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
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
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)
E r ,    E r ,   0   S r  2  O( 4 )
S(r) is the density dependence of symmetry energy, it is a key ingredient of the
isospin asymmetric EOS. However, S(r) uncertainty
Constraining Symmetry energy with heavy ion collisions
Heavy Ion Collisions
large regions of r, T,  ,
• 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,
1. the symmetry energy information can be
extracted. Indirectly! (depends on models)
2. Understanding the reaction mechanism of
Heavy Ion Collisions
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.
EOS, symmetry energy
Solved with test particle methods
B, QMD type: solve N-body equation of motion
nucleon
Two body collision: occurs between nucleons
Rearrange whole nucleon-> large flucturation
EOS, symmetry energy
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
from Skyrme potential energy density functional
H=T+U+U_coul
EOS
potential energy density functional:
Surface symmetry energy term
 Isospin dependent nucleon-nucleon cross sections
are adopted, the medium corrections are
med
 np
 (1  r / r0 ) npfree
med
free
 nn

(
1


r
/
r
)

, pp
0
nn, pp
 npfree,nn( pp) , d / d
Cugnon, et al., Nucl.Instr.Meth.Phys. B111, 215(1996)
 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

pot
wasy
Cs  r  2
   r

2  r0 
pot
i  
vasy
pot
wasy
r i
The density dependence of symmetry
energy for cold nuclear matter
ImQMD05
A. n/p ratio and DR(n/p) ratio
Rn / p
dM n / dEk

dM p / dEk
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)
•
more pre-equilibrium neutrons get
emitted from the neutron rich
124Sn+124Sn system
• Significant cluster and
sequential decay effects are at
low energy!
•
relatively more pre-equilibrium
neutrons are also emitted in the
calculations with softer symmetry
energy
• Over the whole energy range
for both free and coalescenceinvariant DR(n/p) the data seem
closer to the gi=0.5 calculation
B. isospin diffusion (isospin transport ratio)
Isospin diffusion occurs only in
asymmetric systems A+B, and diffusion
ability depends on the symmetry energy.
124
112
124
Ri = 1
112
124
Ri = -1
112
No isospin diffusion between
symmetric systems
Isospin transport ratio
Ri=(2X-XAA-XBB)/(XAA-XBB)
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)
Ri as a function of impact parameters
Zhang,, et.al.,PRC85,024602(2012)
• Larger symmetry energy at
subsaturation density leads to
smaller Ri
• Ri depend 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
Constraints on symmetry energy at subsaturation density from
NSCL data of n/p ratio and isospin transport ratio
Tsang, Zhang, et al., PRL102,122701(2009)
Detailed comparison with data by varying i
Esym r   12.5r / r0 
2/3
 17.5r / r0  i
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]

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
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)
But also, Dynamical reaction mechanism:
Compare with Maria’s
Calculations(SMF and ImQMD)
• two fragments events: M(Z>=3)=2,
•Three fragments events: M(Z>=3)=3,
•Multi-fragments events: M(Z>=3) >=4
Zhang/Zhou/Chen, et.al,
• two, three: ~50%; mult-fragmentation: ~50%.
• binary: narrow rapidity distribution, Multi: broad
rapidity distribution
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.
Yield ratios for LCPs and constraints on S(r)
6He
t
4He
d
p
3He
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.
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.
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!!