Cluster emission and Symmetry Energy Constraints with HIC observables Yingxun Zhang ( 张英逊 ) 2015 年 12 月 15 日， Shanghai China Institute of Atomic Energy SINAP-CUSTIPEN

1, Cluster formation in transport model and its problems 2, Improvements on the cluster recognition method 3, Coalescence invariant observables and its correlations to symmetry energy 4, Summary Outline

Fragmentation: intermediate energy heavy ion collisions Infer the properties of nuclear matter at high density and temperature (nuclear equation of state, transport coefficient, ….) Excited nuclear matter at lower density (liquid-gas phase transition, non-equilibrium statistical break-up, multi-fragmentation)

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 Simulating the HICs with transport models

Fragmentation in QMD approaches: dynamical process, mechanism instability In QMD model, He3, He4 are loosely bound Initial fluctuation and correlation

Problems of cluster formation in current QMD models 1 Z=1 largely overestimated, Z=2, underestimated, K. Zbiri, A Le Fever, J. Aichelin, et.al, PRC75, 2007

2, Enhancements of the productions of neutron-rich isotopes observed in isoscaling, Y 2 / Y 1 TXLiu, et.al., Phys.Rev.C 69, (2004) The predicted final isotope distributions are narrower than the experimental data, …… 3, Strong enhancement of heavy fragments in neutron- rich reaction system, 124Sn+64Ni 112Sn+58Ni ~ 2 times P.Russotto, et.al., PRC81

4, Predict more transparency than that observed experimentally in central collisions at intermediate energy Insufficient production of fragments in the mid-rapidity region R.Nebauer, J.Aichelin, NPA658(1999)

Improve cluster formation in HICs is very important, since the observables are related to them. Improve the dynamics in simulations Improve the cluster recognition methods 1), Nucleonic potential 2), In medium XS 3), Pauli-blocking 4), nucleon-nucleon correlation, cluster-cluster correlation (pBUU and AMD)

Cluster recognition methods in the QMD and BUU models: 1.MST, Aichelin, et.al., PR202(1991) 2.ECRA, C. O. Dorso and J. Randrup, Phys. Lett. B 301, 328 (1993). 3.SACA, R. K. Puri and J. Aichelin, J. Comput. Phys. 162, 245 (2000). 4.MSTB, P. B. Gossiaux, R. K. Puri, C. Hartnack, and J. Aichelin, Nucl. Phys. A 619, 379 (1997). 5.Coalescence model, LWChen, et.al., NPA …… Cluster recognition methods R nn 0= R np 0= R pp 0= R 0 ∼ 3.5 fm In Regular MST, nucleons with relative distance of coordinate and momentum of |r i − r j |<R 0 and |p i − p j |<P 0 belong to a fragment. ~ range of nucleon-nucleon interaction, determined by fitting the global experimental data, such as the IMF multiplicities.

Previous algorithms do not address the lack of isospin dependence in cluster recognition, which is the main focus of this work. Failed in details, such as problem 1 ， 2 ， 3) and 4) Isospin dependent cluster recognition methods (iso-MST) Rnn0= Rnp0~6.0 fm Rpp0~3.0fm 11Be 1.properties of neutron-rich nuclei, such as neutron skin or neutron halo effect 2. long-range repulsive Coulomb force between protons in the cluster, and finite range nucleon-nucleon interaction 3. hints from neutron-rich heavy ion collisions Physical point of view:

Effect of iso-MST on fragments yield YXZhang, Zhuxia Li, Chengshuang Zhou, MBTsang, PRC85,051602(2012)(R) 1, Charge distribution 1, obviously reduce the yield of Z=1 part. 2, strongly enhance the yield of heavy fragments. (Z>=12) 3, enhance the neutron-rich isotope 2,isotope distribution and isoscaling

3, rapidity distribution and stopping power MST: Vartl=0.58 Iso-MST: Vartl=0.62 YXZhang, Zhuxia Li, Chengshuang Zhou, MBTsang, PRC85,051602(2012)(R) Refine the results constructed from the cluster yields, but …… 4, n/p and DR(n/p) ratios

D.D.S.Coupland, et al., arXiv: Coalescence invariant observables  constructed from nucleons and light particles Coalescence invariant energy spectra n/p ratio n-like p-like Alleviate the cluster formation problem

D.D.S.Coupland, et al., arXiv: Coalescence invariant observables for probing the symmetry energy  constructed from nucleons and light particles Coalescence invariant energy spectra n/p ratio n-like p-like Alleviate the cluster formation problem

Coalescence invariant observables for probing the symmetry energy  constructed from nucleons and light particles Coalescence invariant energy spectra n/p ratio n-like p-like Y.X.Zhang, P.Danielewicz, et al., PLB664,145(2008) Data: Famiano, et al, PRL97,052701(2006) Alleviate the cluster formation problem

Q.H.Wu, Y.X.Zhang*, Z.G.Xiao, et al., PRC91, (2015) Coalescence invariant angular n/p ratio distribution Coalescence invariant observables for probing the symmetry energy  constructed from nucleons and light particles Gradient Coulomb field Isospin diffusion ability

M.B.Tsang, Yingxun Zhang, et.al., PRL2009 Lattimer, EPJA 50 (2014) 40 Consensus on symmetry energy have been obtained at subsaturation density. Model uncertainties are left! Symmetry energy constraints Large uncertainties on  L of constraints

Covariance analysis for correlation coefficient: coalescence invariant observables and nuclear matter parameters We quantitatively give strength of correlation in theory No fitting to the data! No finding the best parameter sets!

C_AB=10 A: model parameters, B: observables: A: B: CIR 2 (n/p), CIDR(n/p), CIR 21 (n/n), CIR 21 (p/p), R diff CI-DR(n/p)=CI-R 2 (n/p)/CI-R 1 (n/p) ＝ CI-R 21 (n/n)/CI-R 21 (p/p) Model parameter space R diff =(2X-X AA -X BB )/(X AA -X BB ) In absence of isospin diffusion R=1 or R=-1, R~0 for isospin equilibrium    0.16fm MeV

Correlation coefficient of A={} and B={} Y.X.Zhang,M.B.Tsang, Z.X.Li, PLB749,262(2015) Ms* also play important roles for isospin diffusion, and neutron to proton yield ratio observables at 120MeV/u. Blue: negative correlation Red: Positive correlation The ratios are constructed with Ek>40MeV

Y.X.Zhang,M.B.Tsang, Z.X.Li, PLB749,262 (2015) Ms* also play important roles for isospin diffusion, and neutron to proton yield ratio observables at 120MeV/u, one can reasonable determine it by combination analysis. Blue: negative correlation Red: Positive correlation The ratios are constructed with Ek>40MeV Correlation coefficient of A={} and B={} E beam =50MeV/u E beam =120MeV/u

Summary 1.we introduce a phenomenological isospin dependent cluster recognition method in transport models by adopting different R0 values for pp, nn, and np, Rpp0= 3 fm and Rnn0= Rnp0= 6 fm. 2.The isospin-dependent minimum spanning tree method show suppression of Z = 1 particles and enhancement of fragments, especially for heavier fragments with Z >=12, and it refines the production of neutron-rich isotopes and stopping power. 3. Correlation analysis suggest that there is lager influence of isoscalar effective mass on isospin sensitive observables, one should narrow its ranges in order to further improve the constraints on SE. 4.Combination analysis from R(n/p), R(p/p) and Rdiff may disentangle the effects of ms*, fi and L, and place constraints on that with reasonable uncertainties after best fit data.

Thanks 合作者： Zhuxia Li, (CIAE) Chengshuang Zhou, Qianghua Wu (CIAE, GXNU) M.B.Tsang, P.Danielewicz (MSU) Z.G.Xiao, R.S.Wang, Y.Zhang (TSU) H.Liu (TACC) N.Wang (GXNU)