1 / 31

The Race for 100Sn – History and Status of Experimental and Shell Model Approach

This article provides a comprehensive overview of the race to study the nucleus 100Sn, including its history, experimental approaches, and the current understanding of its properties. The article discusses topics such as spin gap isomerism, seniority in the g9/2 hole space, large-scale shell model, and the future prospects of studying 100Sn. The article also mentions other doubly-magic and almost-magic nuclei like 56Ni, 78Ni, and 132Sn.

pdove
Download Presentation

The Race for 100Sn – History and Status of Experimental and Shell Model Approach

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The race for 100Sn – History and status of experimental and shell model approach H. Grawe, M. Górska, T. Faestermann SMUV Strasbourg 8. – 10. 10. 2012 (cf. FGG, Progr. in Part. Nucl. Phys., in print) Topics: • History: the past 50 years • Experimental approach • Spin gap isomerism and seniority in the g9/2 hole space • Excitation of the100Sn core and large scale shell model • Super Gamow-Teller decay of 100Sn • Z=N=50 shell gaps • The doubly-magic neighbours56Ni, 78Ni and 132Sn • The future has started !

  2. On the road to 100Sn 2d5/2,1g7/2,3s1/2,1h11/2,2d3/2 1f5/2,2p3/2,2p1/2,1g9/2 The Start ! 88Sr,89Y, 90Zr, 92Mo 2d5/2,3s1/2,2d3/2,1g7/2,1h11/2 "classical"and "new‘‘ doubly-magic and "almost" magic nuclei

  3. The race for 100Sn – landmarks part I – the start (a very personal view) • 90Zr up to (0-8)+N.H. Lazar et al., PR 110, 513(58) • 89Y,90Zr,91Nb, excited states ESM analysis I.Talmi, I.Unna, NPA19, 225 (60) • 88Sr - 92Mo binding energies, 8+ isomersN. Auerbach, I. Talmi, NPA64, 458(65) • TBME in proton (p1/2,g9/2) space yield 100Sn Sp=1.83 MeV • 1970-75NaI(Tl) replaced by Ge g-detectors, (4He/3He,xn) by (HI,xn yp za) reactions • ESM in pn (p1/2,g9/2) space, seniority conservationSp=2.92 MeV • F.J.D Serduke, R.D. Lawson, D.H. Gloeckner, NPA 256, 45 (76) • R. Gross, A. Frenkel 267, 85 (76) • Excited states (Ex) and binding energies (BE) for N=48-50 and Z < 43 (Tc) • 1980-85 (g9/2)n mid-shell nuclei Ru-Pd studied in ISOL and in-beam • seniority breaking in 95Rh: E. Nolte et al., ZPA 298, 191 (80); A. Amusa, • R.D.Lawson, ZPA 307,333(82) ; J.Blomqvist, L.Rydström, Phys. Scr. 31,31(85) • 1985-90 Multi-detector arrays for g, n, p, a OSIRIS, NORDBALL, EUROGAM • OXBASH shell model code B.A. Brown et al., MSU-NSCL report No. 524 (85)

  4. The race for 100Sn - part II – detector arrays and shell model analysis 1990-95 97Ag p-3, 104Sn n4, 100Cd p-2n2 closest approach in-beam and excited states 98Cd Gamow-Teller b-decay @ISOLDE A. Plochocki et al., ZPA 342,43(92) 100Sn: SPE/SHE, gaps: 5.92 (Z=50)/6.80 (N=50) MeV H.G. et al.,Phys.Scr.T56,71(95) SM summary in pn(p1/2,g9/2)D. Rudolph et al., NPA 597, 298(96) Z=50,N=50GT reviewK.Rykaczewski et al., IOP Conf. Ser. No. 132, 215(93) Fragmentation and in-flight separators FRS/GSI, LISE/GANIL 1994 Identification of 100Sn @GANIL and GSI M. Lewitowicz et al., PLB 332, 20(94) in projectile fragmentation R. Schneider et al., ZPA 348, 241 (94) GAMMSPHERE, GASP,EUROBALL I-IV + ancillaries, fusion-evaporation and fragmentation for isomers R. Grzywacz et al., PLB 355,439(97) 1995-99 98Cd, 8+ isomer p-2M. Górska et al., PRL 79, 2415 (97) 102Sn, 6+ isomer n2 M. Lipoglavšek et al., PLB 440, 246 (98) G-matrix based realistic interactionsM. Hjorth-Jensen et al., PR 261,125(95) ANTOINE and NATHAN E.Caurier, F.Nowacki, Acta Phys. Pol. B30, 705(99)

  5. The race for 100Sn - part III – the new century • 2000-05 103Sn prompt n(d5/2,g7/2)C. Fahlander et al., PRC 63, 021307(R) (01) • 99Cd core excitation M. Lipoglavšek et al., PRC 66,011302(R) (02) • 98Cd core excited 12+ isomer, N=50 gap A. Blazhev et al., PRC 69, 064304(04) • based on LSSM 100Sn core excitation F. Nowacki, NPA 704, 223c(02) • 2005-11 106-110Sn 2+ Coulex @GSI, MSU, REX-ISOLDE A.Banu et al.,PRC 72,061305(05) • C. Vaman et al., PRL 99,162501 (07), A.Ekström et al., PRL 101, 012502 (08) • 106Te next to 100Sn in recoil - g tagging B. Hadinia et al., PRC 72, 041303 (05) • 101Sn n(d5/2,g7/2)in 105Te ag-decay, sequence still disputed • D. Seweryniak et al., PRL 99, 022504 (07), I.G. Darby et al., PRL 105, 162502 (10) • 96Cd 16+ spin trap b-decay and 96Ag 19+ core excited isomer, LSSM • B.S. Nara Singh et al., PRL 107, 172502 (11), P. Boutachkov et al., PRC 84, 044311 (11) • 100Sn Super-GT decay, bg, gg coinc., QEC Ch. Hinke et al., Nature 486, 341 (12) • LSSM ; Z=50, N=50robust shell closure verified !! (K. Sieja, F. Nowacki) • Quenching of GT operator ~0.75

  6. Coulex of radioactive and stable beams @ relativistic and „safe“ energy GSI/RISING 108Sn / 197Au v/c = 0.45 P/B ~ 1-2 2+→ 0+ REX/ISOLDE 108Sn / 58Ni v/c = 0.08 P/B ~ 4-5 2+→ 0+ A. Banu et al., PRC 72, 061305 (2005) GSI/UNILAC 108In 114Sn / 58Ni v/c = 0.07 P/B ~ 40 2+→ 0+ A. Ekström et al., PRL 101, 012502 (2008) 58Ni P. Doornenbal et al., PRC 78, 031303 (2008)

  7. Valence and core excited isomers in N=5098Cd 8+ 8+ 12+!! Sum gg gg(4207) 6+ 6+ 4+ 2+ 4+ 2+ NORDBALL+2 EUROBALL cluster EUROBALL IV @ Strasbourg t1/2(8+)=0.48(16)ms t1/2(8+)=0.17(+6-4) ms t1/2(12+)=0.23(+4-3) ms M. Górska et al., PRL 79, 2415 (1997) A. Blazhev et al., PRC 69, 064304 (2004)

  8. Valence and core excited isomers in N=5098Cd 8+ 8+ 12+!! Sum gg gg(4207) 6+ 6+ 4+ 2+ 4+ 2+ A. Blazhev et al., J. Phys. Conf. Ser. 205, 012035 RISING@GSI(2010) B(E2; 8+→ 6+) = 1.2(3) W.u. B(E2;12+→10+)=2.2(8) W.u. B(E4;12+→ 8+)=3.0(8) W.u. See Andrey Blazhev‘s talk NORDBALL+2 EUROBALL cluster EUROBALL IV @ Strasbourg t1/2(8+)=0.48(16)ms t1/2(8+)=0.17(+6-4) ms t1/2(12+)=0.23(+4-3) ms M. Górska et al., PRL 79, 2415 (1997) A. Blazhev et al., PRC 69, 064304 (2004)

  9. 100Sn Super Gamow-Teller decay (I) Ch. Hinke et al., Nature 486, 341 (2012) b spectrum Identification Z vs. A/Z 124Xe fragmentation 100Sn bg 100In levels

  10. Close-up view of the 100Sn region

  11. Spin gap isomers belowN = Z = 50 @ RISING, GSI – ISOL and EUROBALL IV b • proton –neutron • hole-hole interaction • in png9/2-n • core excitation in large-scale SM • in pn g9/2-1 (d5/2,g7/2)1 ?

  12. The g9/2n seniority scheme and distortion by core excitation schematic experiment g9/2(+p1/2) <jn,v,J|OL|jn,v,J> ~ const 1 – body, L=odd, v - ve.g. M1, m 2 - body, odd, v - v , e.g. d-interaction 1 – body, L=even,v - v-2 e.g. B(E2) 1 – body, L=even, v – v, e.g. E2, Q 2 – body, even, v – v-2 <jn,v,J|V|jn,v,J> ~ const + (n-v)/2 N=50 isotones p g9/2n <jn,v,J|OL|jn,v-2,J´>2 ~ f(1-f) corex! <jn,v,J|OL|jn,v,J´> ~ (1-2f) <jn,v,J|V|jn,v-2,J> ~ (1-2f)√f(1-f)

  13. Symmetry rules in the seniority scheme • Excitation energies are independent of shell occupation n • Matrix elements of even-tensor one- and two particle operators change sign in mid-shell, i.e. they vanish for n = (2j+1)/2 • Odd-tensor one- and two particle operators are diagonal in v • Proton-neutron interaction, e.g T=0 core excitations, break seniority A. De Shalit, I. Talmi, Nuclear Shell Theory, Academic Press, New York, 1963 R.F.Casten, Nuclear Structure from a Simple Perspective, Oxford University Press, 2000 H. G., The Euroschool Lectures on Physics with Exotic Beams, Vol. I, Lect. Notes Phys. 651, 33 (2004) A. Amusa, R.D. Lawson, ZPA 307, 333 (1982) H. Grawe et al., EPJA 27, s01, 257 (2006) H. Mach et al., Proc. Int. Symposium A New Era of Nuclear Structure Physics, Niigata, Japan 2003, World Scientific, Singapore, 2004, p.277 F. Nowacki, priv. comm. A. Escuderos, L. Zamick, PRC73, 044302 (2006) P. Van Isacker, Int. J. Mod. Phys. E20, 191 (2011) 95Rh 96Pd 94Ru }

  14. Valence mirror g9/2n nuclei in Z=28 isotopes and N=50 isotones The 8+ isomers disappear in mid-shell Ni isotopes due to stronger Ip = 2+ two-body matrix element (Ex(2+)~1.0 vs. 1.5 MeV), which shifts the seniority v=4, 6+ state (*) below the v=2, 8+ enabling a strong Dv=2 B(E2) Z=28 No 8+ isomers ! N=50 8+ isomers ! H.G. et al., NPA 704, 211c (2002) A. Lisetskiy et al., PRC 70, 044314 (2004)

  15. A. Blazhev et al., PRC 69, 064304 • 100Sn core excitation • LSSM smoothly converged at t=5 (F.Nowacki, E. Caurier) • 100Sn neutron shell gapN=50 inferred • 6.46 (15) MeV • remaining E2,E4 deficiency is due to • interaction and/or • proton gap Z=50 • effective E2 charge will • not help ! pairing 98Cd E2 ph states pg9/2-2ng9/2-t (d5/2,g7/2)t E4 • Valence excitation energy • increases with t • ph excitation energy • decreases with t • Exception t=2 : pairing • overbinds valence states preliminary ! E2 Valence states pg9/2-2 • Blazhev et al., PRC 69, • 064304 (04)

  16. First core excited odd-parity isomer in N=5096Pd corex • p = + states well reproduced in LSSM @t=5 in gds space • p = - states calculated @ t=1 for neutrons in fpgd5/2 valence M. Palacz et al., PRC 86, 014318 (2012) 96Pd

  17. Valenceand core excited isomers inN=4996Ag 96Ag core excited isomer P. Boutachkov et al., PRC 84, 044311 (2011) see A. Blazhev ! valence isomers SM f5/2,p,g9/2 LSSM gds

  18. 100Sn excited states predictions from shell model and mean field • Ip = 6+ isomer? • 2+, 3- position? • B(E2;2+→0+) ~ 10 W.u. • LSSM: • gds, “Tokyo“ interaction, t=4 • M. Hjorth-Jensen, et al., • PR 261,125(95) • monopole tuned • F. Nowacki, NPA 704,223(2000) • by Etienne Caurier ! (2005) • SM: • gd5/2 , H7B interaction, t=3 • Hosaka et al., NPA 244,76(1985) • monopole tuned by H.G. • HF-RPA: • V.I. Isakov, K.I. Erokhina, • Phys. At. Nucl. 65,1431(2002) • RQRPA: • A. Ansari, P. Ring, • PRC 74,054313(2006)

  19. 100Sn Super Gamow-Teller decay (II) Ch. Hinke et al., Nature 486, 341 (2012) QEC = 4.35(-17+19) MeV b+ T1/2 = 1.09 (18) s LSSM 100In EXP log(ft) = 2.62(+0.13-0.11) record low ! (pg9/2-1ng7/2) 1+ B(GT) = 9.3 (+2.3-3.0) record high ! Single 1+ feeding

  20. 100Sn Super Gamow-Teller decay (III) Ch. Hinke et al., Nature 486, 341 (2012) Why “Super“ ? B(GT) =160/9 × 1 × 1 for pg9/2 → ng7/2 spin-flip transition Unique in the Segrè chart ! 100Sn LSSM in gds K. Sieja, F. Nowacki LSSM guided correction: 3 more 1+ states fed with B(GT)>0.1 SB(GT) = 9.9 (+2.8-3.2) B(GT;1+1) = 7.6 (+2.2-2.5) LSSM value 5.7 robust shell gaps >6 MeV q~0.75 quenching of GT operator confirmed

  21. Monopole driven shell structure Single particle/hole energies (SPE/SHE) and shell gaps from extrapolation of experimental data from known CS´to next CS e.g. N=50 99,100,101Sn 99In Two-body matrix elements (TBME) and monopoles from binding energies (BE), SPE/SHE (e) and excitation energies (Ex) within each multiplet j´j for particle-particle and j´k for particle-hole 92Mo See FGG ! 90,91,92Nb 89,90,91Zr

  22. Shell gap along N=50 Exp. gaps from separation energies S1n,S2n ESPE from exp. multiplets corrected for p occupation theoretical monopole T. Otsuka et al., PRL104,012501 (10) SM in valence space, no corex 100Sn : 6.35(13) MeV for d5/2g.s. 3.9(5)/3.0(3) MeV for d5/2/g7/2g.s. O. Sorlin, M.-G. Porquet, PPNP 61, 602 (08) robust shell gaps ! 78Ni : 4.05(18) MeV for d5/2g.s. 3.4 MeV for d5/2g.s. M.-G. Porquet, O. Sorlin,PRC 85, 014307(12) 4.7 from LSSM and d5/2 g.s. K. Sieja, F. Nowacki, PRC 85,051301(R) (12)

  23. 100Sn and56Ni SPE/SHE and g7/2 monopole migration n d5/2, g7/2 problem in 101Sn Analogy of N=3, 4 HO shells and intruders from N=4, 5 100Sn gaps:5.96(20) (p) and 6.35(13) (n) MeV D. Seweryniak et al., PRL 99, 022504(07) (ANL) I.G. Darby et al.,PRL105, 162502(10) (ORNL) Extrapolation “safe“ for pg9/2nd5/2 multiplet (92Nb) pg9/2ng7/2 monopole from G-matrix (MHJ) modified to fit N=51 single particle states (MHJm)

  24. 100Sn extrapolated SPE vs. SM and global predictions (just a selection from many) “EX“: extrapolated H.G. SKX : Skyrme B.A. Brown PRC 58,220(98) PL40: RMF K. Rutz et al., NPA 634,67 (98) DZ: SM based global monopole scaling J. Duflo, A.P Zuker, PRC 59, R2347(99)

  25. 100Sn and its magic neighbours 56,78Ni and 132Sn • f5/2(p) − g9/2: gap increase from 56Ni to 78Ni /100Sn and decrease from 100Sn to 132Sn due to strong monopole; Z=40 subshell at N=82? nf5/2(p)g9/2 – g7/2(ds)h11/2: N=4 intruder g9/2 well separated N=40subshell in Ni´s N=5 intruder h11/2 embedded in s1/2,d3/2 orbits no subshells in Sn´s

  26. 56Ni vs. 100Sn – fp vs. gds structure analogies - Why and why not? (a) valence states Imax = 6+ vs. 8+ B(E2) = 3.3 vs. 1.2 W.u. core excited isomers Ip =10+ vs. 12+ = Imax + 4 B(E2) = 1.7 vs. 2.2 W.u. B(E4) = 0.8 vs. 3.0 W.u. correspondence principle ! (Jan Blomqvist) (b) valence states Imax = 11+ vs. 15+ Imax-2 = 9+ (!) vs. 13+ Isomer destroyed ! 9+2 needs p3/2 ! No core excited isomers due to proximity to proton mid-shell

  27. Z=50shell gap for 100-132Sn and B(E2;0+→2+) Extrapolated • B(E2) enhanced below A~114 • correlation with reduced Z=50 shell gap and pg9/2-1d5/2 E2 excitation? • B(E2) evolution below N=56 ? AMDC sys B(E2; 0+→ 2+) • SM 100Sn core n only • LSSM80/90Zr core pn • Banu et al., PRC 72, 061305 (2005) pn n LSSM 80Zr • RQRPA • Ansari et al., PLB 623, 37 (2005) • EXP: ENSDF

  28. E(2+) and B(E2;2+ 0+) in semi-magic valence mirrors fpg and gdsh nuclei Experiment and shell model (SM/LSSM) N=50 Z=28 Z=50 No gap ! s,d,g7/2 h11/2 p,f5/2 g9/2 p,f5/2 g9/2 ModerateN=40 and Z=(38),40 gaps NoN=64,66 nor 70 gaps between p1/2 and g9/2orbits due to closely packed g7/2dsh11/2 orbits SM: A. Lisetskiy et al., PRC 70, 044314 (04) SM and LSSM: O. Kenn et al., PRC 63,064306(01) LSSM: A. Banu et al., PRC 72 ,061305(05) O. Sorlin et al., PRL 88,092501(02) S. Lenzi et al., PRC 82,054301(10)

  29. Apparent scaling of effective g9/22 two-body matrix elements • S = E(8+)-E(2+) ~ A-1 ? • valence space pf5/2g9/2 ~ A-1/3 • Coulomb and pairing negligible • Cross shell excitation different N=3, N=4, N=5 HO shells ! • Quadrupole interaction scales as EQ =O(D-1 A-1/3), Degeneracy D M. Dufour and A. P. Zuker, PRC54, 1641 (1996) • Normalise to 98Cd LSSM in gds Frederic Nowacki, priv. comm. S S S Normalised to 2+ to minimise effect of p1/2, Coulomb and pairing EX D A-1 A-1/3 76Ni 1428 1353 1336 1128 98Cd 1036 1036 1036 1036 (reference) 130Cd 803 785 781 943 LSSM EXP 9848Cd50 t=0 1 2 3 4 5

  30. Summary of status and outlook Done: • g9/2 isomerism,pn interaction, seniority scheme and distortions • core excitation across Z,N=50 and E2/E4 isomerism and strength • super Gamow-Teller decay and implication for shell structure • verification of general GT quenching factor ~0.75 for N=4 HO shell • robustness of Z=N=50 shells 3 MeV from the proton dripline • monopole driven evolution of single particle energies • shell structure evolution towards HO shell neighbours • A-1 scaling of empirical TBME • masses and half lives along the rp path • super-alloweda decay close to N=Z • experimental verification 100Sngaps and single particle/hole energies • excited statesand mirror symmetryin, below and beyond 100Sn • precision masses and GT strengthalong the rp path • precision studies of super-allowed Fermidecay andCVChypothesis • proton emissionbelow Z=50 • super-allowed a-decay atN=Z • realistic interaction beyond 0 ħ • consistentLSSMdescription ofexcitation andmasses To do:

  31. Collaborations EUROBALL I-IV, the home of European Gamma Arrays RISING Rare ISotope INvestigation at GSI EURICA EUroball Riken Cluster Array PreSPEC Pre- (HI-DE-SPEC) campaign @GSI plus AGATAAdvanced Gamma Tracking Array SM2Strasbourg-Madrid Shell Model Special thanks go to: A. Blazhev, P. Boutachkov, B.A. Brown, E. Caurier, T. Faestermann, M. Górska, Ch. Hinke, M. Hjorth-Jensen, G. Martinez-Pinedo, B.S. Nara Singh, F. Nowacki, T. Otsuka, K. Sieja

More Related