Neutron Star ar Mat atter 2016 ( (NSMAT2016) (21 – 24th Nov. v., 2 2016 a at Tohoku Univ. v.) Medium effect up to twice the normal density on nucleus-nucleus elastic scattering Takenori Furumoto (Yokohama National University) Collaborators Y. Sakuragi (Osaka City Univ.) Y. Yamamoto (RIKEN Nishina Center)
Contents 1. Purpose 2. Three-body force (TBF) effect for the heavy-ion elastic scattering • Complex G-matrix folding model 3. Medium effect in high density region for the heavy-ion elastic scattering • Introduction of the investigation methods • Interaction dependence • Incident energy and target mass dependences 4. Summary
Purpose • Toward nuclear matter from the experimental data Heavy-ion reaction? Nuclear structure Neutron star Few-body 2 3 4 0 0 0 0 0
v NN ( s ) Frozen Density Approximation r 2 r 1 (FDA) R Projectile(1) Target(2) U ( R ) ( r ) ( r ) v ( s ; , E ) d r d r 1 1 2 2 D 1 2 K s r r s r r s s r r ( , ) ( , ) v ( ; , E ) exp i d d 1 1 1 2 2 2 EX 1 2 M R R V ( ) iW ( ) 2 DFM DFM 0 Frozen-density approx. (FDA) 0 1 2
16 O + 16 O elastic scattering cross section at E/A = 70 MeV ESC MPa MPb MPc Important effect of three-body force Y. Yamamoto, T. Furumoto, N. Yasutake, and Th. A. Rijken, Phys. Rev. C90, 045805 (2014)
Introduction of the investigation methods 1. Where is the visible region for the cross section? ? ESC MPa MPb MPc normal density Y. Yamamoto, T. Furumoto, N. Yasutake and Th. A. Rijken, Phys. Rev. C90, 045805 (2014)
v NN ( s ) Method 1 r 2 r 1 Cutting method R Projectile(1) Target(2) U ( R ) ( r ) ( r ) v ( s ; , E ) d r d r 1 1 2 2 D 1 2 K s r r s r r s s r r ( , ) ( , ) v ( ; , E ) exp i d d 1 1 1 2 2 2 EX 1 2 M V ( R ) iW ( R ) DFM DFM 2 0 ( ) 1 2 1 2 cut cut 0 ( ) cut 1 2 cut
16 O + 16 O elastic scattering cross section at E/A = 70 MeV T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C90, 041601(R) (2014)
v NN ( s ) Method 2 r 2 r 1 Replacement method R Projectile(1) Target(2) U ( R ) ( r ) ( r ) v ( s ; , E ) d r d r 1 1 2 2 D 1 2 K s r r s r r s s r r ( , ) ( , ) v ( ; , E ) exp i d d 1 1 1 2 2 2 EX 1 2 M V ( R ) iW ( R ) DFM DFM 2 0 MPa ( ) 1 2 rep. v rep. 0 ESC ( ) 1 2 rep.
16 O + 16 O elastic scattering cross section at E/A = 70 MeV →We can see the medium effect up to k F = 1.6-1.7 fm -1 from the experimental data T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C90, 041601(R) (2014)
Interaction dependence 2. If the interaction is changed, can we give the same conclusion? CEG07 MP model with phenomenological TBF MPa CDM3Y6 MPb with phenomenological density dependence MPc Others out of the range of application
16 O + 16 O elastic scattering cross section at E/A = 70 MeV T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C94, 044620 (2016)
16 O + 16 O elastic scattering cross section at E/A = 70 MeV T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C94, 044620 (2016)
Incident energy and target mass dependences 3. What system is the most suitable to investigate the medium effect in the high density region? Potential The medium effect is clearly seen with all interactions Elastic cross section It is difficult to see the medium effect up to twice normal density
Heavy-ion elastic scattering cross sections U V iN W T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C94, 044620 (2016) W
Application to the high-energy region T. Furumoto, Y. Sakuragi and Y. Yamamoto, Phys. Rev. C94, 044620 (2016)
Summary • Multi-pomeron (MP) potential (TBF effect) - successful for nucleus-nucleus elastic scattering • Medium effect including TBF effect in high density region - needs up to k F = 1.6-1.7 fm -1 for heavy-ion elastic scattering • Interaction dependence (MPa/b/c, CEG07b & CDM3Y6) - slightly different but the conclusion is not changed ( k F = 1.6-1.7 fm -1 ) • Incident energy and target mass dependences - The high energy (around 200 MeV) and large nucleus not seems to be suitable to investigate the medium effect, however the effect again appears in E/A > 300 MeV.
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