Shell-model study of exotic nuclei above 132Sn with a realistic effective interaction

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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

Exotic nuclei beyond 132Sn: where do we stand?

L. CoraggioA. C.Angela GarganoN. Itaco

124Sn (stable) 136Te 137Te 134Sb 135Sb 136Sb 134Sn 135Sn* 136Sn*

Z 50 52 52 51 51 51 50 50 50 N 74 84 85 83 84 85 84 85 86 N/Z 1.48 1.61 1.63 1.63 1.65 1.67 1.68 1.70 1.72

* Unknown

Exoticity of nuclei beyond doubly magic 132SnExoticity of nuclei beyond doubly magic 132Sn

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Veff derived from the free nucleon-nucleon potentialVeff derived from the free nucleon-nucleon potential

Realistic shell-model calculations with two-body forces Realistic shell-model calculations with two-body forces

Two main ingredients Two main ingredients

Nucleon-nucleon potentialMany-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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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”Vietri10

Renormalization of the NN interactionRenormalization 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, 051301(R) (2002).S. Bogner, T.T.S. Kuo, A. Schwenk, Phys. Rep. 386, 1 (2003).

Λk

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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 approachVlow-k approach

Vlow-k is a smooth NN potential

Low-momentum effective interactions

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N=82 N=83 N=84 N=85 N=86

N/Z

N/Z

Z=50

Z=51

Z=521p1n

2n

1p3n

Z=54

4n

3n

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Valence neutrons in the 1f7/2, 2p3/2, 0h9/2, 2p1/2,

1f5/2,0i13/2 levels of the 82-126 shellProtons 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

Model space & single-particle energies

Shell-model calculations with two-body effective interaction derived from the CD-Bonn potential through the Vlow-k approach

Shell-model calculations with two-body effective interaction derived from the CD-Bonn potential through the Vlow-k approach

- L. Coraggio, A. Covello, A Gargano, N. Itaco, Phys. Rev. C 72, 057302 (2005)- L. Coraggio, A. Covello, A. Gargano, N. Itaco, Phys. Rev. C 73, 031302(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, 041303(R) (2007).- L. Coraggio, A. Covello, A. Gargano, N. Itaco, Phys. Rev. C 80, 061303(R) (2009).

Λ = 2.2 fm-1

132Sn region132Sn region

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Theory

B(E2;0+ 2+) = 0.033 e2b2

134Sn Coulex (Oak Ridge)

B(E2;0+ 2+) = 0.029(4) e2b2

Lowest first-excited 2+ level in semi-magic even-even nuclei over the whole chart of nuclei

Expt. Theory

0.726

2n

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B(E2;42 ) = 1.64 W.u.

B(E2;64) = 0.81 W.u.

B(E2;222) = 0.34 W.u.

B(E2;224) = 0.22 W.u.

Q(2) = -1.3 efm2

µ(2) = -0.56 nm

134Sn (Theoretical predictions)

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BE 134Sn (relative to 132Sn)

Old value (Fogelberg et al., 1999): 6.365 MeV

New expt. value 5.916 MeV Theory: 5.914 MeVVietri10

Expt.

Theory

Theory

N/Z=1.72

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0

0,5

1

1,5

2

0+ 2+ 4+ 6+ 8+

E(M

eV

)

136Sn Calc 212Pb Calc 212Pb Expt

Striking similarity of nuclear structure in the region of “exotic” doubly magic 132Sn and in the region of stable doubly magic208Pb

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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8313451 Sb 1p1n

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Diagonal matrix elements of Vlow-k and contribution from two-body second order diagrams for the πg7/2νf7/2 configuration.

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136Sb is at present the most exotic open-shell nucleus beyond 132Sn for whichinformation exists on excited states

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8513651 Sb 1p3n

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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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