1. 重イオン弾性散乱における 多体斥力効果の分析 古本 猛憲 ( 一関工業高等専門学校 ) 第８回 RIBF 討論会：直接反応で探る状態方程式 (Mar. 4, 2014 at 九州大学 ) 岩手 青森 秋田 山形 福島 宮城 東北地方

2. Contents 1.Introduction 2.Analysis with complex G-matrix interaction (CEG07) proton-nucleus elastic scattering nucleus-nucleus elastic scattering - important role of the three-body force effect 3.Analysis with Multi-Pomeron (MP) potential model nucleus-nucleus elastic scattering effect of the multi-body forces sensitivity of the local density 4.Summary

3. 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 the microscopic view point. Introduction

4. 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

5. 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) T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C78 (2008) 044610)

6. Single-folding model T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C.78 (2008) 044610) Proton Target nucleus R r v(s)v(s) (Incident proton case) Spin-orbit part is also obtained by the folding model calculation

7. p - 12 C elastic scattering T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C78 (2008) 044610) 122, 160 MeV のエネルギー領域で 偏極量において三体斥力の効果が見えている

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

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

10. 16 O + 16 O elastic scattering E/A = 70 MeV T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C79 (2009) 011601(R)) T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C.80 (2009) 044614) Important effect of three-body force

11. Heavy-ion elastic scattering T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C.80 (2009) 044614)

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

13. Local density approximation (LDA) FDA

14. 16 O + 16 O folding potentials with CEG07b (with TBF) ＠ E/A = 70 MeV T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C.80 (2009) 044614) Local density approx. (LDA) FDA

15. Local density approx. (LDA) 16 O + 16 O elastic scattering with CEG07b (with TBF) ＠ E/A = 70 MeV FDA T. Furumoto, Y. Sakuragi and Y. Yamamoto, (Phys. Rev. C.80 (2009) 044614)

16. Next step CEG07MP model renewal three-body forces four-body force three-body forces ESC08 MPa MPb MPc : two-body only : with three- & four-body forces : with three-body forces

17. 16 O + 16 O elastic scattering cross section at E/A = 70 MeV w/o renormalization factor (N W )

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

19. 16 O + 16 O elastic scattering cross section at E/A = 70 MeV w/o renormalization factor (N W )

20. We apply DFM with multi-pomeron (MP) potential to nucleus-nucleus elastic scattering MP model is successful for 16 O + 16 O elastic scattering However, Effect of four-body force in MP model -not seen in the 16 O + 16 O elastic scattering @E/A = 70 MeV Investigation of the sensitivity of the local density -needs up to k F = 1.6 fm -1 (ρ~1.5ρ 0 ) →How can we investigate more inner part (high density region) ? Summary

21. Folding potentials & S-matrix elements T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C82, 044612 (2010)