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

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.

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

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  1. International Workshop onHadron Nuclear Physics 2009(RCNP, Osaka University, November 16-19, 2009 )Present status of microscopic theory for complex nucleus-nucleus interactions VNN T. Furumoto (Osaka City Univ.) Y.Sakuragi (Osaka City Univ.) Y. Yamamoto (Tsuru Univ.) R T.Furumoto, Y. Sakuragi , Y. Yamamoto, Phys. Rev. C 80 (2009) 044614

  2. 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 nucleifar from stability lines (N>>Z, Z>>N), where few/no elastic-sacttering data & phenom. potential informations. VNN R

  3. 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

  4. R

  5. Volume integral per nucleon ( JV and JW ) for AA optical potentials : E-dependence

  6. 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

  7. Complex G-matrix interaction to be used in Folding-model calculations • JLM interaction : • by J.P.Jeukenne, A.Lejeune, C.Mahaux, • Phys. Rev. C 16, 80 (1977) designed for N-A system, only up to normal density • 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) • Melbourne G-matrix : • by K. Amos et al., (Melbourne group) • Adv. Nucl. Phys. Vol.25 (2000) 275

  8. Double-Folding Model (DFM) vNN(s) r2 r1 R Target Projectile effective NN interaction

  9. Double-Folding Model (DFM) VNN rj ri R Projectile Target Double-Folding Model • effective NN interaction (Direct+Exchange) • folding model AA interaction (Direct+Exchange)

  10. Double-Folding Model (DFM) VNN ri rj R Projectile Target • Simple M3Y( 1975～1985 ) • real part only (add aphenom. 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 forHeavy 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)] R

  11. Double-Folding-model potentials with M3Y (density-independent) Double-Folding Model (DFM) VNN ri rj R Projectile Target E/A=22 MeV M.Katsuma, Y.Sakuragi, S.Okabe, Y.Kondo, Prog.Theor.Phys. 107 (2002) 377

  12. Introduction of density-dependence： DDM3Y-ZR(withzero-rangeexchange term) ⇒ greatlyreducethe potential strength atshortdistances ⇒ reproduce refractive phenomena, such as nuclear-rainbow (eg.4He+A, 16O+16O )

  13. Double-Folding-model potentials with M3Y (density-independent) with DDM3Y (density-dependent) Double-Folding Model (DFM) VNN ri rj R Projectile Target E/A=22 MeV M.Katsuma, Y.Sakuragi, S.Okabe, Y.Kondo, Prog.Theor.Phys. 107 (2002) 377

  14. Double-Folding Model (DFM) VNN rj ri R Projectile Target Double-Folding Model • effective NN interaction (Direct+Exchange) zero-range exch. • folding model AA interaction (Direct+Exchange) finite-range exch.

  15. DFM potential with 　・DDM3Y-ZR (zero-range exchange term) compated with 　・DDM3Y-FR ( finite-range exchange term) M.Katsuma, Y.Sakuragi, S.Okabe, Y.Kondo, Prog.Theor.Phys. 107 (2002) 377

  16. New complex G-matrix interaction（CEG07） 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 Th. Rijken, Y. Yamamoto, Phys. Rev. C 73 (2006) 044008

  17. Complex G-matrix interaction（CEG07） T.Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C 78 (2008) 044610 Extended Soft-Core model : “ESC04” force designed for NN, YN and YY interactions Th. Rijken, Y. Yamamoto, Phys.Rev.C 73 (2006) 044008 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

  18. New complex G-matrix interaction（CEG07） Incompressibility K (at kF = 1.35 fm-1) ・259 MeV (with TBF) ・106 MeV (w/o TBF) CEG07b +Three body repulsive (TBR) +Three body attractive (TBA) Decisive role to make the saturation curve realistic CEG07a With only Two-Body Force T.Furumoto, Y. Sakuragi , Y. Yamamoto, Phys. Rev. C 78 (2008) 044610

  19. Double folding Potential with complex-G (CEG07) • 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 ) vNN(s) r2 r1 R projectile(P) target(T) • ComplexG-matrix interaction (CEG07) • ComplexG-matrix interaction (CEG07)

  20. Double folding Potential with complex-G (CEG07) • 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 ) vNN(s) r2 r1 R projectile(P) target(T) • Renormalization factor for the imaginary part

  21. ・・・・・ ・・・・・ Continuum Continuum Discrete BHF theory (G-matrix) Finite nuclei Renormalization of the imaginary part strength So, we renormalize (suppress) the imaginary part strength

  22. 16O + 16O elastic scattering E/A = 70 MeV important effect of three-body force T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C79 (2009) 011601(R) ) T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C80 (2009) 044614 )

  23. 16O + 16O elastic scattering E/A = 70 MeV Without TBF important effect of three-body force T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C79 (2009) 011601(R) ) T.Furumoto, Y. Sakuragi, Y. Yamamoto, (Phys. Rev. C80(2009)044614 )

  24. 16O + 12C, 28Si, 40Ca 12C + 12C elastic scattering important effect of three-body force T.Furumoto, Y. Sakuragi , Y. Yamamoto, (Phys. Rev. C 80 (2009) 044614)

  25. 16O + 16O elastic scattering at E/A = 100～400 MeV • becomes repulsive around E/A = 300～400 MeV

  26. coupled-channel (CC) calculation with complex-G (CEG07) preliminary 21+ 31- 0+ 16O

  27. 9,11Li + 12C “quasi-elastic” scattering 9Li 12C + 31- 02+ 3α 12C 21+ + 11Li 9Li 0+ 2n 12C

  28. 9,11Li + 12C “quasi-elastic” scattering • 9Li density : proton, neutron ⇒ single Gaussian form • 11Li density : 9Li + di-neutron model 11Li 9Li 2n Y.Hirabayashi, S.Funada and Y. Sakuragi (Proceedings of International Symposium on Structure and Reactions of Unstable Nuclei, pp227-pp232 (1991) )

  29. 9,11Li + 12C “quasi-elastic” scattering E/A ~ 60 MeV coupled-channel (CC) calculation with complex-G (CEG07) preliminary Exp. data : J. J. Kolata et al., (Phys. Rev. Lett. 69 (1993) 2631

  30. 6Li elastic scattering with 6Li→α+d break-up ⇒ Continuum-Discretized Coupled-Channels (CDCC) method 6Li α d Y. Sakuragi, M, Ito, Y. Hirabayashi , C. Samanta (Prog. Theor. Phys. 98 (1997) 521)

  31. elastic scattering of 6Li by 12C, 28Si at E/A = 53 MeV • CDCC cal. with complex-G (CEG07) folding model preliminary Exp. data : A. Nadasen et al., (Phys. Rev. C. 47 (1993) 674

  32. Summary • We have proposed a new complex G-matrix (“CEG07”), • - derived from ESC04(extended soft-core) NN force • - include three-body force (TBF)effect • - calculated up to higher density (about twice normal density) • We have apply DFM with new complex G-matrix (“CEG07”) • to nucleus-nucleus (AA) elastic scattering • CEG07 is successful for nucleus-nucleus elastic scattering • - reproduce cross section data for 12C, 16O elastic scattering • by 12C, 16O, 28Si, 40Ca targets at various energies. • We have found a decisive role of Three-body repulsiveforce effect • We also demonstrated possible applications to nuclear reactions including unstable nuclei

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