t. furumoto (osaka city univ.) y. sakuragi (osaka city univ.) y. yamamoto (tsuru univ.)
DESCRIPTION
International Workshop on Hadron Nuclear Physics 2009 (RCNP, Osaka University, November 16-19, 2009 ) Present status of microscopic theory for complex nucleus-nucleus interactions. V NN. T. Furumoto (Osaka City Univ.) Y. Sakuragi (Osaka City Univ.) Y. Yamamoto (Tsuru Univ.). R. - PowerPoint PPT PresentationTRANSCRIPT
International Workshop onInternational Workshop on
Hadron Nuclear Physics 2009Hadron Nuclear Physics 2009(RCNP, Osaka University, November 16-19, 2009 )(RCNP, Osaka University, November 16-19, 2009 )
Present status of microscopic theory Present status of microscopic theory for for
complex nucleus-nucleus interactionscomplex nucleus-nucleus interactions
T. Furumoto (Osaka City Univ.)T. Furumoto (Osaka City Univ.)
Y.Y. Sakuragi (Osaka City Univ.)Sakuragi (Osaka City Univ.)
Y. Yamamoto (Tsuru Univ.)Y. Yamamoto (Tsuru Univ.)VNN
RT.Furumoto, Y. Sakuragi , Y. Yamamoto, Phys. Rev. C 80 (2009) 044614
Understanding the interactions between composite nuclei (AA interactions), starting from NN interaction :
one of the fundamental subject
in nuclear physics one of the key issue to understand various
nuclear reactions: optical potentials: elastic scattering distorting potentials as doorway to various reactions
(inelastic, transfer, knockout, breakup … )
important to survey unknown nuclear structures/reaction of unstable nuclei far from stability lines (N>>Z, Z>>N), where few/no elastic-sacttering data & phenom. potential informations.
VNN
R
Phenomenolocical optical potentials: needs Exp. Data ( elastic scattering )
to determine potential parameters ( e.g. Woods-Saxon form )
Uopt (R) = Vopt (R) + i Wopt (R) : complex
optical potential for composite systems (AA) has
large ambiguity of depth & shape
due to strong absorption ( in most cases ) → only sensitive to potential at nuclear surface
R
R
Volume integral per nucleon ( JV and JW )for AA optical potentials : E-dependence
Microscopic / semi-microscopic models : starting from NN interactions ( VNN )
VNN : effective NN interaction in nuclear medium should have proper density-dependence (ρ-dep)
consistent with nuclear saturation properties should have proper energy-dependence (E-dep) should be complex ( real-part + imaginary part )
However, no such ideal effective VNN so far !
VNN
R
Melbourne G-matrix : by K. Amos et al., (Melbourne group) Adv. Nucl. Phys. Vol.25 (2000) 275
JLM interaction : by J.P.Jeukenne, A.Lejeune, C.Mahaux, Phys. Rev. C 16, 80 (1977)
CEG : (Complex Effective potential with Gaussian form factor) by N.Yamaguchi, S.Nagata, T.Matsuda. (Miyazaki group)
Prog.Theor.Phys.70, 459 (1983), ibid. 76, 1289 (1986)
Complex G-matrix interaction to be used in Folding-model calculations
designed fordesigned forN-A systemN-A system,,only only up to up to normal densitynormal density
R
r1
r2
vNN(s)
Projectile Target
Double-Folding Model (DFM)
212211 ),;()()()( rrsrrR ddEvU NNDFM ρρρ
effective NN interaction
)( , )( )(
e),,(),(),(
dd),,()()(
)(
21)EX(
DFM)D(
DFM
21/
EX22T11P
21D2T1P
TPTPDFM,
rrRsRVRV
drdrEsvsrrsrr
rrEsvrr
rrRvRV
MSiK
jiNNTjPi
VNN
R
ri
TargetProjectile
Double-Folding Model (DFM)
rj
Double-Folding Model
EXD vvvNN
effective NN interaction (Direct+Exchange)
folding model AA interaction (Direct+Exchange)
Simple M3Y ( 1975 ~ 1985 ) real part only (add a phenom. imag. pot) zero-range exchange term
no density-dependence ⇒ too deep at short distances, but gives a reasonable strength at nuclear surface
due to strong absorption for Heavy Ions (HI) ⇒ sensitive only to nuclear surface
⇒ “Successful” for low-energy (E/A<30 MeV) scattering of heavy-ion (HI) projectiles with Ap<40
[ G.R.Satchler and W.G.Love, Phys.Rep.55,183(1979) ]
VNN
R
ri
TargetProjectile
Double-Folding Model (DFM)
rj
R
Double-Folding-model potentials with M3Y (density-independent)
M.Katsuma, Y.Sakuragi, S.Okabe, Y.Kondo, M.Katsuma, Y.Sakuragi, S.Okabe, Y.Kondo, Prog.Theor.Phys. Prog.Theor.Phys. 107107 (2002) 377 (2002) 377
VNN
R
ri
TargetProjectile
Double-Folding Model (DFM)
rj
E/A=22 MeV
Introduction of density-dependence : DDM3Y-ZR (with zero-range exchange term)
⇒ greatly reduce the potential strength
at short distances
⇒ reproduce refractive phenomena, such as
nuclear-rainbow (eg.4He+A, 16O+16O )
Double-Folding-model potentials with M3Y (density-independent) with DDM3Y (density-dependent)
M.Katsuma, Y.Sakuragi, S.Okabe, Y.Kondo, M.Katsuma, Y.Sakuragi, S.Okabe, Y.Kondo, Prog.Theor.Phys. Prog.Theor.Phys. 107107 (2002) 377 (2002) 377
VNN
R
ri
TargetProjectile
Double-Folding Model (DFM)
rj
E/A=22 MeV
)( , )( )(
e),,(),(),(
dd),,()()(
)(
21)EX(
DFM)D(
DFM
21/
EX22T11P
21D2T1P
TPTPDFM,
rrRsRVRV
drdrEsvsrrsrr
rrEsvrr
rrRvRV
MSiK
jiNNTjPi
VNN
R
ri
TargetProjectile
Double-Folding Model (DFM)
rj
Double-Folding Model
EXD vvvNN effective NN interaction (Direct+Exchange)
folding model AA interaction (Direct+Exchange)
zero-range exchzero-range exch..
finite-range exch.finite-range exch.
M.Katsuma, Y.Sakuragi, S.Okabe, Y.Kondo, M.Katsuma, Y.Sakuragi, S.Okabe, Y.Kondo, Prog.Theor.Phys. Prog.Theor.Phys. 107107 (2002) 377 (2002) 377
DFM potential with ・ DDM3Y-ZR (zero-range exchange term) compated with ・ DDM3Y-FR ( finite-range exchange term)
Th. Rijken, Y. Yamamoto, Phys. Rev. C 73 (2006) 044008
New complex G-matrix interactionNew complex G-matrix interaction (( CEG07CEG07 ))T.Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C 78 (2008) 044610
1. derived from ESC04 “ESC04” : the latest version of Extended Soft-Core force designed for NN, YN and YY systems
2. Three body force Three-body attraction (TBA) Three-body repulsion (TBR)
3. up to higher density region for the local density prescription in the case of DFM
Extended Soft-Core model : “ESC04” force designed for NN, YN and YY interactions
Th. Rijken, Y. Yamamoto, Phys.Rev.C 73 (2006) 044008
Complex G-matrix interactionComplex G-matrix interaction (( CEG07CEG07 ))T.Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C 78 (2008) 044610
1. Three-body attractive (TBA) ・ originated from Fujita-Miyazawa diagram ・ important at low density region
2. Three-body repulsive (TBR) ・ universal three-body repulsion (NNN, NNY, NYY) originated from triple-meson correlation ・ important at high-density region
New complex G-matrix interactionNew complex G-matrix interaction (( CEG07CEG07 ))
CEG07bCEG07b+Three body repulsive (TBR)+Three body attractive (TBA)
CEG07aCEG07aWith only Two-Body Force
Decisive role to make the saturation curve realistic
Fkkk
F kkGkkm
k
A
E
21 ,2121
2
)(2
1
25
3
Incompressibility KIncompressibility K (at k(at kFF = 1.35 fm = 1.35 fm-1-1))・・ 259 MeV (with TBF)259 MeV (with TBF)・・ 106 MeV (w/o TBF)106 MeV (w/o TBF)
T.Furumoto, Y. Sakuragi , Y. Yamamoto, Phys. Rev. C 78 (2008) 044610
Double folding PotentialDouble folding Potential with complex-G (CEG07) with complex-G (CEG07) R
r1
r2
vNN(s)
projectile(P)target(T)
)()(
ddexp),;(),(),(
dd),;()()()(
21222111
212211
RR
rrsK
ssrrsrr
rrsrrR
DFMDFM
EX
D
iWV
MiEg
EgU
T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C 79 (2009) 011601(R) ) T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C 80 (2009) 044614 )
)(,
)(,,
imagEXD
realEXDEXD iggg
Complex G-matrix interaction (CEG07) Complex G-matrix interaction (CEG07)
Double folding PotentialDouble folding Potential with complex-G (CEG07) with complex-G (CEG07) R
r1
r2
vNN(s)
projectile(P)target(T)
)()(
ddexp),;(),(),(
dd),;()()()(
21222111
212211
RR
rrsK
ssrrsrr
rrsrrR
DFMDFM
EX
D
iWV
MiEg
EgU
DFMWDFMDFM WiNVU
Renormalization factor for the imaginary part
T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C 79 (2009) 011601(R) ) T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C 80 (2009) 044614 )
Renormalization of the imaginary part strength
So, we renormalize (suppress) the imaginary part strength
)()( RR DFMWDFM WiNV
Discrete
Continuum
Finite nuclei
・・
・・
・
Continuum
BHF theory (G-matrix)
・・
・・
・
16O + 16O elastic scattering E/A = 70 MeV
DFMWDFMDFM WiNVU
T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C79 (2009) 011601(R) ) T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C80 (2009) 044614 )
important effect of three-body force
16O + 16O elastic scattering E/A = 70 MeV
DFMWDFMDFM WiNVU important effect of three-body force
Without TBF
T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C79 (2009) 011601(R) ) T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C80(2009)044614 )
16O + 12C, 28Si, 40Ca 12C + 12C elastic scattering
DFMWDFMDFM WiNVU
important effect of three-body forcethree-body force
T.Furumoto, Y. Sakuragi , Y. Yamamoto, (Phys. Rev. C 80 (2009) 044614)
16O + 16O elastic scattering at E/A = 100 ~ 400 MeV
becomes repulsive around E/A = 300 ~ 400 MeV
0+
31-
21+
16O
coupled-channel (CC) coupled-channel (CC) calculation with calculation with complex-G (CEG07)complex-G (CEG07)
)()()( RRR DFMijW
DFMij
DFMij WiNVU
9,11Li + 12C “quasi-elastic” scattering
9Li 2n
11Li
0+
31-
21+
12C
02+
3α
9Li 12C
12C
+
+
)()()( RRR DFMijW
DFMij
DFMij WiNVU
9,11Li + 12C “quasi-elastic” scattering
Y.Hirabayashi, S.Funada and Y. Sakuragi(Proceedings of International Symposium on Structure and Reactions of Unstable Nuclei, pp227-pp232 (1991) )
9Li density : proton, neutron single Gaussian form⇒
(fm) 39.2
(fm) 18.2
r.m.s
r.m.s
n
p
R
R
11Li density : 9Li + di-neutron model
(fm) 16.3r.m.s R
9Li 2n
11Li
)(|)11
9()
11
2(|)()( 0
)2n()Li(0
)Li( 911
RRrRrRr
9,11Li + 12C “quasi-elastic” scattering E/A ~ 60 MeV
)()()( RRR DFMWDFMDFM WiNVU
Exp. data : J. J. Kolata et al., (Phys. Rev. Lett. 69 (1993) 2631
coupled-channel (CC) coupled-channel (CC) calculation with calculation with complex-G (CEG07)complex-G (CEG07)
⇒ Continuum-Discretized Coupled-Channels (CDCC) method
α d
6Li
6Li elastic scattering with 6Li→α+d break-up
Y. Sakuragi, M, Ito, Y. Hirabayashi , C. Samanta(Prog. Theor. Phys. 98 (1997) 521)
)()()( RRR DFMijW
DFMij
DFMij WiNVU
elastic scattering of 6Li by 12C, 28Si at E/A = 53 MeV CDCCCDCC cal. cal. with with complex-Gcomplex-G ( (CEG07CEG07) folding model) folding model
)()()( RRR DFMijW
DFMij
DFMij WiNVU
Exp. data : A. Nadasen et al., (Phys. Rev. C. 47 (1993) 674
SummarySummary
• We have proposed a We have proposed a new complex G-matrixnew complex G-matrix (“ (“CEG07CEG07”),”), - derived from - derived from ESC04ESC04(extended soft-core) (extended soft-core) NN forceNN force - include - include three-body force (TBF)three-body force (TBF) effect effect - calculated up to higher density (about twice normal density)- calculated up to higher density (about twice normal density)
• We have apply DFM with We have apply DFM with new complex G-matrixnew complex G-matrix (“ (“CEG07CEG07”)”) to to nucleus-nucleus (AA)nucleus-nucleus (AA) elastic scattering elastic scattering
• CEG07CEG07 is successful for is successful for nucleus-nucleusnucleus-nucleus elastic scattering elastic scattering - reproduce - reproduce cross sectioncross section data for data for 12 12C, C, 16 16O elastic scattering O elastic scattering by by 1212C, C, 1616O, O, 2828Si, Si, 4040Ca targets at various energies.Ca targets at various energies.
• We have found a decisive role of We have found a decisive role of Three-body Three-body repulsiverepulsive force effectforce effect
• We also demonstrated possible applications to We also demonstrated possible applications to nuclear reactions nuclear reactions including including unstableunstable nuclei nuclei