 2+2+ (2g 9/2 ) 8 ν = 0 ν = 2 SENIORITY SCHEME 6+6+ 8+8+ 4+4+ 6+6+ 8+8+ 4+4+ 6+6+ 8+8+ 4+4+ The seniority scheme

38. Another possibility is the inclusion of 2p-2h excitations from the N=126 core. Calculations in BCS, but unable to reproduce results with shell-model codes 210 Pb(νg9/2) 4 same sign of (νg9/2) 2,but smallerSlightly smaller B(E2) 212 Pb(νg9/2) 6 opposite sign of (νg9/2) 4, same magnitude Smaller B(E2): close exp. value 214 Pb(νg9/2) 8 same sign of (νg9/2) 6, but 3 time larger Larger B(E2): too large ? Core excitations below N=126 Developing a new interaction with A. Zuker and F. Nowacki to break up the N=126 shell gap.

39. 3N forces in the 208 Pb region

40. 215Pb_sett Br1 - Br2 Z 217Pb_sett 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=0 DQ=+1 DQ=-1 DQ=-2 Br1 - Br2 Charge state selection

41. 210 Pb 212 Pb 214 Pb 216 Pb Isomer t 1/2 (μs)0.20 (2)6.0 (8)6.2 (3)0.40 (4) B(E2) e 2 fm 4 Exp.47(4)1.8(3)1.4-1.924.7-30.5 B(E2) e 2 fm 4 KH4180.2616.4 B(E2) calculated considering internal conversion coefficients, and a 20-90 keV energy interval for unknown transitions. Reduced transition prob. B(E2) Large discrepancies: -Seniority scheme -Shell model KH Large discrepancies: -Seniority scheme -Shell model KH Pure seniority scheme for g 9/2 9 : 1 : 1 : 9 PLB 606, 34 (2005) ? e ν = 0.8

42. 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.

43. 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.

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

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

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