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

Shell-model study of exotic nuclei above 132 Sn with a realistic effective interaction. Exotic nuclei beyond 132 Sn: where do we stand?. Shell-model calculations with realistic low-momentum effective interactions: sketch of theoretical framework.

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

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  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 Vietri10

  2. 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

  3. Nucleon-nucleon potential Many-body theory: derivation of the effective interaction Realistic shell-model calculations with two-body forces Veff derived from the free nucleon-nucleon potential Two main ingredients 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

  4. Veff calculated by a many-body perturbation technique In practical applications: diagrams first-, second-, (and third-) order in the interaction Veffshould account for effects of the configurations excluded from the model space: core polarization effects + … “Bubble” Vietri10

  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, 051301(R) (2002). S. Bogner, T.T.S. Kuo, A. Schwenk, Phys. Rep. 386, 1 (2003). Vietri10

  6. Vlow-k approach Vlow-kpreserves the physicsof the original NN interaction up to a certain cut-offmomentumΛ: 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

  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 3n Vietri10

  8. 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, 2s1/2of 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

  9. 134Sn Coulex (Oak Ridge) B(E2;0+2+) = 0.029(4) e2b2 Theory B(E2;0+2+) = 0.033 e2b2 2n Lowest first-excited 2+ level in semi-magic even-even nuclei over the whole chart of nuclei 0.726 Expt. Theory Vietri10

  10. 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

  11. 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

  12. N/Z=1.72 Expt. Theory Theory Vietri10

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

  14. Vietri10

  15. 1p1n Vietri10

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

  17. 136Sb is at present the most exotic open-shell nucleus beyond 132Sn for which information exists on excited states Vietri10

  18. Vietri10

  19. 1p3n Vietri10

  20. Summary and Outlook The properties of exotic nuclei beyond 132Sn are remarkably welldescribed by aunique consistentshell-model Hamiltonianderived from arealistic 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 presentno real evidenceof shell modifications in the 132Sn region. It is a great challenge forRIBsto gain more experimental information on exotic nuclei beyond 132Sn. Vietri10

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