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Nuclear structure in the A~50 region

Nuclear structure in the A~50 region. Roberto V. Ribas Instituto de Física – USP XXVII RTFNB – Santos, 2004. Interpretation of “collective” features in terms of Shell Model. Nuclear Structure at High Spins Collective Model, CSM Large Scale Shell Model

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Nuclear structure in the A~50 region

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  1. Nuclear structure in the A~50 region Roberto V. Ribas Instituto de Física – USP XXVII RTFNB – Santos, 2004

  2. Interpretation of “collective” features in terms of Shell Model • Nuclear Structure at High Spins • Collective Model, CSM • Large Scale Shell Model • Measurement of Transition Probabilities • Examples: 48Cr, 46Ti • Conclusions XXVII RTFNB - Santos 2004

  3. Collective x Shell Models • 80: • Shell Model: A~30 (USD – Wildenthal, Brown) • High Spins: 20-40; A~150 • Rotational Structures • Backbending, Rotation Alignment • CSM, PSM (schematic microscopic structure) • 90: Shell Model: A~50 (fp) • Collective states described by a coherent superposition of (many) single-particle states. XXVII RTFNB - Santos 2004

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  5. XXVII RTFNB - Santos 2004

  6. The Rigid Rotor XXVII RTFNB - Santos 2004

  7. Cranked Shell Model • Effects of the collective rotation in the internal degrees of freedom: Crank the Potential (Routhian) (Semiclassic) XXVII RTFNB - Santos 2004

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  10. Shell Model (No Interaction: Independent Particles) Independent Particles Approximation (mean field) (Slater det.) XXVII RTFNB - Santos 2004

  11. XXVII RTFNB - Santos 2004

  12. Configuration Mixing Most of the excited states are formed by mixing particle-hole configurations = c00p0h+c1 1p1h +c22p2h+... H = T+V = T+Ueff + V-Ueff Particle-hole configurations are mixed by theresidual interaction: interação residual potential de campo médio (configuração diagonal p/ este potencial) Basic idea of theinteracting shell model: Diagonalizethe Hamiltonian H in the base of independent particle configurations. XXVII RTFNB - Santos 2004

  13. Large Scale Models • Need to construct matrix elements for the residual interaction. • Diagonalize very large matrices: • sd (1980): 104 • fp (1990): 107 XXVII RTFNB - Santos 2004

  14. Dimensions: m-scheeme and Lanczos XXVII RTFNB - Santos 2004

  15. Antoine (E. Caurier) • E.C., A. Poves, F. Nowaki, G. Martinez-Pinedo • Nosc=3 (f7/2 p3/2 f5/2 p1/2)=(-) • Residual interaction KB3 (developed by T. Kuo and G. Brown in the 60´s, based on nucleon-nucleon scattering data) • Results are very good! (at least at the lower half of the fp shell) XXVII RTFNB - Santos 2004

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  17. Measuring B(E2), B(M1) • A deeper test of the model should include confrontation of the matrix elements for the electromagnetic transitions. • Collective transitions corresponds to large values of B(E2) and so to very fast transitions (~1ps)=>DSAM. XXVII RTFNB - Santos 2004

  18. GASP-Laboratori Naz. di Legnaro - Italy • S.M. Lenzi, F. Brandolini. C.A. Ur (Padova) • D.R. Napoli, A. Gadea, G. de Angelis (LNL) • J. Sanchez-Solano, A. Poves, G. Martinez-Pinedo (Madrid) • N.H. Medina, J.R.B. Oliveira, RVR (S. Paulo) • 48,49,50Cr • 46,47,49V • 46Ti XXVII RTFNB - Santos 2004

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  20. Doppler Shift Attenuation Method • Line-shape analysis allows determination of the decay rate A(t) XXVII RTFNB - Santos 2004

  21. Complex Spectra: • - coincidence • GateonTranBelow • Gate on Tran Above • Narrow Gate on Transition Below XXVII RTFNB - Santos 2004

  22. NGTB F. Brandolini & RVR – NIM-A 417, 150 (1998) XXVII RTFNB - Santos 2004

  23. XXVII RTFNB - Santos 2004

  24. XXVII RTFNB - Santos 2004 F. Brandolini et al. NPA 642, 387 (1998)

  25. F. Brandolini et al. NPA 642, 387 (1998) XXVII RTFNB - Santos 2004

  26. XXVII RTFNB - Santos 2004 F. Brandolini & C.A. Ur

  27. Origin of Backbending XXVII RTFNB - Santos 2004 Joudagalvis & Aberg PL B428, 227 (1998)

  28. XXVII RTFNB - Santos 2004 K. Hara et al. PRL 83, 1992 (1999)

  29. 46Ti F. Brandolini et al. PRC (2004) XXVII RTFNB - Santos 2004

  30. 46Ti F. Brandolini et al. PRC (2004) XXVII RTFNB - Santos 2004

  31. F. Brandolini et al. PRC (2004) XXVII RTFNB - Santos 2004

  32. 46Ti F. Brandolini et al. PRC (2004) XXVII RTFNB - Santos 2004

  33. Conclusions • Large scale Shell Model calculations reproduces very well not only the level energies, but also the decay rates (quadrupole moments) of fp nuclei. • Band Termination, corresponding to the maximum angular momentum of the fp valence particles is predicted and observed in most of the cases. • States of opposite parity are also well described by coupling a hole in the sd shell to the fp valence particles. • Backbending is in general of different nature, compared to the typical cases in the rare-earth nuclei. XXVII RTFNB - Santos 2004

  34. Thanks! XXVII RTFNB - Santos 2004

  35. XXVII RTFNB - Santos 2004 PRC-66, 024304 (2002)

  36. 48V - PRC-66, 024304 (2002) XXVII RTFNB - Santos 2004

  37. XXVII RTFNB - Santos 2004 PRC-66, 024304 (2002)

  38. 48V - PRC-66, 024304 (2002) XXVII RTFNB - Santos 2004

  39. GXPF1 vs. KB3G Estimated rms error (FDA*) *) Ground states are excluded M. Honma et al., PRC65 (2002) 061301(R) XXVII RTFNB - Santos 2004

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