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

1.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 16 O + 16 O & other systems - Effect of three-body forces on AA elastic scattering Important role of three-body repulsive force effect Contents

Th. Rijken, Phys. Rev. C 73 (2006) Th. Rijken, Y. Yamamoto, Phys. Rev. C 73 (2006) New complex G-matrix interaction （ CEG07 ） T.F, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C 78 (2008) derived from ESC04 “ESC04” : the latest version of Extended Soft-Core NN 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)

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

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

New complex G-matrix interaction （ CEG07 ） CEG07b +Three body repulsive (TBR) +Three body attractive (TBA) CEG07a Two body only Decisive role to make the saturation curve realistic Incompressibility K (at k F = 1.35 fm -1 ) 259 MeV (with TBF) 106 MeV (w/o TBF)

Double folding Potential R r1r1 r2r2 v NN (s) Projectile(1) Target(2) Complex G-matrix interaction (CEG07) Frozen-density approx. (FDA)

Double folding Potential R r1r1 r2r2 v NN (s) Projectile(1) Target(2) Renormalization factor Frozen-density approx. (FDA)

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

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

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

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

Effect of TBR repulsive The role of three-body repulsive effect is important for nucleus-nucleus scattering

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

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 ( 16 O + 12 C, 16 O, 28 Si and 40 Ca, & 12 C + 12 C 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) Summary

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

R r v NN (s) Projectile (nucleon) Target complex G-matrix interaction Folding Model approach Single-Folding Model (SFM)Double-Folding Model (DFM) R r1r1 r2r2 v NN (s) Projectile Target

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

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

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

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

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

G-matrix calculation (scattering boundary condition) G-matrix interaction represented in coordinate space wave function in nuclear matter bare NN interaction

G-matrix calculation (scattering boundary condition) Averaging for J and L for J for L G-matrix interaction finally used bare NN interaction wave function G-matrix interaction represented in coordinate space

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

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

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

Renormalization of the imaginary potential strength fix N W -value to be 0.60 to reproduce the measured total reaction cross sections

p - 12 C elastic scattering

Comparison of the folding potential at E = 122 MeV CEG07a(two body only) vs CEG07b(with TBF) mainly seen in the real central part TBF effect

This difference appears in analyzing power Comparison of the folding potential at E = 122 MeV CEG07a(two body only) vs CEG07b(with TBF) TBF effect

p, n - 16 O elastic scattering

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

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

Double folding Potential R r1r1 r2r2 v NN (s) Projectile(1) Target(2) Local density approximation (LDA) FDA

Local density approximation (LDA) FDA

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

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

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

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

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