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

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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 Measurement of Transition Probabilities Examples: 48 Cr, 46 Ti Conclusions

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XXVII RTFNB - Santos : 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. Collective x Shell Models

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The Rigid Rotor

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

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Shell Model (No Interaction: Independent Particles) Independent Particles Approximation (mean field) (Slater det.)

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XXVII RTFNB - Santos 2004

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Configuration Mixing Most of the excited states are formed by mixing particle-hole configurations = c 0 0p0h +c 1 1p1h +c 2 2p2h +... Particle-hole configurations are mixed by the residual interaction: H = T+V = T+U eff + V-U eff potential de campo médio (configuração diagonal p/ este potencial) interação residual Basic idea of the interacting shell model: Diagonalize the Hamiltonian H in the base of independent particle configurations.

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XXVII RTFNB - Santos 2004 Large Scale Models Need to construct matrix elements for the residual interaction. Diagonalize very large matrices: sd (1980): 10 4 fp (1990): 10 7

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

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XXVII RTFNB - Santos 2004 Antoine (E. Caurier) E.C., A. Poves, F. Nowaki, G. Martinez-Pinedo N osc =3 (f 7/2 p 3/2 f 5/2 p 1/2 ) =(-) 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)

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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.

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XXVII RTFNB - Santos 2004 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) 48,49,50 Cr 46,47,49 V 46 Ti

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Doppler Shift Attenuation Method Line-shape analysis allows determination of the decay rate A(t)

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XXVII RTFNB - Santos 2004 Complex Spectra: - coincidence Gate on Tran Below Gate on Tran Above Narrow Gate on Transition Below

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

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XXVII RTFNB - Santos 2004

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F. Brandolini et al. NPA 642, 387 (1998)

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

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

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

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

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

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

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

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

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XXVII RTFNB - Santos 2004 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.

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XXVII RTFNB - Santos 2004 Thanks!

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XXVII RTFNB - Santos 2004 PRC-66, (2002)

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XXVII RTFNB - Santos V - PRC-66, (2002)

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XXVII RTFNB - Santos 2004 PRC-66, (2002)

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XXVII RTFNB - Santos V - PRC-66, (2002)

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XXVII RTFNB - Santos 2004 GXPF1 vs. KB3G Estimated rms error (FDA*) nucleistatesrms error in MeV (# of data) GXPF1KB3G N, Z<28Yrast *) 0.154(136)0.235(129) Yrare0.201(45)0.263(23) N or Z=28Yrast *) 0.184(92)0.647(87) Yrare0.195(57)0.802(44) N>28, Z<28Yrast *) 0.145(129)0.296(126) Yrare0.145(75)0.302(55) N, Z>28Yrast *) 0.186(55)0.401(51) Yrare0.187(23)0.458(23) *) Ground states are excluded M. Honma et al., PRC65 (2002) (R)

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