study of microscopic complex potentials for nuclear scattering reaction
DESCRIPTION
YIPQS International Molecule on Coexistence of weak and strong binding in unstable nuclei and its dynamics (Mar. 4-22th, 2013 @YITP ). Study of microscopic complex potentials for nuclear scattering reaction. Takenori Furumoto ( Ichinoseki National College of Technology). Collaborators - PowerPoint PPT PresentationTRANSCRIPT
Study of microscopic complex potentials for nuclear scattering reaction
Takenori Furumoto(Ichinoseki National College of Technology)
YIPQS International Molecule on Coexistence of weak and strong binding in unstable nuclei and its dynamics (Mar. 4-22th, 2013 @YITP)
CollaboratorsY. Sakuragi (Osaka City Univ.)Y. Yamamoto (RIKEN)
Contents
1. Microscopic complex nucleus-nucleus (AA) potential- based on the double folding model (DFM) with complex G-matrix (CEG07) interaction
2. Application of the microscopic complex potential model to the high-energy region
3. Application of the microscopic complex potential model to the coupled channel calculation
4. Summary
R
r1r2
vNN(s)
Projectile Target
Double-Folding Model (DFM)
212211 ),;()()()( rrsrrR ddEvU NNDF ρρρ
nucleon-nucleon (NN) interactionnucleon density
R
r1r2
vNN(s)
Projectile(1)Target(2)
212211 dd),;()()(
)()()(
rrsrr
RRR
Ev
iWVU
NN
DFMDFM
Double-Folding Model (DFM)with complex G-matrix interaction
T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C.79 (2009) 011601(R)), ibid. 80 (2009) 044614)
Folding model potential
InteractionCEG07 (complex G-matrix interaction)
CEG07a (w/o TBF)CEG07b (with TBF)
Incompressibility K (at kF = 1.35 fm-1) 259 MeV (with TBF) 106 MeV (w/o TBF)
Heavy-ion elastic scattering
T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C.79 (2009) 011601(R)), ibid. 80 (2009) 044614)
Application of the microscopic complex potential model to the high energy region
12C + 12C folding model potential at various energies
becomes large
becomes repulsive
prediction of repulsive potential
T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C82, 044612 (2010)
About repulsive potential
In general, nuclear interaction is attractive.
By several reasons, nuclear interaction becomes repulsive
• medium effect (Pauli principle, three-body force)• energy dependence
The repulsive potential is obtained in the high-energy region.
Examples• Dirac phenomenology (p-A, d-A)• microscopic approach (p-A)• phenomenological optical model analysis (α-A)
L.G.Arnold, (Phys.Rev.C25(1982)936
L.Rikus, K.Nakano, H.V.V.Geramb, (Nucl.Phys.A414 (1984) 413
L.Rikus, H.V.V.Geramb, (Nucl.Phys.A426 (1984) 496
N.V.Sen, (Nucl.Phys.A464 (1987) 717
12C + 12C elastic scattering at various energies
becomes large
becomes repulsive
prediction of repulsive potential
T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C82, 044612 (2010)
(a) Attractive potential (V < 0)
nearside
farside
)(log
scattering angle
scattering wave
potential
The cross sectionby semi-classical schematic representation
classical trajectoryN
F
(b) Repulsive potential (V > 0)
scattering angle
scattering wave
classical trajectory
potential
nearside
farside
)(log
The cross sectionby semi-classical schematic representation
N
F
CEG07b@300 MeV/u
The strong interference appears.
T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C82, 044612 (2010)
Prediction of repulsive potential forHeavy-ion High-energy scattering
Application of the microscopic complex potential model to the coupled channel calculation
N
R UEUT
)()()()( RRRR
Microscopic Coupled Channel (MCC) with CEG07Coupled Channel equation
The diagonal and coupling potentials are derived from microscopic view point.
Transition density
i
kiiik )()()()( rrr R
r1
r2
vNN(s)
Projectile Target
transition density212
)(1
)( ),;()()()( rrsrrR ddEvU NNT
jlP
ik ρ CEG07
Channel Coupling Effecton
high-energy heavy-ionelastic scatterings
1. Backward cross section comes down
2. Diffraction pattern goes backward
The coupling effect is clearly seen!
T. Furumoto and Y. Sakuragi, Phys. Rev. C87, 014618 (2013)
Dynamical Polarization Potential (DPP)
N
JJJJDPP RRRURU
)(/)()()( )()()()(
N
R UEUT
)()()()( RRRR
Coupled Channel equation
0)()(/)()()(
RRRRR
EUUTN
R
Coupling effect is described as potential form
Dynamical Polarization Potential (DPP)
By partial wave expansion
N
DPP UU
)(/)()()( RRRR
Dynamical Polarization Potential (DPP)
Coupling potential (01 → 21)
Repulsive
Attractive AttractiveT. Furumoto and Y. Sakuragi, Phys. Rev. C87, 014618 (2013)
)4( 2 .. fmb
EbJ gr
mcgrgr
Dynamical Polarization Potential (DPP) for high-energy heavy-ion systems
Repulsive
Attractive Attractive
Coupling potential (01 → 21)
T. Furumoto and Y. Sakuragi, Phys. Rev. C87, 014618 (2013)
Role of Dynamical Polarization Potential (DPP) in the elastic cross section
(a) attractive potential (V < 0 ) + repulsive DPP ( V △ > 0 )
Scattering angle: θ
V(a)
Pote
ntia
l
Range
VVV
F
N
Real part
Elastic cross section
log
σ(θ)
0
T. Furumoto and Y. Sakuragi, Phys. Rev. C87, 014618 (2013)
Role of Dynamical Polarization Potential (DPP) in the elastic cross section
(b) repulsive potential (V > 0 ) + attractive DPP ( V △ < 0 )
V
Pote
ntia
l
Range
VVV N
F
Real part Elastic cross section
Scattering angle: θ
log
σ(θ)
0
(b)
T. Furumoto and Y. Sakuragi, Phys. Rev. C87, 014618 (2013)
Channel Coupling Effecton
high-energy heavy-ionelastic scatterings
The channel coupling effect looks very similar to each other
The origin of the effect - very different from each other
T. Furumoto and Y. Sakuragi, Phys. Rev. C87, 014618 (2013)
But!
Role of imaginary part of coupling potential
Coupling potential (01 → 21)
T. Furumoto and Y. Sakuragi, Phys. Rev. C87, 014618 (2013)
.)(0,
)(0,
2)(00
)(22
2)(00
)(0,
)()(
)()(
imagreal
WV
WV
RUNN
RUiNN
Role of imaginary part of coupling potential
T. Furumoto and Y. Sakuragi, Phys. Rev. C87, 014618 (2013)
Coupling potential (01 → 21)
.)(0,
)(0,
2)(00
)(22
2)(00
)(0,
)()(
)()(
imagreal
WV
WV
RUNN
RUiNN
Summary
Microscopic complex potential - constructed with the complex G-matrix (CEG07) interaction. - reproduce the experimental data for various systems.
Repulsive potential in the high-energy region - predicted in the G-matrix folding model. - gives the characteristic angular distribution.
Channel coupling effect and Role of imaginary coupling potential - clearly seen in the elastic cross section, although the incident energy is high enough. - the imaginary part plays dominant role in inelastic scattering in high energy region (200-400 MeV/u).