Transcript Single folding Potential

「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 )T D ( R , r ; k F , E ) d r
  ( R , r )T
EX
R
Target
( R , r ; k F , E ) exp( i k 0  s ) d r
 V C ( R )  iW C ( R )
Complex G-matrix interaction (CEG07)
T D , EX  T
r
( real )
D , EX
 iT
( imag )
D , EX
Single folding Potential
(LS part)
T(LS)(s)
Proton
U LS ( R )    

  i ( r )T D
*
i


i
( LS )
R
( R , r ; k F , E ) L  S  i (r ) d r
Target
  i ( r )T EX ( R , r ; k F , E ) L  S  i ( R ) exp( i k 0  s ) d r
*
( LS )
 V LS ( R )  iW LS ( R )   
Complex G-matrix interaction (CEG07)
T
r
( LS )
D , EX
T
( LS , real )
D , EX
 iT
( LS , imag )
D , EX
Renormalization of the
imaginary potential strength
U opt  V C  iN W W C
 V LS  iN W W LS   
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 )T D ( s ;  , E ) d r1d r2

1
( r1 , r1  s )  2 ( r2 , r2  s )T EX
 V DFM ( R )  iW DFM ( R )
Projectile(1)
Target(2)
 K s 
( s ;  , E ) exp  i
d r1 d r2

 M 
Frozen-density app. (FDA)
  1   2
Complex G-matrix interaction (CEG07)
T D , EX  T D , EX  iT D , EX
( real )
( imag )
vNN(s)
Double folding Potential
r2
r1
R
U (R ) 

  1 ( r1 )  2 ( r2 )T D ( s ;  , E ) d r1d r2

1
( r1 , r1  s )  2 ( r2 , r2  s )T EX
Projectile(1)
Target(2)
 K s 
( s ;  , E ) exp  i
d r1 d r2

 M 
 V DFM ( R )  iW DFM ( R )
Frozen-density app. (FDA)
  1   2
Renormalization factor
U DFM  V DFM  iN W W DFM
16O
+ 16O elastic scattering ＠ E/A = 70 MeV
important effect of three-body force
U DFM  V DFM  iN W W DFM
T.Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys.Rev.C rapid communications (2008) in press)
vNN(s)
Double folding Potential
R
U DFM ( R )  V DFM ( R )  iW DFM ( R )
U (R ) 


1

Projectile(1)
( r1 )  2 ( r2 )T D ( s ;  , E ) d r1 d r2
1
r2
r1
( r1 , r1  s )  2 ( r2 , r2  s )T EX
Target(2)
 K s 
( s ;  , E ) exp  i
d r1 d r2

 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  V DFM  iN W W DFM
16O
+ 12C, 12C + 12C elastic scattering
＠ E/A = 93.9, 135 MeV
important effect of three-body force
U DFM  V DFM  iN W W DFM
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