Bubble structures in exotic nuclei

Marcella Grasso

LEA Workshop - Catania, 13-15 October 2008

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• 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

Bender et al.

Bubbles due to vacancies in s orbitals

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)

Proton 2s state well isolated from d5/2 and d3/2 orbitals in 34Si (doubly magic)

N =20 isotones

B(E2)

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

SLy4-HFB

RHB

SM 34Si

Proton density profiles in 34Si

SLy4-HFB

RMF

DDME2-RHB

34Si

36S with and without pairing

To summarize:To summarize:

F=(max-c)/max

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

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