Probing the symmetry energy with isospin ratio from nucleons to fragments

Yingxun Zhang( 张英逊 )China Institute of Atomic Energy

The 11th International Conference on Nucleus-Nucleus Collisions,

31May, NN2012, San Antonio, TX

Outline1, Symmetry Energy and how to constrain it with HICs

2, Probing the SE with isospin sensitive Observables:

A. n/p ratios, DR(n/p) ratiosB. 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

)(0,, 42 OSEE

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 methodsEOS, symmetry energy

B, QMD type: solve N-body equation of motionnucleon

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:

EOSH=T+U+U_coul

Surface symmetry energy term

Detail of code: Zhang, et alPR C71 (05) 024604, PR C74 (06) 014602, PRC75,034615(07)., PL B664 (08) 145, PRC85(2012)024602

Isospin dependent nucleon-nucleon cross sections are adopted, the medium corrections are

freenp

mednp )/1( 0

freeppnn

medppnn ,0, )/1(

ddfreeppnnnp /,)(,

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

2

02

spot

asyCw

Potential energy density functional

ImQMD05

The density dependence of symmetry energy for cold nuclear matter

i

potasypot

asy

wiv

A. n/p ratio and DR(n/p) ratio

• 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

b=2fm

kp

knpn dEdM

dEdMR//

/

Zhang, P.Danielewicz, et al, PLB664,145(2008)

DR(n/p)=Rn/p(124)/Rn/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 gi=0.5 calculation

Data from Famiano, PRL97, 052701(2006)

No isospin diffusion between symmetric systems

Isospin diffusion occurs only in asymmetric systems A+B, and diffusion ability depends on the symmetry energy.

124124

112112

124112

Ri = 1

Ri = -1

Ri=(2X-XAA-XBB)/(XAA-XBB)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 a (Tsang, PRL)There is linear relationship between and a, So, Ri()=Ri(a)

B. isospin diffusion (isospin transport ratio)

Ri as a function of impact parametersZhang,, 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

isymE 0

3/20 /5.17/5.12

Constraints on symmetry energy at subsaturation density from NSCL data of n/p ratio and isospin transport ratio

Detailed comparison with data by varying gi

Consistent c2 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, PRC83,044601 (2011) Ni,Zn+Ni,Zn @ 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 S0 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)