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Important role of three-body repulsive force effect in nuclear reactions

19th International IUPAP Conference on Few-Body Problems in Physics (Aug. 31 – Sept. 5 2009 at Bonn University). Important role of three-body repulsive force effect in nuclear reactions. Takenori FURUMOTO (Osaka City Univ. ）. Collaborators Y. Sakuragi (Osaka City Univ.)

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Important role of three-body repulsive force effect in nuclear reactions

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  1. 19th International IUPAP Conference on Few-Body Problems in Physics (Aug. 31 – Sept. 5 2009 at Bonn University) Important role of three-body repulsive force effect in nuclear reactions Takenori FURUMOTO (Osaka City Univ.） Collaborators Y. Sakuragi (Osaka City Univ.) Y. Yamamoto (Tsuru Univ.)

  2. Contents • Complex G-matrix interaction “CEG07” - is derived from modern NN interaction in free space “ESC04” - includes three-body forces effect - satisfies the nuclear-matter saturation properties 2. Application to nucleus-nucleus (AA) elastic scattering - Double-folding model approach for 16O + 16O & other systems - Effect of three-body forces on AA elastic scattering Important role of three-body repulsive forceeffect

  3. Newcomplex G-matrix interaction（CEG07） T.F, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C 78 (2008) 044610 1. derived from ESC04 “ESC04” : the latest version of Extended Soft-CoreNN force “ESC model” : to give a consistent description of interactions not only for NN, system but also for YN and YY systems 2. includes Three body force Three-body attraction (TBA) Three-body repulsion (TBR) Th. Rijken, Phys. Rev. C 73 (2006) 044007 Th. Rijken, Y. Yamamoto, Phys. Rev. C 73 (2006) 044008

  4. 1. Three-body attraction (TBA) ・ Fujita-Miyazawa diagram (Δ-resonance) ・ important at low density region effective two-body force three-body force T. Kasahara, Y. Akaishi, and H. Tanaka, Suppl. Prog. Theor. Phys. Vol.56 (1974) 96

  5. 2. Three-body repulsion (TBR) ・ universal three-body repulsion (NNN, NNY, NYY) originated the triple-meson correlation ・ important at high-density region Reduction of meson mass in medium MV(ρ)=MV exp(-αρ) for vector mesons In the ESC model ⇒ density-dependent effective two-body force Th. Rijken, Y. Yamamoto, Phys. Rev. C 73 (2006) 044008

  6. 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 Two body only

  7. vNN(s) r2 r1 R Projectile(1) Target(2) Double folding Potential Frozen-density approx. (FDA) Complex G-matrix interaction(CEG07)

  8. vNN(s) r2 r1 R Projectile(1) Target(2) Double folding Potential Frozen-density approx. (FDA) Renormalization factor

  9. 16O + 16O elastic scattering E/A = 70 MeV Without TBF important effect of three-body force T.F, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C79 (2009) 011601(R)) T.F, Y. Sakuragi and Y. Yamamoto, (Submitted to Phys. Rev. C.)

  10. Effect of Three-body Attractive force Fujita-Miyazawa diagram T. Kasahara, Y. Akaishi, and H. Tanaka, Suppl. Prog. Theor. Phys. Vol.56 (1974) 96

  11. Effect of Three-body Attractive force Effect of TBA The role of three-body attractive force is minor for nucleus-nucleus scattering T.F, Y. Sakuragi and Y. Yamamoto, (Submitted to Phys. Rev. C.)

  12. Effect of Three-body Repulsive force ・ universal three-body repulsion (NNN, NNY, NYY) originated the triple-meson correlation ・ important at high-density region Reduction of meson mass in medium MV(ρ)=MV exp(-αρ) for vector mesons Th. Rijken, Y. Yamamoto, Phys. Rev. C 73 (2006) 044008

  13. Effect of Three-body Repulsive force Effect of TBR The role of three-body repulsive effect is important for nucleus-nucleus scattering

  14. 16O + 12C, 28Si, 40Ca & 12C + 12C elastic scattering important effect of three-body force T.F, Y. Sakuragi and Y. Yamamoto, (Submitted to Phys. Rev. C.)

  15. Summary • We apply DFM with new complex G-matrix (“CEG07”) • to nucleus-nucleus (AA) elastic scattering • CEG07 complex G-matrix interaction • - is successful for nucleus-nucleus elastic scattering • - reproduces cross section for AA systems • ( 16O + 12C, 16O, 28Si and 40Ca, • & 12C + 12C elastic scattering at various energies) • CEG07b (with TBF) is apparently better than CEG07a (without TBF) • - mainly due to Three-body repulsive force effect • (three-body attractive effect is minor for AA systems)

  16. Introduction • Optical model potential (OMP) - is complex potential(U=V+iW) - has the imaginary part that represents the loss of flux in elastic scattering elastic channel • We want a much reliable OMP (real and imaginary parts) • from microscopic view point. non-elastic channel ⇒ imaginary potential

  17. Folding Model approach Single-Folding Model (SFM) Double-Folding Model (DFM) vNN(s) vNN(s) r r2 r1 R Projectile (nucleon) R Target Target Projectile complex G-matrix interaction

  18. Introduction • Optical model potential (OMP) - is complex potential(U=V+iW) - has the imaginary part that represents the loss of flux in elastic scattering elastic channel • We want a much reliable OMP (real and imaginary parts) • from microscopic view point. non-elastic channel ⇒ imaginary potential

  19. G-matrix calculation (scatteringboundary condition) imaginary part Continuous choice starting energy: single-particle potential Pauli operator: momentum-space Q = 0 Incident nucleon nuclear matter

  20. G-matrix calculation (scatteringboundary condition) imaginary part Continuous choice starting energy: single-particle potential Pauli operator: momentum-space Q = 0 Incident nucleon nuclear matter

  21. G-matrix calculation (scatteringboundary condition) imaginary part Continuous choice starting energy: single-particle potential Pauli operator: momentum-space Q = 1 Incident nucleon nuclear matter

  22. G-matrix calculation (scatteringboundary condition) single-particle potential relative momentum G-matrix interaction represented in momentum space bare NN interaction wave function in nuclear matter includes U

  23. G-matrix calculation (scatteringboundary condition) G-matrix interaction represented in coordinate space bare NN interaction wave function in nuclear matter

  24. G-matrix calculation (scatteringboundary condition) bare NN interaction G-matrix interaction represented in coordinate space wave function Averaging for J and L for J for L G-matrix interactionfinally used

  25. T(s) r R Proton Target Single folding Potential(Central part) Complex G-matrix interaction (CEG07)

  26. T(LS)(s) r R Proton Target Single folding Potential(LS part) Complex G-matrix interaction (CEG07)

  27. T(s) r R Proton Target Single folding Potential Complex G-matrix interaction (CEG07) Central part LS part

  28. Renormalization of the imaginary potential strength fix NW-value to be 0.60 to reproduce the measured total reaction cross sections

  29. p - 12C elastic scattering

  30. 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

  31. 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

  32. p, n - 16O elastic scattering

  33. Nucleon-Nucleus (one nuclear matter) Nucleus-Nucleus (two nuclear matters)

  34. 16O + 16O elastic scattering E/A = 70 MeV important effect of three-body force T.F, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C79 (2009) 011601(R)) T.F, Y. Sakuragi and Y. Yamamoto, (Submitted to Phys. Rev. C.)

  35. vNN(s) r2 r1 R Projectile(1) Target(2) Double folding Potential Local density approximation(LDA) FDA

  36. Local density approximation(LDA) FDA

  37. 16O + 16O folding potentials with CEG07b (with TBF) ＠ E/A = 70 MeV Local density approx.(LDA) FDA

  38. 16O + 16O elastic scattering with CEG07b (with TBF) ＠ E/A = 70 MeV Local density approx.(LDA) FDA T.F, Y. Sakuragi and Y. Yamamoto, (Submitted to Phys. Rev. C.)

  39. ω-rearrangement diagram(CEG07c) where χ is an averaged value of χj N. Yamaguchi, S. Nagata, and T. Matsuda, Prog. Theor. Phys. Vol.70 (1983) 459

  40. Effect of ω-rearrangement term The effect of TBF The effect of ω-rearrangement

  41. 16O + 16O elastic scattering E/A = 100～400 MeV

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