Probing the symmetry energy with isospin ratio from nucleons to fragments Yingxun Zhang( 张英逊 ) China Institute of Atomic Energy The 11 th International Conference on Nucleus-Nucleus Collisions, 31May, NN2012, San Antonio, TX

Outline 1, Symmetry Energy and how to constrain it with HICs 2, Probing the SE with isospin sensitive Observables: A. n/p ratios, DR(n/p) ratios B. isospin diffusuion (isospin transport ratio) C. Yield Ratios for LCPs between the Projectile region and mid-rapidity region 3, Summary and outlook

Isospin asymmetric Equation of State S( r ) is the density dependence of symmetry energy, it is a key ingredient of the isospin asymmetric EOS. However, S( r ) uncertainty It is a fundamental properties of nuclear matter, and is very important for understanding properties of nuclear structure properties of neutron star properties of heavy ion reaction mechanism S( r ) (MeV)

Constraining Symmetry energy with heavy ion collisions Heavy Ion Collisions large regions of r, T, d, measure isospin sensitive observables, such as: the N/Z ratios of the emitted particles (n/p ratios, isospin diffusion, t/He3, N/Z ratios of IMFs, flow, pi-/pi+, ……) 1.the symmetry energy information can be extracted. Indirectly! (depends on models) 2.Understanding the reaction mechanism of Heavy Ion Collisions compare with the prediction from the transport model,

A, BUU type: f(r,p,t) one body phase space density Two-body collision: occurs between test part. Mean field Solved with test particle methods EOS, symmetry energy B, QMD type: solve N-body equation of motion nucleon Two body collision: occurs between nucleons Rearrange whole nucleon-> large flucturation EOS, symmetry energy Symmetry energy in transport models

Improved Quantum Molecular Dynamics model (ImQMD05)  the mean fields acting on nucleon wavepackets are derived from Skyrme potential energy density functional potential energy density functional: EOS H=T+U+U_coul Surface symmetry energy term Detail of code: Zhang, et alPR C71 (05) , PR C74 (06) , PRC75,034615(07)., PL B664 (08) 145, PRC85(2012)024602

 Isospin dependent nucleon-nucleon cross sections are adopted, the medium corrections are Cugnon, et al., Nucl.Instr.Meth.Phys. B111, 215(1996) h depend on the beam energy Well reproduce the data of charge distribution, direct flow, elliptical flow and stopping power (30-400AMeV)

Symmetry potential used in following studies Potential energy density functional ImQMD05 The density dependence of symmetry energy for cold nuclear matter

A. n/p ratio and DR(n/p) ratio more pre-equilibrium neutrons get emitted from the neutron rich 124 Sn+ 124 Sn system relatively more pre-equilibrium neutrons are also emitted in the calculations with softer symmetry energy b=2fm Zhang, P.Danielewicz, et al, PLB664,145(2008) DR(n/p)=R n/p (124)/R n/p (112) Significant cluster and sequential decay effects are at low energy! Over the whole energy range for both free and coalescence- invariant DR(n/p) the data seem closer to the g i =0.5 calculation Data from Famiano, PRL97, (2006)

No isospin diffusion between symmetric systems Isospin diffusion occurs only in asymmetric systems A+B, and diffusion ability depends on the symmetry energy R i = 1 R i = -1 R i =(2X-X AA -X BB )/(X AA -X BB ) Isospin transport ratio In absence of isospin diffusion R=1 or R=-1, R~0 for isospin equilibrium Theory: X is the , the isospin asymmetry of projectile residues Exp: X is the isoscaling parameter  (Tsang, PRL) There is linear relationship between  and , So, Ri(  )=Ri(  ) B. isospin diffusion (isospin transport ratio)

Ri as a function of impact parameters Zhang,, et.al.,PRC85,024602(2012) Ri depend on the X tracer. The differences reflect the isospin diffusion mechanism for peripheral collisions. Isospin diffusion mainly occurs around neck region Larger symmetry energy at subsaturation density leads to smaller Ri The rapidity dependence of Ri also sensitive to the density dependence of symmetry energy

Constraints on symmetry energy at subsaturation density from NSCL data of n/p ratio and isospin transport ratio Detailed comparison with data by varying g i Consistent c 2 analysis of these observables within ImQMD model provides with gamma_i=[0.45,0.95] Tsang, Zhang, et al., PRL102,122701(2009) Best fit, gamma_i~0.7, for Cs/2=17.5MeV

Constraints on the symmetry energy Updated results in Tsang, Zhang, et al., PRL102,122701(2009) Need more isospin sensitive data to improve it Density dependence of symmetry energy

C, Yield Ratios for LCPs between the Projectile region and mid-rapidity region Z Kohley, PRC83, (2011) 35AMeV Significant difference !! ?? Statistical decay of QP ?? (Kohley ， 2011) Difference between the SMF calculations and DATA Not only

Dynamical reaction mechanism: Compare with Maria’s Calculations(SMF and ImQMD) Zhang/Zhou/Chen, et.al, two fragments events: M(Z>=3)=2, Three fragments events: M(Z>=3)=3, Multi-fragments events: M(Z>=3) >=4 two, three: ~50%; mult-fragmentation: ~50%. binary: narrow rapidity distribution, Multi: broad rapidity distribution But also,

Rapidity distribution for LCP 1, Calculations with stiff symmetry energy case well reproduce rapidity distribution for LCPs. 2, Width of rapidity distribution for LCP decrease with mass increasing Zhang/Zhou/Chen, et.al, submitted 3, Difference at backward. The decreased efficiency for detection of LCPs at backward region.

1, Reproduce the R^mid_yield for 64Zn reaction system with g_i>0.5 2, Underestimate the R^mid_yield for neutron-rich reaction system, should be further understand. Zhang/Zhou/Chen, et.al, Submitted Yield ratios for LCPs and constraints on S(r) p d t 3He 4He 6He

Summary and outlook 1, n/p ratios, isospin transport ratios, yields ratios for LCPs between the projectile and target are sensitive to the density dependence of symmetry energy. 2, the cluster formation mechanism in transport models play important roles on well describing the HICs observables 3, The constraints on S 0 and L from the data of DR(n/p) ratios, isospin diffusion are obtained. 4, The difference between the data and theoretical predictions on LCPs and isospin migration mechanism in heavy ion collisions should be further understand.

Thanks for your attention!! Colloborator: Chengshuang Zhou 周承双 (CIAE,GXNU), Jixian Chen 陈佶贤 (CIAE,GXNU), Ning Wang 王宁 (GXNU), Zhuxia Li 李祝霞 (CIAE) P.Danielewicz, M.B.Tsang (MSU)