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Bubble structures in exotic nuclei

LEA Workshop - Catania, 13-15 October 2008. Bubble structures in exotic nuclei. Marcella Grasso. First ideas in the 40s: Wilson, PR 69 (1946) 538 Vibrations in a thin spherical shell. Liquid drop models or Thomas-Fermi approximation. Siemens, Bethe, PRL 18 (1967) 704

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Bubble structures in exotic nuclei

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  1. LEA Workshop - Catania, 13-15 October 2008 Bubble structures in exotic nuclei Marcella Grasso

  2. First ideas in the 40s:Wilson, PR 69 (1946) 538Vibrations in a thin spherical shell

  3. Liquid drop models or Thomas-Fermi approximation • Siemens, Bethe, PRL 18 (1967) 704 • Swiatecki, Phys. Scr. 28 (1983) 349 • Bohigas, Campi, Krivine, Treiner, PLB 64 (1976) 381

  4. Superheavy nuclei Bender et al., PRC 60 (1999), 034304 (superheavy, around Z = 120) Skyrme-HFB and RMF Dechargé et al., NPA 716 (2003), 55 (explored regions: 292 ≤ A ≤ 750; 120 ≤ Z ≤ 240 and 750 ≤ A ≤ 920; 240 ≤ Z ≤ 280) D1S-HFB Interplay between Coulomb and nucleon-nucleon interaction

  5. Bender et al.

  6. Bubbles due to vacancies in s orbitals

  7. First microscopic calculations in the 70s. HF + BCSCampi and Sprung, PLB 46 (1973) 291Possible Bubble Nuclei - 36Ar and 200Hg Density dependent interaction G-O (Sprung and Banerjee, NPA 168 (1971) 273)

  8. Bubbles due to vacancies in s orbitals. Possible candidates: • Z, N = 14 (2s) proton,neutron bubbles • Z, N = 80 (3s) 3s case (Cavedon et al. PRL 49 (1982) 978) Electron scattering 206Pb and 205Tl Small central depletion (~ 10%) The proton 3s state is not well isolated (2d3/2) SHELL OR SUB-SHELL CLOSURES

  9. NEUTRON BUBBLES N = 14 22O (doubly magic) Stanoiu et al. PRC 69 (2004) 034312 Thirolf et al., PLB 485 (2000) 16 Becheva et al., PRL 96 (2006) 012501 34Ca (so far not observed) PROTON BUBBLES Z=14 28Si, 42Si (deformed -> correlations) Raman et al., At. Dat. Nucl. Dat. Tab. 78 (2001) 1 Bastin et al., PRL 99 (2007) 022503 34Si (doubly magic)

  10. Proton 2s state well isolated from d5/2 and d3/2 orbitals in 34Si (doubly magic) B(E2) N =20 isotones

  11. Inversion of s and d proton states Z=18 48Ca Z=20 1d3/2 2s1/2 2s1/2 1d3/2 1d5/2 1d5/2 46Ar Z=18 1d3/2 2s1/2 2s1/2 1d3/2 1d5/2 1d5/2

  12. 48Ca 46Ar Proton densities Bubble-nuclei? r (fm) Todd-Rutel, et al., PRC 69, 021301 (R) (2004) Todd and Piekarewicz, PRC 67, 044317 (2003)

  13. HF proton density in 46Ar INVERSION (SkI5) NO INVERSION (SLy4) Khan, Grasso, Margueron, Van Giai, NPA 800, 37 (2008)

  14. Energy difference between the states 2s1/2 and 1d3/2 Non relativistic mean field Relativistic mean field PAIRING !! Grasso, Ma, Khan, Margueron, Van Giai, PRC 76, 044319 (2007)

  15. Adopted models (22O and 34Si) • Shell Model (SM) • Skyrme – Hartree-Fock (HF) and Hartree-Fock-Bogoliubov (HFB) • Relativistic Mean Field (RMF) and Relativistic Hartree-Bogoliubov (RHB) Grasso, Gaudefroy, Khan, Niksic, Piekarewicz, Sorlin, Van Giai, Vretenar, arXiv:0809.4124v1 [nucl-th]

  16. 22O SM [23] Caurier,ANTOINE code, Strasbourg [24] Caurier and Nowacki, Act. Phys. Pol. B 30 (1999) 705 [25] Nowacki et al., in preparation

  17. SLy4-HFB RHB

  18. SM 34Si

  19. Proton density profiles in 34Si SLy4-HFB RMF 36S with and without pairing 34Si DDME2-RHB

  20. To summarize: To summarize: F=(max-c)/max

  21. Experimental measurements • Electron scattering (storage rings) • Excitation spectra and transition probabilities? B(E2;0+ g.s. -> 21+)in 46Ar

  22. B(E2;0+ g.s. -> 21+) (e2fm4) SkI5 SLy4 B (E2) (e2 fm4) 256 24 218  31 e2 fm4 Khan, Grasso, Margueron, Van Giai, NPA 800, 37 (2008) Riley, et al. PRC 72, 024311 (2005) Raman, et al., At. Data Nucl. Data Tables 36, 1 (2001)

  23. What can be done for 34Si Central proton density depletion of 40% 2s proton state empty 34Si(d,3He)33Al transfer reaction

  24. Conclusions • Good candidates for proton and neutron bubbles: 34Si and 22O • Theoretical frameworks: SM, HF and HFB, RMF and RHB • Model-dependent results for 22O • Overhall agreement for a central density depletion of 40% in 34Si • Possible measurements

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