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Probing the symmetry energy with isospin ratio from nucleons to fragments

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

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Probing the symmetry energy with isospin ratio from nucleons to fragments

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

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

  3. S(r) (MeV) Isospin asymmetric Equation of State 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) is the density dependence of symmetry energy, it is a key ingredient of the isospin asymmetric EOS. However, S(r) uncertainty

  4. ConstrainingSymmetry 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+, ……) • compare with the prediction from the transport model, the symmetry energy information can be extracted. Indirectly! (depends on models) Understanding the reaction mechanism of Heavy Ion Collisions

  5. Symmetry energy in transport models A, BUU type: f(r,p,t) one body phase space density Mean field Two-body collision: occurs between test part. 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

  6. Improved Quantum Molecular Dynamics model (ImQMD05) Detail of code: Zhang, et alPR C71 (05) 024604, PR C74 (06) 014602, PRC75,034615(07)., PL B664 (08) 145, PRC85(2012)024602 • the mean fields acting on nucleon wavepackets are derived fromSkyrme potential energy density functional H=T+U+U_coul EOS potential energy density functional: Surface symmetry energy term

  7. 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)

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

  9. n/p ratio and DR(n/p) ratio Data from Famiano, PRL97, 052701(2006) DR(n/p)=Rn/p(124)/Rn/p(112) b=2fm Zhang, P.Danielewicz, et al, PLB664,145(2008) • 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 gi=0.5 calculation • more pre-equilibrium neutrons get emitted from the neutron rich 124Sn+124Sn system • relatively more pre-equilibrium neutrons are also emitted in the calculations with softer symmetry energy

  10. 124 112 Ri = -1 124 112 124 112 Ri = 1 • isospindiffusion (isospin transport ratio) Isospin diffusion occurs only in asymmetric systems A+B, and diffusion ability depends on the symmetry energy. No isospin diffusion between symmetric systems Isospin transport ratio In absence of isospin diffusion R=1 or R=-1, R~0 for isospin equilibrium Ri=(2X-XAA-XBB)/(XAA-XBB) Theory: X is the d, the isospin asymmetry of projectile residues Exp: X is the isoscaling parameter a (Tsang, PRL) There is linear relationship between d and a, So, Ri(d)=Ri(a)

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

  12. Constraints on symmetry energy at subsaturationdensity from NSCL data of n/p ratio and isospin transport ratio Tsang, Zhang, et al., PRL102,122701(2009) Detailed comparison with data by varying gi Best fit, gamma_i~0.7, for Cs/2=17.5MeV Consistent c2 analysis of these observables within ImQMD model provides with gamma_i=[0.45,0.95]

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

  14. C, Yield Ratios for LCPs between the Projectile region and mid-rapidity region Difference between the SMF calculations and DATA Z Kohley, PRC83,044601 (2011) Ni,Zn+Ni,Zn @ 35AMeV Significant difference !! Not only ?? Statistical decay of QP ?? (Kohley， 2011)

  15. But also, 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

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

  17. Yield ratios for LCPs and constraints on S(r) 6He t 4He d 3He p Zhang/Zhou/Chen, et.al, Submitted 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.

  18. 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 S0 and Lfrom 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.

  19. 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) Thanks for your attention!!

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