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

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

4. 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

5. Superheavy nuclei
Bender et al., PRC 60 (1999), (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

6. Bender et al.

7. Bubbles due to vacancies in s orbitals

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

9. 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

10. 22O (doubly magic) Stanoiu et al. PRC 69 (2004) 034312
NEUTRON BUBBLES
N = 14
22O (doubly magic) Stanoiu et al. PRC 69 (2004)
Thirolf et al., PLB 485 (2000) 16
Becheva et al., PRL 96 (2006)
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)
34Si (doubly magic)

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

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

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

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

15. 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, (2007)

16. 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: v1 [nucl-th]

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

18. SLy4-HFB
RHB

19. SM Si

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

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

22. Experimental measurements
Electron scattering (storage rings)
Excitation spectra and transition probabilities?
B(E2;0+ g.s. -> 21+) in 46Ar
Riferimento Khan et al anneaux de staoccage…parlare

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

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

25. 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