important role of three-body force (TBF)

「少数系物理の現状と今後の展望」研究会 (Dec 23-25, 2008 at RCNP)
軽い重イオン散乱における
三体斥力の効果
古本猛憲
(大阪市立大学・理学研究科)
共同研究者
櫻木千典 (大阪市立大学・理学研究科)
山本安夫 (都留文科大学)
Contents
1. New complex G-matrix (CEG07)
・ modern NN interaction in free space
“ESC04” (Extended Soft-Core)
・ includes the Three-Body Force (TBF) effects
・ satisfy the nuclear-matter saturation property
2. Application to N-A elastic scattering
・ Single-Folding model for p + 12C
3. Application to A-A elastic scattering
・ Double-Folding model for 16O + 16O & other systems
important role of three-body force (TBF)
Complex G-matrix interaction（CEG07）
T.Furumoto, Y. Sakuragi and Y. Yamamoto, Phys.Rev.C 78 (2008) 044610
“ESC04” : the latest version of Extended Soft-Core force
designed for NN, YN and YY systems
Th. Rijken, Y. Yamamoto, Phys.Rev.C 73 (2006) 044008
1. Three-body attraction (TBA)
・ Fujita-Miyazawa diagram
・ important at low density region
2. Three-body repulsion (TBR)
・ originated the triple-meson correlation
・ important at high-density region
In the ESC04 model
density-dependent effective two-body force

Complex G-matrix interaction（CEG07）
derived from
ESC04 NN force
(Extended Soft-Core)
includes the three-body force
Decisive role to make the
saturation curve realistic
switch off three-body force
(two-body only)
Single folding Potential
(Central part)
T(s)
Proton
U C (R )    (r )TD (R, r; k F , E )dr
r
R
Target
   (R, r )TEX (R, r; k F , E ) exp( ik 0  s)dr
 VC (R )  iWC (R )
Complex G-matrix interaction (CEG07)
TD, EX  T
( real )
D, EX
 iT
(imag)
D, EX
Single folding Potential
(LS part)
T(LS)(s)
Proton
r
R
U LS (R )      i* (r )TD( LS ) (R, r; k F , E )L  Si (r )dr
Target
i
( LS )
   i* (r )TEX
(R, r; k F , E )L  Si (R ) exp( ik 0  s)dr
i
 VLS (R )  iWLS (R )   
Complex G-matrix interaction (CEG07)
)
( LS , real )
( LS ,imag)
TD( LS

T

iT
, EX
D, EX
D, EX
Renormalization of the
imaginary potential strength
U opt  VC  iN W WC
 VLS  iN W WLS   
fix NW-value to be 0.65
to reproduce the measured
total reaction cross sections
p-12C elastic scattering
Comparison of the folding potential at E = 122 MeV
CEG07a(two body only) vs CEG07b(with TBF)
TBF effect
mainly seen in the real central part
Comparison of the folding potential at E = 122 MeV
CEG07a(two body only) vs CEG07b(with TBF)
TBF effect
This difference appears in analyzing power
Nucleon-Nucleus
(one nuclear matter)
Nucleus-Nucleus
(two nuclear matters)
20
0
0
vNN(s)
Double folding Potential
r2
r1
R
U (R )   1 (r1 )  2 (r2 )TD (s;  , E )dr1dr2
Projectile(1)
Target(2)
 K s
  1 (r1 , r1  s)  2 (r2 , r2  s)TEX (s;  , E ) exp i
dr1dr2

 M 
 VDFM (R )  iWDFM (R )
Frozen-density app. (FDA)
  1  2
Complex G-matrix interaction (CEG07)
)
(imag)
TD, EX  TD( real

iT
, EX
D, EX
vNN(s)
Double folding Potential
r2
r1
R
U (R )   1 (r1 )  2 (r2 )TD (s;  , E )dr1dr2
Projectile(1)
Target(2)
 K s
  1 (r1 , r1  s)  2 (r2 , r2  s)TEX (s;  , E ) exp i
dr1dr2

 M 
 VDFM (R )  iWDFM (R )
Frozen-density app. (FDA)
  1  2
Renormalization factor
U DFM  VDFM  iNWWDFM
16O
+ 16O elastic scattering ＠ E/A = 70 MeV
important effect of three-body force
U DFM  VDFM  iNWWDFM
T.Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys.Rev.C rapid communications (2008) in press)
vNN(s)
Double folding Potential
r2
r1
U DFM (R)  VDFM (R)  iWDFM (R)
U (R )   1 (r1 )  2 (r2 )TD (s;  , E )dr1dr2
R
Projectile(1)
Target(2)
 K s
  1 (r1 , r1  s)  2 (r2 , r2  s)TEX (s;  , E ) exp i
dr1dr2

 M 
Local density approximation (LDA)
FDA 1.   1  2
2.   0.5( 1  2 )
1   2 (   0 )
3.   
(   0 )
0
16O
+ 16O folding potentials with CEG07b (with TBF)
＠ E/A = 70 MeV
局所密度近似 (LDA)
1.   1   2
FDA
2.   0.5( 1   2 )
 1   2 (    0 )
3.   
(   0 )
0
16O
+ 16O elastic scattering with CEG07b (with TBF)
＠ E/A = 70 MeV
局所密度近似 (LDA)
1.   1   2
FDA
2.   0.5( 1   2 )
 1   2 (    0 )
3.   
(   0 )
0
U DFM  VDFM  iNWWDFM
16O
+ 12C, 12C + 12C elastic scattering
＠ E/A = 93.9, 135 MeV
important effect of three-body force
U DFM  VDFM  iNWWDFM
Summary
• We have proposed a new complex G-matrix (CEG07)
- derived from modern NN interaction model;
ESC04 (extended soft-core)
- include Three-Body Force (TBF) effect
to be consistent with saturation property
• CEG07 with TBF-effects is successful for both
- proton-nucleus (N-A)
and nucleus-nucleus (A-A) elastic scattering
•Decisive role of Three-Body Force (TBF) effect is found.
- particularly TBR (Three-Body Repulsion) effect is essential,
both for nuclear saturation & nucleus-nucleus scattering

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