Gamow-Teller Transitions for Light Nuclei by the Deformed Quasi-particle RPA(DQRPA)
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Transcript of Gamow-Teller Transitions for Light Nuclei by the Deformed Quasi-particle RPA(DQRPA)
Gamow-Teller Transitions for Light Nuclei Gamow-Teller Transitions for Light Nuclei by the by the Deformed Quasi-particle Deformed Quasi-particle
RPA(DQRPA)RPA(DQRPA)
Soongsil University, KoreaEun Ja HA and Myung-Ki CHEOUNEun Ja HA and Myung-Ki CHEOUN
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ContentsContents
• Motivation • Formalism
- Deformed basis (Nilsson basis) - Deformed Bardeen Cooper Schrieffer (DBCS)- Deformed quasi-particle random phase approximation (DQRPA) - Gamow-Teller transitions for the nuclear beta decay
• Results• Summary
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Motivations
Formalism Results Summary
X-ray and Super Burst
~ 3hours
Time scaleTime scale : ~ : ~ a few hoursa few hours Total energy : 10Total energy : 104242 erg (normal burst ~ 10 erg (normal burst ~ 103939 erg)erg)
Supernovae Type II
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Pycno‐reaction (Haensel & ZdunikPycno‐reaction (Haensel & Zdunik1990 )1990 )Because of high density and low temperature on the
neutron star crust, Coulomb barrier is overcome by the zero-point motion of the nuclei in the
solid lattice !!
Degenerated electrons block the beta decay. Ordinary nuclei become highly unstable, and unstable nuclei become the normal stable nuclei at the neutron-star crusts !!
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Motivations
Formalism Results Summary
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spherical basis deformation np-pairing correlation
proton neutron
Motivations
Formalism Results Summary
☞ The conventional approach so far to understand the nuclear structure is based on the spherical symmetry.
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We extend our previous QRPA based on the spherical symmetry, which turns out to be a very useful tool for relevant reactions in the nuclear-astrophysics.
Motivations
Formalism Results Summary
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Realistic two body interaction
taken by Brueckner G-matrix
based on the Bonn potential
Deformed WS
Deformed BCS
Deformed QRPA
Gamow-Teller transition
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Without np-pairingWith np-pairing(in progress)
Motivations
Results Summary Formalism
FormalismFormalism
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• The single particle states
)p,n(nNb z
zNn
zNn
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Spin w.f
Axially symmetric harmonic oscillator w.f.
Motivations
Results Summary Formalism
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• The deformed basis(Nilsson basis) is expanded
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zNn
rn0N
zNnj
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)(j0N
r
a
)(a
bACB,where
ljnaaB
)jN(
'00)jN( J
)JK(jj
)'()jN(
)()jN('
0 '0
'''00JK,)jN()jN(CBB'
'n0'p0n0p0JK
jjJK
jj
)jN( )jN( )jN( )jN(
)'n()jN(
)'p()jN(
)n()jN(
)p()jN(
J'n'pnp
)jN()jN(G)jN()jN(CC
BBBB'n'pGnp
'n'n'p'pnnpp
p0 n0 'p0 'n0
'n0'p0n0p0
Spherical harmonic oscillator w. f.
Motivations
Results Summary Formalism
By Including deformation
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Deformed BCSDeformed BCS In order to renormalize the G-matrix, theoretical values are adjusted to the empirical pairing potentials by multiplying the G-matrix with a strength parameters gpp(gnn).
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Motivations
Results Summary Formalism
By Including deformation
by a symmetric five term formula
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Description of Intermediate States for Gamow-Teller excitation K=1,0,-1
stategroundQRPA:rpawhererpaQm),K(1 K,m
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Motivations
Results Summary Formalism
DQRPA equation
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particle-hole
particle-particle
Motivations
Results Summary Formalism
Realistic two body interaction taken by Brueckner G-matrix
based on the Bonn potential
By Including deformation
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Beta- transition amplitude
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Motivations
Results Summary Formalism
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Results Formalism Summary Motivations
Results Summary Formalism
Ikeda sum rulein percentage of
3(N-Z)
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Gamow-Teller Strength in 26Mg
Results Formalism Summary Motivations
Results Summary Formalism
0 1 2 3 4 5 6 7 8 9 100
1
2
3
4
0
1
2
3
4
0
1
2
3
4
5
0 1 2 3 4 5 6 7 8 90
1
2
3
4
0
1
2
3
4
5
(e) 2= -0.25
B(G
T- )B
(GT- )
(b) 2= 0.1
Eex
[MeV]
(d) 2= -0.1
Eex
[MeV]
B(G
T- )
(c) 2= 0.25
[ 8 < Eex
< 13.3 ]
(a) 26Mg (p,n)26Al
[ 0 < Eex
< 8 ]
Experimentby Madey
(1987)
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-1 0 1 2 3 4 5 6 7 80
1
2
3
4
0
1
2
3
4
0
1
2
3
4
5
(c) 2= - 0.1
(b) 2= 0.25
B(G
T)
B(G
T)
(a) 2= 0.1
B(G
T)
Ex[MeV]
Gamow-Teller Strength in 60Ni
Results Formalism Summary Motivations
Results Summary Formalism
Experiment
Ours60Ni (p,n)
60Cu
60Ni (n,p) 60Co
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Gamow-Teller strength in 76Ge Experime
nt
Results Formalism Summary Motivations
Results Summary Formalism
0
5
10
15
20
0 5 10 15 200
5
10
15
0 5 10 15 20
(a) 2= 0.1
B(G
T - )
Ex[MeV]
(b) 2= 0.25
Ex[MeV]
B(G
T - )
(c) 2= -0.1
(d) 2= -0.25
Calculatiion by Fedor.
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1. To describe a single particle state in deformed basis, we
used the deformed axially symmetric Woods-Saxon potential.
And then we performed the deformed BCS and deformed QRPA with realistic two-body interaction calculated by Brueckner G-matrix based on Bonn potential.
2. We calculated the Gamow-Teller transitions in 26Mg , 60Ni, and 76Ge. Our results are reproduced well the position of energy with available experimental data and other calculations but we have some problem for the B(GT) strength.
3. We are checking transition operator and np-pairing correlations to improve the B(GT) strength.
Motivations
Formalism Results Summary
Summary
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1. Next stage is E1 and E2 transitions in unstable nuclei to study the inversion island, which comes from the shell evolution sensitive to the deformation .
2. Weak interactions with unstable nuclei by the neutrino, in specific, stemmed from the supernova explosion are also one of the interesting topics, because relevant cross sections are believed to differ from those in stable nuclei and affect rapid processes in the nucleosynthesis on the corecollapsing supernovae and/or the crust of the neutron star with a binary star.
Future works
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Thanks for your attention !!Thanks for your attention !!
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