Probing the nuclear symmetry energy with HIC...Probing the nuclear symmetry energy with HIC: an...

Probing the nuclear symmetry energy with HIC: an overview of different transport models used in China

NuSym2013, FRIB/NSCL, East Lansing, USA, July 22-26, 2013

W. J. Xie(谢文杰), J. Su(苏军), F.S. Zhang(张丰收)College of Nuclear Science and TechnologyBeijing Normal University, Beijing, ChinaTel: +86-10-6220 5602，+86-10 6220 8252-806Fax: +86-10-6223 1765E-mail: fszhang@bnu.edu.cnhttp://lenp.bnu.edu.cn/hkxyweb/zhangfengshou.htm

M. Liu(刘敏): Guangxi Normal UniversityB. A. Bian(卞宝安): Jiangnan UniversityZ.Q. Feng(冯兆庆): Institute of Modern Physics, CASL. W. Chen(陈列文): Shanghai Jiaotong University

Contributions also by：

Outline1.Introduction

2.Different transport models used in China

3.Observables for symmetry energy

Nuclear dynamics at intermediate and high energies by IQMD and IBL

ProjectileTarget

?

What happened?

Size?Lifetime?

Shape?

T Detectors

dense, hot, and asymmetric nuclear matter

Equation of StateOf Nuclear Matter

E(,T

From compound nuclei ( 0, T1-2 MeV,)

hot nuclei( 0,T>5 MeV),

highly excited nuclei ( 30,T>5 MeV)

asymmetrical highly excited nuclei

( 2-30,T>5 MeV, >0)

Physical indications IEOS

0, T > 0, >0

E(, T, ) = ?

MSU, 1996-1998 112,124Sn(40MeV/nucl.)+112,124Sn

isospin effects in multifragmentation 58Fe(45-105 MeV/nucl.)+58Fe,

58Ni(45-105 MeV/nucl.)+58Ni,

disappearance of isospin effects in multifragmentation

Physical indications and challenges 0, T > 0, >0E(, T, ) = ?

Important to production of RIB &Neutron Stars !!!

G. J. Kunde et al., Phys. Rev. Lett. 77, 2897 (1996)

Quantum molecular dynamics model (QMD)The QMD model represents the many body state of the system and thus contains correlation effects to all orders. In QMD, nucleon i is represented by a Gaussian form of wave function.

After performing Wigner transformations, the density distribution of nucleon i is:

Improved isospin dependent quantum molecular dynamics model

From QMD model to IQMD model (1997,1998) mean field (corresponds to interactions)

MDISymCoulYuklocz UUUUUU ),(

two-body collisions

pauli blocking

initialization

coalescence model

Uloc : density dependent potential

UYuk: Yukawa (surface) potential

UCoul: Coulomb energy

USym: symmetry energy

UMD: momentum dependent interaction

IQMD model for studying isospin dependence of collective flow, PRC58(1998)2283

Averaged number of IMF <NIMF> as a function ofNC, NLC, and NN (4 analyzing)

Exp data, G. J. Kunde et al., Phys. Rev. Lett. 77, 2897 (1996)

IQMD model for studying isospin dependence of multifragmentation, PRC60(1999)064604

Average n multiplicity <NN>, as afunction of charged-particle multiplicity NC

Exp data, G. J. Kunde et al., Phys. Rev. Lett. 77, 2897 (1996)

Averaged number of IMF <NIMF> as a function of NC, NLC,and NN (4 pre equilibrium emissions)

Exp data, G. J. Kunde et al., Phys. Rev. Lett. 77, 2897 (1996)

IQMD model for studying isospin dependence of radial flow, PLB459(1999)21

Chapter 10:Isospin-Dependent Quantum Molecular Dynamics Model and Its Applications in

Heavy Ion Collisions, F. S. Zhang, L. W. Chen, et al.

PLB319(1993)35PRC51(1995)3201

BUU BLEfor studying nuclear multifragmentation

BLE IBLE for studying isospin effects in nuclear multifragmentation, NPA807(2008)71

Nuclear Multifragmentation，F. S. Zhang and L. X. Ge,

Science Press, Beijing, 1998

Transport models in heavy ion collisions in China, 2011.9(20)

2011.9 Transport models in HIC in China (Huzhou)1. CIAE(YZ Zhuo, ZX LI, XZ Wu, YX Zhang, K Zhao, XH Lu, …)2. ITP(EG Zhao, SG Zhou, …)3. IHEP(B Liu, …)4. IMP(JQ Li, W Zuo, ZQ Feng, GC Yong, …)5. SINAP(YG Ma, DQ Fang…)6. PKU(FR Xu, YX Liu,…)7. TsinghuaU(ZG Xiao, …)8. BNU(JB Bao, FS Zhang, …)9. NJU(ZZ Ren, C Xu,…)10.USTC(Q Wang, …)11.SJTU(LW Chen, ..) 12.FudanU(ZH Li, BR Wei, …)13.SZU(N Wang,…)14.GXNU(N Wang, M Liu, L O, …)15.HNNU(CW Ma, …)16.HUTC(CW Shen, QF Li, …)17.TSTC(YZ Xing, …)18.AYTC(JL Tian, …)19.SHIT (WJ Guo, …)20.JNU(BA Bian, …)

Relativistic Mean-Field predictions

Nuclear Matter Symmetry Energy

: confirm some of isospin-dependent effects, constrain the symmetry energy : even the trend of the symmetry energy with increasing is not constrained

Skyrme Hartree-Fock

Experimental work, M.B. Tsang et al. PRC86, 015803 (2012)

Fuchs, et.al., arXiv:nucl-th/0511070L.W.Chen,et.al., PRC72, 064309 (2005)

Outline1.Introduction

2.Different transport models used in China

3.Observables for symmetry energy

2 Different Transport Models Used in China

2 3/4 2

( )21( ) exp(2 ) 4

ii i

r r

r r ir r p

Quantum Molecular Dynamics like: solve N-body equation of motion

Version: QMD, IQMD, ImQMD, LQMD, CoMD, UrQMD , ……AMD, FMD

2 22

3 2 2

( ) 21( , ) exp ( )( ) 2

i ri

i r

r rf r p p p

Two body collision: occurs between nucleons, i ii i

H Hp rr p

ˆ ˆ ˆ, , , ,r r pp U f f r p t K f K r p t

t m

1( , ) ( ) ( )i if r p r r p pN

Boltzmann-like: f(r,p,t) one body phase space density

Version: IBUU04, BLE,……

Two-body collision: occurs between test part.

2 3/4 2

( )21( ) exp(2 ) 4

ii i

r r

r r ir r p

Quantum Molecular Dynamics like: solve N-body equation of motion

Version: QMD, IQMD, ImQMD, LQMD, UrQMD , ……AMD, FMD

2 22

3 2 2

( ) 21( , ) exp ( )( ) 2

i ri

i r

r rf r p p p

Two body collision: occurs between nucleons

, i ii i

H Hp rr p

2.1Quantum Molecular Dynamics Like Models

Quantum Molecular Dynamics model (J. Aichelin, Phys. Rep. 202 (1991) 233)and Extension of the QMD model (isospin, low and high energies etc.)

Isospin QMD (IQMD) by Nantes group (Hartnack, Aichelin);Ch. Hartnack, R.K. Puri, J. Aichelin, et al., EPJA 1 (1998) 151

IQMD extend by Feng-Shou Zhang, Lie-Wen Chen, et al., BNU, Beijing and Lanzhou); PRC 58(1998)2283, PLB 459(1999)21

Lanzhou QMD (LQMD, IMP CAS, Lanzhou) Z.-Q. Feng et al., NPA 750 (2005) 232, PLB 683 (2010) 140

IQMD in SINAP, Shanghai Yu-Gang Ma et alPRC 84(2001)034612, PRC 83(2011)064607……

QMD (Fuchs et al., Tuebingen Uni, Germany);Improved QMD (ImQMD) by Zhuxia Li, Ning Wang et al., CIAE, Beijing)

PRC 65(2002)064608……

Ultra-relativistic QMD (UrQMD) by Frankfurt groupS.A. Bass et al., Prog. Part. Nucl. Phys. 41 (1998) 255Extend by Qing-Feng Li et al. Huzhou Teachers College, Huzhou

PRC 72(2005)034613

IQMD in BNU

IQMD in SINAP

LQMD in IMP

ImQMD in CIAE

UrQMD in Huzhou

2 3

, i ii i

Coul sym sur MDI

H Hp rr p

H T U U U U U U

QMD

wave function

Hamiltonian equations

two-body collision

Fermionic nature

2 22

3 2 2

( ) 21( , ) exp ( )( ) 2

i ri

i r

r rf r p p p

The N-body phase-space distribution function

, ,, ,

,

N N N N N N NN N N N N

Pauli blocking

phase-space density constraint

Difference in EOS

2 3

, i ii i

Coul MDI sym sur

H Hp rr p

H T U U U U U U

2 2/30 0 0 0( / ) ( / ) ln ( ( / ) 1) /U

5/30 0 0( / ) ( / ) ( / )U g

EOS of symmetric nuclear matter

Soft EOS plus MDI: K=200 MeVHard EOS plus MDI: K=380 MeV

derived directly from the Skyrme energy-density functional3

0 0 0

2 2/3 5/31 2 2 2 0

3 , ,2 8 1 16

3 3(3 5 4 )( )80 2

tt

g t t x t

K=200 ~ 380 MeV

Form 1

Form 2

N. Wang et al. PRC 65.064608; Z.Q. Feng et al., NPA 750 (2005)

J. Aichelin, Phys. Rep. 202 (1991) 233

Difference in symmetry energy3

is the potential energy densitysym sym

sym

U V d r

V

2 1 8/3 2( )symV A B C Y. X. Zhang et al. PhysRevC 74, 014602(2006)

n p

2

0

( )2

isymsym

CV

2 2

0 0

( ) ( )sym sym symV a b

2 3

, i ii i

Coul MDI sym sur

H Hp rr p

H T U U U U U U

Change the density dependence of the symmetry energy

2 2 2

0

( ( ) )2

symsym s

CV

2 2

02sym

sym

CV

or

Form 1

Form 2

Form 3

Form 4

Y. X. Zhang PRC 85, 051602(2012); J. Pu PRC 87, 047603(2013)

N. Wang et al. PRC 85, 034601(2012)

Z. Q. Feng, PRC 87, 064605(2013)

Difference in surface energy

2 3( )2sur

surgU d r

Derived from the Skyrme energy-density functional

Yukawa interaction21 exp( )[exp( ) ( / 4 )

2

exp( ) ( / 4 )]

yYuk ij ij

i j ij

ij ij

VU Lm mr erfc Lm r L

m r

mr erfc Lm r L

2 3

, i ii i

Coul MDI sym sur

H Hp rr p

H T U U U U U U

reflect the surface effects in the finite system

Form 1

Form 2

Aichelin, Phys. Rep. 202 (1991) 233

N. Wang et al. PRC 85, 034601(2012)

Difference in momentum dependent interactions

3 31 2 1 1 2 261

0

4 2 2

1 1 ( ) ( )2 16

1.57[ln(1 5 10 ( ) )]

md N NNU d p d p f p f p

p

Isospin independent

3 3 3, , ,

, , ,0

22

12

( , , ) ln ( ) 1) ( , , )

i jmdi j i j

i j

U C d pd p d r

f r p t p p f r p t

2 3

, i ii i

Coul MDI sym sur

H Hp rr p

H T U U U U U U

Form 1

Form 2 Isospin dependent

Z. Q. Feng, PLB 707,83(2012)

Y. X. Zhang, PRC 85, 051602(2012)

Difference in two-body collisionsNucleon-nucleon cross section in free space

example

difference in parametrizatoinbut fit to the experimental data nn pp np isospin dependent isospin independent

Z.Q. Feng, PhysRevC 85 014604,2012

Difference in in-medium NN cross sections

*

0

(1 ) 0.2freenn nn

** 2( )( ) freenn nn

mm

*

NN 0 NN

NN 0 NN

( , , )

( , , )2=1+ exp( / 0.54568) 1 / 1 (p / ) , p 1GeV/c3

=1+ 0.85 / (1 3.25 ) / 1 (p / ) , p 1GeV/c

1,

freenn nn

p pu

pu

pij

p pu

F u p

F u p F F

F u p

F u p

F F

NN

p >1GeV/c

* freenn medium nnf

Form 1

Form 2

Form 3

Q.F. Li et al.,PRC 62 014606(2000)D. Persram et al.,PRC 65 064611(2002)

G. D. Westfall et al. PRL 71, 1986(1993)

Yuan. PhysRevC 81 034913,2012

Difference in Fermionic nature

1 2

2 2

i 3 2 2,

1 1 min( ,1) 1 min( ,1)

( ) ( )1P = exp exp( ) 2 2

block

Ai k i k

k k i r p

P P P

r r p p

1 (for two nucleon)if

3

3 3

1 (for all nucleon)

( , )i j i j

i

i s s jhj

f

f f r p d rd p

Pauli blocking

phase-space density constraint

block with a probability

33 34 4

3 3 4ij ijhr p

Final states satisfy

2 2 2

2 2

2

2

( ) ( )exp( ) exp( )4

( )exp( )2

i i

i

ifit fit

i

r r L p pL

r ra bL

Final states satisfy

Final states satisfy

Aichelin,Phys. Rep. 202 (1991) 233

Su, Zhang, PhysRevC 87 017602,2013

LI, PhysRevC 64 064612, 2001

Li PhysRevC 83, 044617, 2011

2.2 Boltzmann-like models

ˆ ˆ ˆ, , , ,r r pp U f f r p t K f K r p t

t m

1( , ) ( ) ( )i if r p r r p pN

Boltzmann-like: f(r,p,t) one body phase space density

Version: IBUU04, BLE,……

Two-body collision: occurs between test part.

The differences among the Vlasov, BUU and BL models

F. S. Zhang and L.X. Ge, Nuclear Multifragmentation, Science Press, Beijing,1998A. Ono, J. Randrup, Eur. Phys. J. A 30 (2006) 109

ˆ ˆ ˆ, ,r r pp U f f r p t K f

t m

ˆ ˆ ˆ, ,

, ,

r r pp U f f r p t K f

t mK r p t

ˆ ˆ , , 0r r pp U f f r p t

t m

Vlasov

BUU

BL

IBUU Model for HIC's

, ,r r pp U f f r p t K f

t m

J. Aichelin, G.F. Bertsch, S. Das Gupta, W. Bauer, Bao-An Li, ……

Phase-space distributions f(r, p, t) satify the Boltzmann equation

Solve the Boltzmann equation using test particle methodIsospin-dependent initializationIsospin- (momentum-) dependent mean field potential

Isospin-dependent N-N cross sectionsa. Experimental free space N-N cross section σexp

b. In-medium N-N cross section from the Dirac-Bruecknerapproach based on Bonn A potential σin-medium

c. Mean-field consistent cross section due to m*

Isospin-dependent Pauli Blocking

01 (1 )2 z c symV V V V

Has been extended to IBUU04 by Bao-An Li

IBUU04--- potential1

2

0 0 0 0

, ,3 32 2 2 2

0 0

( , , , , ) ( ) ( ) (1 ) 81

2 2( , ) ( , ) .1 ( ) / 1 ( ) /

2 2( ) 95.98 , ( ) 120.571 1

u l

u l

BU p x A x A x B x x

C Cf r p f r pd p d pp p p p

B BA x x A x x

Isospin- and momentum-dependent potential (MDI)

-30

0

0

0

*

0.16 fm( ) / 16 MeV

( ) 31.6 MeV

K =211 MeV

m /m=0.68

sym

E AE

Das/Gupta/Gale/Li, PRC67,034611 (2003)

MDI Interaction: Gogny

Chen/Ko/Li, PRL94,032701 (2005);Li/Chen,PRC72, 064611 (2005)

IBUU04In-medium Nucleon-nucleon cross sections

2*

*

/ NNmedium free

NN

NN

Neglecting medium effects on the transition matrix

Medium effects: effective mass on the incoming current in initial state and leveldensity of the final state

is the reduced mass of thecolliding pair NN in mediumJ.W. Negele and K. Yazaki, PRL 47, 71 (1981)V.R. Pandharipande and S.C. Pieper, PRC 45, 791 (1992)M. Kohno et al., PRC 57, 3495 (1998)D. Persram and C. Gale, PRC65, 064611 (2002).

1. In-medium cross sections are reduced2. nn and pp cross sections are splitteddue to the neutron-proton effective masssplitting in neutron-rich matterLi/Chen, PRC72 (2005)064611

/medium free

BUU (f) BL( )

ˆ ˆ ˆ, ,r r pp U f f r p t K f

t m

Phase-space distributions f(r, p, t) satify the Boltzmann equation

Isospin- (momentum-) dependent mean field potential

0 1 2 3 40

20

40

60

80

100

Esy

m (M

eV)

/0

soft linear hard supersoft

2 2

0 02

( )( , , ) ( ) ( )

( )

locsymloc

sym

locsym M DI

EU p E

E U

2 2

0

1.57 ln [0.0005 1]MDIU p

2.14 5/3

0 0 0

0

0

( ) 38.9 18.4 3.8

( ) 14.7

( ) 29.4

s

potsym

potsym

sym

E

E

E MeV

B.A. Bian, et al., Nucl. Phys. A807,71(2008); W.J. Xie, et al., Phys. Lett. B 718,1510(2013)

BLThe inelastic channels and cross sections

*

*

, , ,,

NN N NN NN NNN N N

The parameterized cross sections for each channel to produce resonances are obtained in terms of the one-boson exchange model. The resonance lifetime are calculated according to the following figure.

Z.Q. Feng, Phys. Rev. C 82 (2010) 057901; S. Huber, et al. Nucl. Phys. A573, (1994) 587;A.B. Larionov, et al., Phys. Rev. C66,(2002)054604

BL---deal with the fluctuation term

1 1 1 2 2 2 1 2 1 2 1 2, , , , , .K r p t K r p t C p p r r t t

1 2 3 4 1 2 3 4

, ,

12 , 34 1 1 .

L M L M L M L M

L M L M

C r t dpdp Q p Q p C p p

dp dp dp dp Q Q W f f f f

F.S. Zhang et al. Phys. Rev. C 51(1995) 3201, Y. Abe, S. Ayik, et, al. Phys. Rep. 275 (1996)49

20 20 20 2

30 30 30 3

ˆ , , , ,

ˆ , , , .

Q r t t Q r t t tC r t W

Q r t t Q r t t tC r t W

ˆ ˆ ˆ, ,

, ,

r r pp U f f r p t K f

t mK r p t

The fluctuating collision term can be interpreted as a stochastic force acting on density and is characterized by a correlation function,

A projection method is used in the BL model. The fluctuations are projected on a set of low-order multipole moments of the momentum distribution,

Developing processes from BL,IBL to ImIBL

0 0

( , , ) ( ) sym MDIU p U U

0 0

( ) ( )U

0 0

( , ) ( ) symU U

No isospin effects,noinelastic channels

No inelastic channels

Inelastic channels and MDI

F.S. Zhang, Phys. Rev. C51,3201(1995)

B.A. Bian, et al., Nucl. Phys. A807,71(2008)

W.J. Xie, et al., Phys. Lett. B 718,1510(2013)

BL

IBL

ImIBL

*

*

, , ,,

NN N NN NN NNN N N

Outline1.Introduction

2.Different transport models used in China

3.Observables for symmetry energy

How to use those models to probe the nuclear symmetry energy with heavy-ion collisions ?

3.1 At sub-saturation densities (know something) X√

Global nucleon optical potentials from n/p-nucleus and (p,n) reactions

Thickness of n-skin in 208Pb measured using various approaches and sizes of n-skins of unstable nuclei from total reaction cross sections

n/p ratio of FAST, pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusion/transport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t/3He ratio and their differential flow

3.2 Towards supra-saturation densities (know nothing ) X X π -/π + ratio, K+/K0 ? Neutron-proton differential transverse flow n/p ratio of squeezed-out nucleons perpendicular to the reaction plane Nucleon elliptical flow at high transverse momentum t-3He differential and difference transverse flow

(1)Correlations of multiple observables are important(2) Detecting neutrons simultaneously with charged particles is critical

B.A. Li, L.W. Chen and C.M. Ko, Physics Reports 464, 113 (2008)

Stiff Esym

n/p ratio at supra-normal densities

Central density

2( , ) ( , 0 ) ( )symE E E

B.A. Li et al, Phys. Rev. C 71 (2005) 014608

With the soft symmetry energy then/p ratio of the high-density region can be significantly higher than that of the reaction system.

Based on RBUU model, by calculating the excitation function of pion and kaon ratio, due to the inclusion of delta meson field, a stiffer symmetry energy results in a larger pion and kaon ratios.

stiffer

Based on the IBUU04 model, by calculating the excitation function of pion ratio, a very soft symmetry energy was obtained. A soft symmetry energy results in a larger pion ratio.

FOPI data, W. Reisdorf, et al., Nucl. Phys. A 781, 459 (2007).

Based on the LQMD model, a hard symmetry energy results in a larger pion ratio. A hard symmetry energy was predicted by comparing with the FOPI data.

FOPI data, W. Reisdorf, et al., Nucl. Phys. A 781, 459 (2007).

Based on the improved isospin-dependent BL model, a supersoft symmetry energy is obtained by calculating the excitation functions of pion ratios in comparison with the FOPI data, which is consistent with the IBUU04 calculations.

FOPI data, W. Reisdorf, et al., Nucl. Phys. A 781, 459 (2007).

Bulk nuclear properties from pion yields and other dataH. Jun and P. Danielewicz, by PBUUPBUU: Danielewicz et al., NPA 533, 712 (1991)

1. Molecular dynamics like: N-body approachesCMD, QMD, CoMD,IQMD, LQMD, ImQMD,…

AMD, FMD,…2. Boltzmann-like: 1-body approaches

IBUU (BNV, LV), IBL

Important: Input quantities, numerical treatments,…

How to manage this inconsistency: transport models with the same + the simplest input quantities

Thank you for your attention