Nuclear structure in the A~50 region

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Nuclear structure in the A50 region

• Roberto V. Ribas
• Instituto de Física USP
• XXVII RTFNB Santos, 2004

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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

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Collective x Shell Models

• 80
• Shell Model A30 (USD Wildenthal, Brown)
• High Spins 20-40 A150
• Rotational Structures
• Backbending, Rotation Alignment
• CSM, PSM (schematic microscopic structure)
• 90 Shell Model A50 (fp)
• Collective states described by a coherent
  superposition of (many) single-particle states.

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The Rigid Rotor
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Cranked Shell Model

• Effects of the collective rotation in the
  internal degrees of freedom Crank the Potential

(Routhian)
(Semiclassic)
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Shell Model (No Interaction Independent
Particles)
Independent Particles Approximation (mean field)
(Slater det.)
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Configuration Mixing
Most of the excited states are formed by mixing
particle-hole configurations
? c0?0p0hc1 ?1p1h c2?2p2h...
H TV TUeff V-Ueff
Particle-hole configurations are mixed by the
residual interaction
interação residual
potential de campo médio (configuração diagonal
p/ este potencial)
Basic idea of the interacting shell
model Diagonalize the Hamiltonian H in the base
of independent particle configurations.
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Large Scale Models

• Need to construct matrix elements for the
  residual interaction.
• Diagonalize very large matrices
• sd (1980) 104
• fp (1990) 107

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Dimensions m-scheeme and Lanczos
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Antoine (E. Caurier)

• E.C., A. Poves, F. Nowaki, G. Martinez-Pinedo
• Nosc3 (f7/2 p3/2 f5/2 p1/2) ?(-)
• Residual interaction KB3 (developed by T. Kuo and
  G. Brown in the 60s, 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)gtDSAM.

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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

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Doppler Shift Attenuation Method

• Line-shape analysis allows determination of the
  decay rate A(t)

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Complex Spectra

• ?-? coincidence
• Gate on Tran Below
• Gate on Tran Above
• Narrow Gate on Transition Below

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NGTB
F. Brandolini RVR NIM-A 417, 150 (1998)
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F. Brandolini et al. NPA 642, 387 (1998)
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F. Brandolini et al. NPA 642, 387 (1998)
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F. Brandolini C.A. Ur
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Origin of Backbending
Joudagalvis Aberg PL B428, 227 (1998)
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K. Hara et al. PRL 83, 1992 (1999)
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46Ti
F. Brandolini et al. PRC (2004)
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46Ti
F. Brandolini et al. PRC (2004)
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F. Brandolini et al. PRC (2004)
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46Ti
F. Brandolini et al. PRC (2004)
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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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Thanks!
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PRC-66, 024304 (2002)
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48V - PRC-66, 024304 (2002)
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PRC-66, 024304 (2002)
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48V - PRC-66, 024304 (2002)
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GXPF1 vs. KB3G
Estimated rms error (FDA)
nuclei states rms error in MeV ( of data) rms error in MeV ( of data)
nuclei states GXPF1 KB3G
N, Zlt28 Yrast) 0.154(136) 0.235(129)
N, Zlt28 Yrare 0.201(45) 0.263(23)
N or Z28 Yrast) 0.184(92) 0.647(87)
N or Z28 Yrare 0.195(57) 0.802(44)
Ngt28, Zlt28 Yrast) 0.145(129) 0.296(126)
Ngt28, Zlt28 Yrare 0.145(75) 0.302(55)
N, Zgt28 Yrast) 0.186(55) 0.401(51)
N, Zgt28 Yrare 0.187(23) 0.458(23)
) Ground states are excluded
M. Honma et al., PRC65 (2002) 061301(R)
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