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

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


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


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


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)


VNN

R

ri

TargetProjectile


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


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.


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

t. furumoto (osaka city univ.) y. sakuragi (osaka city univ.) y. yamamoto (tsuru univ.)

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