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![Page 1: Consistent analysis of nuclear level structures and nucleon interaction data of Sn isotopes J.Y. Lee 1*, E. Sh. Soukhovitskii 2, Y. D. Kim 1, R. Capote.](https://reader035.fdocuments.us/reader035/viewer/2022081602/551b7d25550346167e8b4848/html5/thumbnails/1.jpg)
Consistent analysis of nuclear level structures
and nucleon interaction data of Sn iso-topes
J.Y. Lee1*, E. Sh. Soukhovitskii2,Y. D. Kim1, R. Capote3, S. Chiba4, and J. M. Quesada5
1Dep. of Physics, Sejong University, Korea
2Joint Institute for Energy and Nuclear Research, Belarus3Nuclear Data Section, IAEA, Austria
4Advanced Science Research Center, JAEA, Japan5Universidad de Sevilla, Spain
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Why Study Tin Isotopes ?
A main component of nuclear reactor material. A candidate material for superconducting
magnets in fusion reactors. Energy splittings of yrast 0+, 2+, 4+ and 6+
levels are irregular. ⇒ may suggest non-harmonic vibrational
states? Sn isotopes are single-closed-shell nuclei of
Z=50.determine whether the calculations using a
self-consistent CC optical model may produce different nuclear deformations for different ex-ternal probes (protons, neutrons) for Sn iso-topes.
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Present soft-rotator model
- Lee et al., PRC 79, 064612 (‘09) - Soukhovitskii et al., PRC 72, 024604 (‘05) - Capote et al., PRC 72, 064610 (‘05) - Soukhovitskii et al., J. Physics G 30, 905(‘04)
Non-axial quadrupole, octupole, hexade-capole deformations
γ-vibrations Soft-octupole and rigid hexadecapole de-
formations Identify positive and negative parity bands,
associated with octupole surface vibrations
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Calculations
i) Nuclear Hamiltonian parameters to reproduce experimental collective levels (determined by fitting the calculated levels to
the evaluated nuclear structure data )ii) Contruct wave functions from these parame-
ters.iii) CC optical Model calculations ⇒ “ Self-consistent ! ”
![Page 5: Consistent analysis of nuclear level structures and nucleon interaction data of Sn isotopes J.Y. Lee 1*, E. Sh. Soukhovitskii 2, Y. D. Kim 1, R. Capote.](https://reader035.fdocuments.us/reader035/viewer/2022081602/551b7d25550346167e8b4848/html5/thumbnails/5.jpg)
Present soft-rotator model⇒ Quite successful in explaining
– Nuclear collective level structures, – Nucleon interaction cross sections,– Proton non-elastic scattering cross sec-
tions,– γ -transition probabilities,
for 12C, 28Si, 56Fe, 58Ni, & 238U.
- Lee et al.,, PRC 79, 064612 (‘09) - Soukhovitskii et al, PRC 72, 024604 (‘05) - Capote et al, PRC 72, 064610 (‘05) - Soukhovitskii et al., J. Physics G 30, 905(‘04) - Soukhovitskii et al., J. Nucl. Sci. Tech. 40, 69 (‘03), - Soukhovitskii et al., PRC 62, 044605(‘00), NPA 624, 305
(‘98).
![Page 6: Consistent analysis of nuclear level structures and nucleon interaction data of Sn isotopes J.Y. Lee 1*, E. Sh. Soukhovitskii 2, Y. D. Kim 1, R. Capote.](https://reader035.fdocuments.us/reader035/viewer/2022081602/551b7d25550346167e8b4848/html5/thumbnails/6.jpg)
Goals
Consistent description of collective nuclear level structures & nucleon scattering proper-
ties for 116,118,120Sn using the soft-rotator model.
50
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Description of soft-rotator model
ASSUME : An excited state of even-even non-spherical nucleus can be described as a combination of rotation, β-quadrupole and octupole vibrations, & γ-quadrupole vibra-
tion.
Multipole-deformed instant nuclear shape
Deformations
4,3,2 ,)','(1)','(
θYRθR
:
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Hamiltonian of the soft-rotator model
where,
)()()(ˆ2
ˆ2
ˆ1ˆ2
ˆ322
2
420
3
22
222
2
32
VVVTB
TTTB
H r
.ˆˆ
ˆ,1ˆ
,3sin3sin
1ˆ,1ˆ
3
1)4()3()2(
23
1
2
3
33
333
2
42
242
3
2
i iii
i
i i
ir JJJ
I
J
ITT
TT
inertia of moments Principal:ˆ
axisth in operator momentumangular theof Projection:
energy rotationalnuclear deformed ofOperator :ˆ
i
i
J
i-I
T
![Page 9: Consistent analysis of nuclear level structures and nucleon interaction data of Sn isotopes J.Y. Lee 1*, E. Sh. Soukhovitskii 2, Y. D. Kim 1, R. Capote.](https://reader035.fdocuments.us/reader035/viewer/2022081602/551b7d25550346167e8b4848/html5/thumbnails/9.jpg)
Description of soft-rotator model
ASSUME : An excited state of even-even non-spherical nucleus can be described as a combination of rotation, β-quadrupole and octupole vibrations, & γ-quadrupole vibra-
tion.
Multipole-deformed instant nuclear shape
Deformations
4,3,2 ,)','(1)','(
θYRθR
:
(Review)
![Page 10: Consistent analysis of nuclear level structures and nucleon interaction data of Sn isotopes J.Y. Lee 1*, E. Sh. Soukhovitskii 2, Y. D. Kim 1, R. Capote.](https://reader035.fdocuments.us/reader035/viewer/2022081602/551b7d25550346167e8b4848/html5/thumbnails/10.jpg)
Deformed nuclear potential :
max
1
00 )','(
!
),(),())','(,(
0t
tt
RR
t
t
Yt
RrR
R
VRrVRrV
)','( YASSUME : is small.
![Page 11: Consistent analysis of nuclear level structures and nucleon interaction data of Sn isotopes J.Y. Lee 1*, E. Sh. Soukhovitskii 2, Y. D. Kim 1, R. Capote.](https://reader035.fdocuments.us/reader035/viewer/2022081602/551b7d25550346167e8b4848/html5/thumbnails/11.jpg)
))','(,()ˆˆ)(,(
))','(,()()()(
))','(,()()()(
))','(,()()(
CoulCoulSO
SWSSCoulSS
VWSVCoulVV
RWSCoulRHF
RrVlErV
RrgEiWEVEV
RrfEiWEVEV
RrfEVEV
(Non-spherical) Dispersive Optical Potential
![Page 12: Consistent analysis of nuclear level structures and nucleon interaction data of Sn isotopes J.Y. Lee 1*, E. Sh. Soukhovitskii 2, Y. D. Kim 1, R. Capote.](https://reader035.fdocuments.us/reader035/viewer/2022081602/551b7d25550346167e8b4848/html5/thumbnails/12.jpg)
(“Lane consistent dispersive CC OMP”)deal with (p,n) charge exchange reactions [to the elastic Isobaric Analogue States(IAS)]
)(4
)()(
)(4
)()()(
)(4
)()()(
1
10
10
EVA
ZNEV
EVA
ZNEVEV
EVA
ZNEVEV
pn
FFnnn
FCFCppp
Isospin-dependent dispersive CC OMP
Lane equations Soukhovitskii et al, PRC 72, 024604 (‘05) Capote et al, PRC 72, 064610 (‘05)
![Page 13: Consistent analysis of nuclear level structures and nucleon interaction data of Sn isotopes J.Y. Lee 1*, E. Sh. Soukhovitskii 2, Y. D. Kim 1, R. Capote.](https://reader035.fdocuments.us/reader035/viewer/2022081602/551b7d25550346167e8b4848/html5/thumbnails/13.jpg)
Applications to Sn isotopes
For 120Sn(32.59%), 118Sn (24.22%), 116Sn (14.54%),
Collective nuclear level structures Total neutron & proton reaction cross sections Nucleon elastic & inelastic scattering cross
sections [(n,n), (n,n’), (p,p), (p,p’)] Quasi-elastic (p,n) reactions.
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Collective level structures of 120Sn & 118Sn ⇒ All the levels are involved in CC calcula-tions.
EXP.
CALCULATIONS
CALCULATIONS
EXP.
(i) K≈0,nβ=nγ=0 (g.s. rotational band) (ii) K≈0,nβ=1,nγ=0
(iii) K≈2,nβ=0,nγ=0 (positive parity band) (iv) K≈0,nβ=0,nγ=0 (negative parity band) (v)
K≈0,nβ=0,nγ=1
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120Sn total neutron & proton reaction cross sec-tions
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Neutron elastic scattering cross sec-tions
116Sn(n,n) 118Sn(n,n) 120Sn(n,n)
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Neutron inelastic scattering cross sec-tions
116Sn(n,n’)2+ 118Sn(n,n‘)2+ 120Sn(n,n’)2+
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Neutron inelastic scattering cross sec-tions
116Sn(n,n’)3- 118Sn(n,n‘)3- 120Sn(n,n’)3-
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Proton elastic scattering cross sections
116Sn(p,p) 118Sn(p,p) 120Sn(p,p)
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Proton inelastic scattering cross sections
116Sn(p,p’)2+ 118Sn(p,p‘)2+ 120Sn(p,p’)2+
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Proton inelastic scattering off 3- state
116Sn(p,p’)3- 118Sn(p,p‘)3- 120Sn(p,p’)3- •
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Quasi-elastic (p,n) reactions
116Sn(p,n) 118Sn(p,n) 120Sn(p,n)
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Deformation Parameters
Isotopeβ20 β30 β40
n p n p
116Sn 0.025 0.027 0.050 0.053 -0.080
118Sn 0.029 0.035 0.047 0.049 -0.060
120Sn 0.034 0.037 0.043 0.045 -0.094
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Summary
For 116Sn, 118Sn, 120Sn, Collective level structures Total neutron cross sections Nucleon elastic/inelastic scattering cross sec-
tions Quasi-elastic (p,n) reactions.
⇒ well described within the soft-rotator model self-consistently. [ χ2 : 6.882(116Sn), 8.369(118Sn), 6.74(120Sn) ]