T. Furumoto (Osaka City Univ.) Y. Sakuragi (Osaka City Univ.) Y. Yamamoto (Tsuru Univ.)
description
Transcript of T. Furumoto (Osaka City Univ.) Y. Sakuragi (Osaka City Univ.) Y. Yamamoto (Tsuru Univ.)
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