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Shell Model Applications
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132Sn
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• Start with one of the doubly-magic nuclei as the vacuum• Exact solution of H within the model space for the orbits
inside the shell gaps• Single-particle energies U from experiment• Two-body matrix elements (G) from NN interaction
renormalized to the model space
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Single-particle energies for 132Snfrom data on 131Sn, 133Sn and 133Sb
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Renormalization of NN
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2+
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Model for shell gap vs pairing gap
• Treat the calcium isotopes as neutrons in the 0f7/2, 1p3/2, 0f5/2 and 1p1/2 model space.
• Use the NN G matrix
• Vary the gap between the 0f7/2 and the others
• Look at the energy of the 2+ states
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2+ Energies of the Ca isotopes
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2+ Energies of the Ca isotopes
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2+ Energies of the Ca isotopes
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2+ Energies of the Ca isotopes
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2+ Energies of the Ca isotopes
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2+ Energies of the Ca isotopes
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2+ Energies of the Ca isotopes
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2+ Energies of the Ca isotopes
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2+ Energies of the Ca isotopes
48Ca
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Theory vs Experiment for oxygen 2+ energies
22O
24O
18O 20O
Recent experimental results from the NSCL and GANIL (France) for the energies of 2+
states in 22O and 24O
24O is on the neutron drip line
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Theory vs Experiment for 22O
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USD
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USD NN
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Experiment vs Theory for Ca 2+ energies (2001)
• Single-particle energies from 41Ca
• (KB3G) Renormalized G matrix with some modified diagonal two-body matrix elements
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Experiment vs Theory for Ca 2+ energies (2002)
• Single-particle energies from 41Ca
• (GX1) Renormalized G matrix, with some modified linear combinations of two-body matrix elements
• Otsuka, Honma, Mizusaki, Brown (2002)
48Ca 54Ca
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Effective spe for GX1
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• Start with one of the doubly-magic nuclei as the vacuum• Exact solution of H within the model space for the orbits
inside the shell gaps• Single-particle energies U from experiment• Two-body matrix elements (G) adjusted to obtain a
“best fit” to known data – to get the USD interaction
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Two-body matrix elements – USD-05A vs NN
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28Si with USD (d5/2 d3/2 s1/2 model space)
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30P with USD (d5/2 d3/2 s1/2 model space)
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Gamow-Teller strength from 26Mg(p,n), R. Zegers et al.
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Gamow-Teller strength from 26Mg(p,n), R. Zegers et al.
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Renormalization of NN
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Ongoing project with Taka Otsuka’s group in Japan
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56Ni in fp-shell, GX1A effective interaction.
M. Horoi and B.A. Brown, to be submitted.
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Current project of Alexander Lisetskiy
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A. Lisetskiy et al., PRC 70, 044312 (2004)
ii
Faded seniority isomerism near 78Ni
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Islands of Inversion