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 Vietri10

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 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 Vietri10

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) Vietri10

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 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). Vietri10

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 Vietri10

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 Vietri10

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 82-126 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, 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). Vietri10

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+) = 0.033 e2b2 134Sn Coulex (Oak Ridge) B(E2;0+ 2+) = 0.029(4) e2b2 Vietri10

134Sn (Theoretical predictions) B(E2;42 ) = 1.64 W.u. B(E2;64) = 0.81 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) = -0.56 nm Vietri10

BE 134Sn (relative to 132Sn) Old value (Fogelberg et al., 1999): 6.365 MeV New expt. value 5.916 MeV Theory: 5.914 MeV Vietri10

N/Z=1.72 Expt. Theory Theory Vietri10

Striking similarity of nuclear structure in the region of “exotic” doubly magic 132Sn and in the region of stable doubly magic208Pb Vietri10

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1p1n Vietri10

Diagonal matrix elements of Vlow-k and contribution from two-body second order diagrams for the πg7/2νf7/2 configuration. Vietri10

information exists on excited states 136Sb is at present the most exotic open-shell nucleus beyond 132Sn for which information exists on excited states Vietri10

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1p3n Vietri10

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. Vietri10