Shell Model Applications

132Sn

• 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

Single-particle energies for 132Snfrom data on 131Sn, 133Sn and 133Sb

Renormalization of NN

2+

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

2+ Energies of the Ca isotopes

2+ Energies of the Ca isotopes

2+ Energies of the Ca isotopes

2+ Energies of the Ca isotopes

2+ Energies of the Ca isotopes

2+ Energies of the Ca isotopes

2+ Energies of the Ca isotopes

2+ Energies of the Ca isotopes

2+ Energies of the Ca isotopes

48Ca

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

Theory vs Experiment for 22O

USD

USD NN

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

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

Effective spe for GX1

• 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

Two-body matrix elements – USD-05A vs NN

28Si with USD (d5/2 d3/2 s1/2 model space)

30P with USD (d5/2 d3/2 s1/2 model space)

Gamow-Teller strength from 26Mg(p,n), R. Zegers et al.

Gamow-Teller strength from 26Mg(p,n), R. Zegers et al.

Renormalization of NN

Ongoing project with Taka Otsuka’s group in Japan

56Ni in fp-shell, GX1A effective interaction.

M. Horoi and B.A. Brown, to be submitted.

Current project of Alexander Lisetskiy

A. Lisetskiy et al., PRC 70, 044312 (2004)

ii

Faded seniority isomerism near 78Ni

Islands of Inversion