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Probing the density dependence of symmetry energy at subsaturation density with HICs

Probing the density dependence of symmetry energy at subsaturation density with HICs. Yingxun Zhang ( 张英逊 ). B.Tsang, Zhuxia Li, P.Danielewicz, W.G.Lynch. China Institute of Atomic Energy JINA/NSCL, Michigan State Uni. outline. Introduction on E sym ( r ) and ImQMD05

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Probing the density dependence of symmetry energy at subsaturation density with HICs

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  1. Probing the density dependence of symmetry energy at subsaturation density with HICs Yingxun Zhang (张英逊) B.Tsang, Zhuxia Li, P.Danielewicz, W.G.Lynch • China Institute of Atomic Energy • JINA/NSCL, Michigan State Uni.

  2. outline • Introduction on Esym(r) and ImQMD05 • Reaction mechanism Sn+Sn @ 50AMeV • the n/p ratio, isospin diffusion, N/Z ratio of IMFs • Conclusion and outlook

  3. Introduction Isospin asymmetry nuclear Equation of State • It is a fundamental properties of nuclear matter, and is very important for understanding • masses, • fission barriers, • thickness of the neutron skins of neutron-rich nuclei. • properties of NS, …. Esym(r) is the density dependence of symmetry energy, it is a key ingredient of the isospin asymmetry EOS.

  4. How to constrain the Esym(r) in Lab? • By comparing the HICs Observables with transport model predictions: • So, lot of observables have been proposed • At subsaturation density: • n/p ratios, isospin transport ratios, isoscaling, t/3He,C(q) …… • At supersaturation density: • pi-/pi+, n/p ratio and flow, C(q), K, S…… (BALi, Tsang, LWChen, M.Colonna, Q.F.Li, Y.Zhang, ……) In this research, we focus ourselves on constraining the density dependence of symmetry energy at subsaturation densities by comparing the transport model predictions with the NSCL’s Sn+Sn @ 50AMeV data. • Transport model: ImQMD05 • Study the influence of cluster emission mechanism on observables for the intermediate energy HICs

  5. Brief introduction on ImQMD05 • the mean fields acting on nucleon wavepackets are derived fromSkyrme potential energy density functional potential energy density functional: • Change the symmetry potential in the transport model by varying the g Parameters in Vloc are obtained from standard Skyrme interactionsparameters

  6. isospin independent Momentum dependence interaction Aichelin, et al., PRL58,1926(1987) and the MDI contributions at T=0MeV are subtracted in order to use the Skyrme interaction parameters and the MDI. • Phase space constraint for considering Pauli principle The occupation number in cubic of h3 should be small than1(Pauli principle) • Isospin dependent nucleon-nucleon cross sections • are adopted, the medium corrections are Cugnon, et al., Nucl.Instr.Meth.Phys. B111, 215(1996)

  7. Several aspects (Such as, collective flow, stopping, charge distributions) have been successfully described by this model Charge distribution Zhang, Li, PRC71(2005)24606 Zhang, Li, PRC71(2005)24606 stopping flow Data: Residorf, PRL 92(2004)232301 • The reasonable charge distribution is important for prediction the HICs observables.

  8. Reaction mechanism for Sn+Sn at E/A=50MeV b=2fm b=6fm

  9. The charge distributions for 112Sn+112Sn at E/A=50MeV for b=2, 6, 8fm. The solid symbols are for stiff symmetry energy case (gamma=2.0) and open symbols are for the soft symmetry energy case (gamma=0.5). The contour plots for fragment charge Z vs rapidity at different impact parameters b=2, 6, 8 fm for 112Sn+112Sn with soft symmetry energy cases (gamma=0.5). • Reaction mechanism of fragments productions depend on the impact parameters • Charge distribution depend on the stiffness of EoS

  10. the n/p ratio, isospin diffusion, N/Z ratio of IMFs n/p ratio and DR(n/p) ratio • the emitted nucleons directly feel the symmetry potential • n/p ratio is related to the stiffness of symmetry potential at subsaturation density (BALi, PRL(1997)) b=2fm • 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

  11. DR(n/p)=Rn/p(124)/Rn/p(112) Data from Famiano, PRL97, 052701(2006) • Over the whole energy range for both free and coalescence-invariant DR(n/p) the data seem closer to the gi=0.5 calculation Detailed comparison with data by varying gi • Significant cluster and sequential decay effects are at low energy! • For very small gi, the system completely disintegrated, DR decreases and approaches the limit of reaction system. the double ratio values peak around gi~0.7. • By comparing with data, the gi=[0.4,1.05] within c2<2s Tsang, et.al., PRL102(2009)

  12. isospin diffusion 124 112 b=6fm • Time scale of the isospin diffusion ~100fm/c Isospin diffusion Ri=(2X-XAA-XBB)/(XAA-XBB) (isospin transport ratio or isospin imbalance ratio) • X is the isospin dependent observable. A, B refer to 124Sn, 112Sn • Theory: X is the d, the isospin asymmetry of emitting source • Exp: X is the isoscaling parameter a, ln(Y(7Li)/(Y(7Be))) • There is linear relationship between Xth and Xexp, So, R(Xth)=R(Xexp)

  13. Detailed comparison with data Observable from heavy fragments Tsang,, et.al., PRL102,122701(2009) Consistent c2 analysis of these observables within ImQMD model provides • Ri depend on the X definition. The differences reflect the isospin diffusion mechanism for peripheral collisions. Isospin diffusion mainly occurs around neck region. with gamma_i=[0.4,1.0]

  14. N/Z ratio of IMFs N/Z ratios from bound fragments (Z=3-8)  complementary to n/p ratios • N/Z ratio of IMFs depend on the density dependence of symmetry energy • After decay, Data from NSCL favor the soft symmetry energy • at low energy, the N/Z ratio of IMFs obtained with stiff symmetry energy case is larger than that with soft symmetry energy case. • Coulomb effects are important at lower kinetic region

  15. Conclusions and outlook: • n/p ratio and DR(n/p) ratio of the emitted nucleons strongly depend on the density dependence of symmetry energy, and the significant cluster emission effects are at low energy on the DR ratio. • Isospin transport ratio depend on the density dependence of symmetry energy and its values also depend on the tracer. The difference reflects the isospin diffusion mainly occurs around the neck region. • Detailed comparison with data of DR(n/p), Ri, and R7 have been done, and the analysis provide consistent constraints on the density dependence of symmetry energy from ImQMD model. • N/Z ratio of the IMFs also depend on the density dependence of symmetry energy, and the sequential decay effects are important.

  16. “ Constrain the Esym(r) is a complex problem, and further work on the theory and experiment are needed” • There is no transport models do the MF and NN cs consistently. • Uncertainty of the transport model need to be reduced • More and accurate data are needed for developing the transport model in future. Thanks for your attention !

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