1. Shell-model study of exotic nuclei above 132Sn with a realistic effective interaction
Exotic nuclei beyond 132Sn: where do we stand?
Shell-model calculations with realistic low-momentum effective interactions: sketch of theoretical framework
Comparison of theory with available data and predictions
for future experiments
Summary and outlook
L. Coraggio
A. C.
Angela Gargano
N. Itaco
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2. 124Sn (stable) 136Te 137Te 134Sb 135Sb 136Sb 134Sn 135Sn* 136Sn*
Exoticity of nuclei beyond doubly magic 132Sn
124Sn (stable) 136Te 137Te 134Sb 135Sb 136Sb 134Sn 135Sn* 136Sn* Z N
N/Z
* Unknown
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3. Realistic shell-model calculations with two-body forces
Veff derived from the free nucleon-nucleon potential
Two main ingredients
Nucleon-nucleon potential
Many-body theory: derivation of the effective interaction
No adjustable parameter in the calculation of two-body matrix elements
L. Coraggio, A. Covello, A.Gargano, N.Itaco, T.T.S. Kuo, Prog. Part. Nucl. Phys. 62, 135 (2009)
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4. Veff calculated by a many-body perturbation technique
In practical applications: diagrams first-, second-, (and third-) order in the interaction
Veff should account for effects of the configurations excluded from the model space: core polarization effects
+ …
“Bubble”
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5. Renormalization of the NN interaction
Traditional approach to this problem: Brueckner G-matrix method.The G matrix is model-space dependent as well as energy dependent
Vlow-k approach: construction of a low-momentum NN potential Vlow-k confined within a momentum-space cutoff
S. Bogner,T.T.S. Kuo,L. Coraggio,A. Covello,N. Itaco, Phys. Rev C 65, (R) (2002).
S. Bogner, T.T.S. Kuo, A. Schwenk, Phys. Rep. 386, 1 (2003).
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6. Vlow-k approach
Vlow-k preserves the physics of the original NN interaction up to a certain cut-off momentum Λ: the deuteron binding energy and low-energy scattering phase-shifts of VNN are reproduced.
Vlow-k is a smooth NN potential
Low-momentum effective interactions
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7. 1p3n Z=54 1p1n Z=52 N/Z Z=51 4n Z=50 N=82 N=83 N=84 N=85 N=86 N/Z 2n
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8. Protons in the 0g7/2, 1d5/2, 1d3/2, 0h11/2, 2s1/2 of the 50-82 shell
Shell-model calculations with two-body effective interaction derived from the CD-Bonn potential through the Vlow-k approach
132Sn region
Λ = 2.2 fm-1
Model space & single-particle energies
Valence neutrons in the 1f7/2, 2p3/2, 0h9/2, 2p1/2, 1f5/2,0i13/2 levels of the shell
Protons in the 0g7/2, 1d5/2, 1d3/2, 0h11/2, 2s1/2 of the
50-82 shell
Single-particle energies from the spectra of 133Sb and 133Sn
- L. Coraggio, A. Covello, A Gargano, N. Itaco, Phys. Rev. C 72, (2005)
- L. Coraggio, A. Covello, A. Gargano, N. Itaco, Phys. Rev. C 73, (R) (2006)
- A.Covello, L. Coraggio, A. Gargano, N. Itaco, Prog. Part. Nucl. Phys. 59, 401 (2007)
- A. Covello, L. Coraggio, A. Gargano, N. Itaco, Eur. Phys. J. ST 150, 93 (2007)
- G.S. Simpson, J.C. Angelique, J. Genevey, J.A. Pinston, A. Covello, A. Gargano, U. Köster,
R. Orlandi, A. Scherillo, Phys. Rev. C 76, (R) (2007).
- L. Coraggio, A. Covello, A. Gargano, N. Itaco, Phys. Rev. C 80, (R) (2009).
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9. 2n 0.726 Theory B(E2;0+ 2+) = 0.033 e2b2 134Sn Coulex (Oak Ridge)
Lowest first-excited 2+ level in
semi-magic even-even nuclei over the whole chart of nuclei
0.726
Expt.
Theory
Theory
B(E2;0+ 2+) = e2b2
134Sn Coulex (Oak Ridge)
B(E2;0+ 2+) = 0.029(4) e2b2
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10. 134Sn (Theoretical predictions)
B(E2;42 ) = 1.64 W.u.
B(E2;64) = W.u.
B(E2;222) = 0.34 W.u.
B(E2;224) = 0.22 W.u.
Q(2) = -1.3 efm2
µ(2) = nm
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11. BE 134Sn (relative to 132Sn)
Old value (Fogelberg et al., 1999): MeV
New expt. value MeV Theory: MeV
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12. N/Z=1.72
Expt.
Theory
Theory
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13. Striking similarity of nuclear structure in the region of “exotic” doubly magic 132Sn and in the region of stable doubly magic208Pb
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15. 1p1n
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16. Diagonal matrix elements of Vlow-k and contribution from two-body second order diagrams for the πg7/2νf7/2 configuration.
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17. information exists on excited states
136Sb is at present the most exotic open-shell nucleus beyond 132Sn for which
information exists on excited states
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19. 1p3n
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20. Summary and Outlook
The properties of exotic nuclei beyond 132Sn are remarkably well described by a unique consistent shell-model Hamiltonian derived from a realistic free NN potential (CD-Bonn) renormalized through the Vlow-k procedure. This outcome gives confidence in its predictive power and may stimulate, and be helpful to, future experiments.
At present no real evidence of shell modifications in the 132Sn region.
It is a great challenge for RIBs to gain more experimental information on exotic nuclei beyond 132Sn.
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