Testing shell model on nuclei across the N=82 shell gap 1. Test nuclei 2. New experimental data 3. Realistic shell model calculations: basic ingredients 4. Results and comparison with experiment 5. Analysis of the two-body matrix elements 6. Summary Angela Gargano Angela Gargano INFN - Napoli INFN - Napoli
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Testing shell model on nuclei across the N=82 shell gap Testing shell model on nuclei across the N=82 shell gap 1.Test nuclei 2.New experimental data 3.Realistic.
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Testing shell model on nuclei across the N=82 shell gap
Testing shell model on nuclei across the N=82 shell gap
1. Test nuclei
2. New experimental data
3. Realistic shell model calculations: basic ingredients
4. Results and comparison with experiment
5. Analysis of the two-body matrix elements
6. Summary
Angela Gargano Angela Gargano
INFN - NapoliINFN - Napoli
Napoli-Stony Brook Collaboration
Napoli-Stony Brook Collaboration
L. Coraggio
A. Covello
A. G.
N. Itaco
T.T.S. Kuo
A. Gargano – Napoli
Pisa 2005
130Sn
131Sn
132Sn
133Sn
134Sn
131Sb
132Sb
133Sb
134Sb
135Sb
132Te
134Te
136Te
Across the N=82 shell gapAcross the N=82 shell gap
Behavior of the first 2Behavior of the first 2+ + state in even Sn isotopesstate in even Sn isotopes
"" in even Te isotopes in even Te isotopes
Behavior of the B(E2; 0Behavior of the B(E2; 0++22++) value in even Sn ) value in even Sn isotopesisotopes
"" in even Te in even Te isotopesisotopes
Behavior of the first 5/2Behavior of the first 5/2+ + in odd Sb isotopes in odd Sb isotopes
Multiplets in odd-odd Sb isotopesMultiplets in odd-odd Sb isotopes A. Gargano – Napoli
Pisa 2005
B(E2;0+ 2+) = 0.103(15) e2b2
A. Gargano – Napoli
Pisa 2005
D. Radford - ENAM04
A. Gargano – Napoli
Pisa 2005
132Sn and 134Sn results from J.R. Beene –ENAM04
A. Gargano – Napoli
Pisa 2005
● Many-body theory: derivation of the effective interaction
High-precision NN potential based upon the OBE model
2/Ndata= 1.02
(1999 NN Database: 5990 pp and np scattering data)
43 parameters
A. Gargano – Napoli
Pisa 2005
Renormalization of the NN interactionRenormalization of the NN interaction
Difficulty in the derivation of Veff from any modern NN potential:existence of a strong repulsive core which prevents its direct use in nuclear structure calculations.
Traditional approach to this problem: Brueckner G-matrix method
New approach: construction of a low- momentum NN potential Vlow-k
confined within a momentum-space cutoff
S. Bogner, T.T.S. Kuo, L. Coraggio, A. Covello, N. Itaco, Phys. Rev C 65, 051301(R) (2002).
Derived from the original VNN by integrating out the high-momentum components by means of an iterative method. Vlow-k preserves the physics of the original NN interaction up to the cut-off momentum Λ: the deuteron binding energy and low-energy scattering phase-shifts are reproduced.
k
A. Gargano – Napoli
Pisa 2005
3210 FFFFVeff
Derivation of the realistic effective interaction by means of the folded-diagram expansion
Derivation of the realistic effective interaction by means of the folded-diagram expansion
1. Calculation of boxQ
Vertex function composed of irreducibile and valence linkeddiagrams in Vlow-k
2. Sum of the folded-diagram expansion by Kreciglowa-Kuo or Lee-Suzuki method
boxQ
derivative 1
boxQst
boxQ
sderivative 2 & 1
boxQndst
boxQ
A. Gargano – Napoli
Pisa 2005
We include one and two-body diagrams up to second order in Vlow-k
“Bubble”
50
82
.
.
.
132Sn
i13/2f5/2p1/2h9/2p3/2f7/2
h11/2s1/2d3/2d5/2g7/2
d3/2h11/2s1/2g7/2d5/2
space
space
-1space
NN-potential CD-Bonn
g7/2
d5/2
d3/2
s1/2
h11/2
-9.663
-8.701
-7.223
-6.870*
-6.836
SP energies
133Sb
p3/2
h9/2
p1/2
f5/2
i13/2
f7/2
-1.601
-0.894
-0.805
-0.450
0.239*
-2.455
SP energies
133Sn
7.325
7.425
7.657
8.980
9.759
d3/2
h11/2
s1/2
d5/2
g71/2
-1 SP energies
131Sn
A. Gargano – Napoli
Pisa 2005
126
134Sn
in 82-126 shell
= 70 keV
86% (f7/2)2
81% (f7/2)2
BEExpt =6.365 ± 0.104 MeV PRL 1999BECalc=6.082 ± 0.064 MeV