Tetsuya MURAKAMI For SAMURAI-TPC Collaboration Physics Using SAMURAI TPC

 Equation of State for nuclear matter is still ｕｎｃｌｅａｒ  How much do we know?

Incompressibility of symmetric nuclear matter Around saturation density ρ 0 231±5 MeV ← TAMU GMR Youngblood et al. PRL 82 (1999) 691. Inclusion of recent RCNP ISGDR data Uchida et al. P.L. B557 (2003) 12. At 2ρ 0 <ρ<5ρ ～ 300 MeV ←Flow analysis Do we know enough about EOS then?Do we know enough about EOS then?

Symmetry energy Symmetry energy Constraining the symmetry energy at supra-saturation densities  2  0.

B.A. Brown, Phys. Rev. Lett. 85 (2000) Precise measurement of neutron Radius in 208 Pb

Why do we have to know symmetry energy? Density, radius and proton fraction of neutron stars strongly depends on it!!!! Lattimer and Prakash, APJ 550 (2001) 426. soft E 0 F : Fermi energy

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8 Symmetry Energy around normal density Through GMR GMR T.Li et al., Phys. Rev. Lett (2007)

GDR: Trippa, PRC77, Skin(Sn): Chen et al., arXiv:1004/4672 (2009) IAS : Danielewicz, Lee, NPA 818, 36 (2009) PDR: A. Klimkiewicz, PRC 76, (2007) A.Carbone, O.Wieland PRC81,041301(201 0) Constraints on symmetry energy at subnormal density from existing data Tsang et al., PRL 102, (2009) S(  )=12.5(  /  o ) 2/ (  /  o ) 

Au+Au ? MSU RIBF GSI Isospin diffusion, n-p flow Pion production RIBF can constrain the symmetry energy at ~ 2  0. Requires data with controlled variations in system asymmetry RIBF can constrain the symmetry energy at ~ 2  0. Requires data with controlled variations in system asymmetry Xiao, et al., arXiv: (2008) Reisdorf, et al., NPA 781 (2007) 459.

According to Bao-An Li’s predictions using VUU Should know n/p ratio in HD nuclear matter 1. Pre-equilibrium neutron and proton spectra 2. Fragment isotopic distribution in central collision 3. Transverse collective flow 4. Neutron-proton differential flow       ratio

Zhang et al., arXiv: v2 (2009 ) Xiao, et al., arXiv: (2008) Reisdorf, et al., NPA 781 (2007) 459.  Sensitivity to symmetry energy is larger for neutron-rich beams  Largest sensitivity requires rare isotope beams such as 132 Sn and 108 Sn.  Sensitivity increases with decreasing incident energy.  Most sensitive measurements of  - /  + ratios would be with beams available at RIBF or FAIR.

B.-A. Li et al., Phys. Rep. 464 (2008) 113.  Most models predict the differences between neutron and proton flows and t and 3 He flows to be sensitive to the symmetry energy.  The flows out of plane show a significant sensitivity. Yong et al., PRC 73, (2006)) Most model predict pion spectral ratios to be sensitive to symmetry. Double ratio removes sensitivty to differences between  - and  + acceptances Most model predict pion spectral ratios to be sensitive to symmetry. Double ratio removes sensitivty to differences between  - and  + acceptances

50cm θlab Beam Target Range Counter Multiplicity Array Ion Chamber Target Multiplicity Array Vacuum Air NOT YET Analyzed Beam : 28 Si Intensity : ~ 10 7 ppp Energy : 400, 600, 800 A MeV Target : 115 In ~ 390 mg/cm 2 Range Counter : 14 layers (+2) of Sci. measured angle (θlab) : 30, 45, 60, 75, 90, 120 degree solid angle : 10 msr Beam : 28 Si Intensity : ~ 10 7 ppp Energy : 400, 600, 800 A MeV Target : 115 In ~ 390 mg/cm 2 Range Counter : 14 layers (+2) of Sci. measured angle (θlab) : 30, 45, 60, 75, 90, 120 degree solid angle : 10 msr Vacuum

log scale π-/π+ ratio E rap (MeV) 400 MeV600 MeV 800 MeV ● 45deg ■ 60deg ▲ 90deg △ 120deg Slopes depend on Beam Energy Red Line : Fitting C*exp(-αx) slope α: 400 : (8.5±1.1)× : (4.8±0.9)× : (2.9±0.7)×10 -3

The SAMURAI TPC would be used to constrain the density dependence of the symmetry energy through measurements of: –Pion production –Flow, including neutron flow measurments with the NEBULA array. The SAMURAI TPC would be used to constrain the density dependence of the symmetry energy through measurements of: –Pion production –Flow, including neutron flow measurments with the NEBULA array. Experimental setup Nebula scintillators SAMURAI dipole TPC

 Typical rates at 10 4 /s are 3-4 pions/s of each charge and about 5 n’s/s Goal is to run up to 10 5 /s  Ideal would be to run 3-4 weeks/y. This corresponds to two experiments that each measure two pairs of systems: e.g. 132 Sn+ 124 Sn, 105 Sn+ 112 Sn at one incident energy. ProbeDevicesE lab /A (MeV) Part./sMain Foci Possible Reactions FY  +  -,p, n,t, 3 He TPC Nebula E sym m n *, m p * 132 Sn+ 124 Sn, 105 Sn+ 112 Sn, 52 Ca+ 48 Ca, 36 Ca+ 40 Ca 124 Sn+ 124 Sn, 112 Sn+ 112 Sn  +  - p, n,t, 3 He TPC Nebula  nn,  pp  np 100 Zr+ 40 Ca, 100 Ag+ 40 Ca, 107 Sn+ 40 Ca, 127 Sn+ 40 Ca