Bubble structures in exotic nuclei
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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
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
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)
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
NEUTRON BUBBLES
N = 1422O (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=1428Si, 42Si (deformed -> correlations) Raman et al., At. Dat. Nucl. Dat. Tab. 78 (2001) 1
Bastin et al., PRL 99 (2007) 022503
34Si (doubly magic)
Inversion of s and d proton states48Ca 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
Z=18
Proton densities
r (fm)
48Ca
46Ar
Bubble-nuclei?
Todd-Rutel, et al., PRC 69, 021301 (R) (2004)
Todd and Piekarewicz, PRC 67, 044317 (2003)
HF proton density in 46Ar
INVERSION (SkI5)
NO INVERSION (SLy4)
Khan, Grasso, Margueron, Van Giai, NPA 800, 37 (2008)
Energy difference between the states 2s1/2 and 1d3/2
Non relativistic mean field Relativistic mean field
Grasso, Ma, Khan, Margueron, Van Giai, PRC 76, 044319 (2007)
PAIRING !!
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]
22OSM
[23] Caurier,ANTOINE code, Strasbourg
[24] Caurier and Nowacki, Act. Phys. Pol. B 30 (1999) 705
[25] Nowacki et al., in preparation
Experimental measurements
• Electron scattering (storage rings)
• Excitation spectra and transition probabilities?
B(E2;0+ g.s. -> 21
+)
in 46Ar
B(E2;0+ g.s. -> 21
+) (e2fm4)
Riley, et al. PRC 72, 024311 (2005)
Raman, et al., At. Data Nucl. Data Tables 36, 1 (2001)
218 31 e2 fm4
SkI5 SLy4
B (E2) (e2 fm4) 256 24
Khan, Grasso, Margueron, Van Giai,
NPA 800, 37 (2008)
What can be done for 34Si
Central proton density depletion of 40%
2s proton state empty
34Si(d,3He)33Al transfer reaction
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