Zhuxia Li (China Institute of Atomic Energy)

Collaborators: Yinxun Zhang (CIAE), Qingfen Li (FIAS),

Ning Wang(CIAE)

Probing the density dependence of the symmetry energy term

2005.8 CCAST 2

Outline

1) Introduction

2) Improved Quantum Molecular Dynamics model

3) Probing the density dependence of the symmetry energy at subnormal and supra-normal densities

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I. Intruduction

)0,(),( 0 EE ),()( 42 OEsym

EOS of asymmetric nuclear matterEmpirical parabolic law:

Esym(ρ)=E(ρ,neutron matter) -E(ρ,symmetric matter)

pn

pn

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EOS for Asymmetric Nuclear Matter

EOS of Neutron matter for 18 Skyrme Parameter sets( B. Alex Brown, PRL85 5296)

extreme variation is observed Other interactions such as Gogny,density dependent M3Y also give either positive or negative symmetry energies at high densitiesThe sign of symmetry energy at ρ>3ρ0 is very uncertain. At ρ~0.5ρ0 Esym is variant. Even at normal density the values of Esym(symmetry energy coefficient) are different for different interactions.

MeV

MeVEK symsym 460

400)(9

0

2

222

icrelativistMeV

icrelativistnonMeVEa sym

4035

3827

2

1

0

2

22

4

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The implication of the Esym(ρ) in astrophysics:

a) Nucleosynthesis in pre-supernova evolution of massive starb) Mechanism of supernova explosionc) Composition of protoneutron stard) Cooling mechanism of protoneutron starse) Kaon condensation of neutron starsf) Quark-hadron phase transition in neutron starsg) Mass-radius correlation of neutron starsh) Isospin separation instability and structure of neutron stars Refs. H.A.Bethe, Rev.of Mod. Phys. 62(1990)801 C.J. Pethick and D.G. Ravenhall, Annu.Rev.Nucl.Part.Sci.85(95)429

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Obtaining more accurate information of the symmetry energy term is highly requisite

By nuclear structure:the accurate measurements of of Pb,Snisovector giant resonance…

pn rr

MeVaMeV 3634 4

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Study dynamical effect of symmetry potentialon the reaction mechanism

Search for sensitive observables to the density dependence of symmetry potential

Eventually, obtain the more accurate information of the symmetry energy term of EOS

heavy ion collisions- unique means to study the density dependence of the symmetry energy

The matter of various density and isospin asymmetry can be produced during reaction process

2005.8 CCAST 8

N/Z ratio of emitted nucleons ratio between the yields of 3H and 3He isospin fractionation isoscaling in multifragmantation proton differential elliptic flow neutron-proton transverse flow more…

the promising probes for the symmetry energy term at subnormal density:

central or semi-central collisions

2

2

1 uCv ssym To obtain γ

B. A. LiB.T. TsangL.W. ChenD.V. Chetty

2005.8 CCAST 9

the promising probes for the symmetry energy term

at supra-normal density:

The ratios between negative and positive charged produced particles are enhanced for neutron-rich heavy ion collisions

2)(2

)( uFC

v ssym

B.A. Li, et.al, T.Gaitanos, et.al.Q.Li and Z.Li

2005.8 CCAST 10

A comprehensive study of the effects of different forms of the density dependence of the symmetry energy in a broad range of densities including subnormal and supra-normal densities

UrQMD+Vsym is applied

Study the effects of different forms of the density dependence of symmetry energy on peripheral HIC at intermediate energies (impact parameter dependence of the effects of symmetry energies) ImQMD model is applied

Our recent work

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II. Improved Quantum Molecular Denamics model (ImQMD) Wang,Li,et.al., PRC 65(2002)064648, 69(2004)034608)

2

2

1 uCv ssym 0/ u

Nuclear potential energy density functional

Version I

Vsym + Vsursym

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Version II The energy density functional is taken from the mean field with Skyrme interaction directly

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The relations between the parameters in ImQMD and Skyrme interaction

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Charge distribution of products in HIC

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III) Probing the density dependence of the

symmetry energy at subnormal and

supra-normal densities1) 112,124Sn+86Kr peripheral reactions @25AMeV

2) a comprehensive study of the effect of different forms of the symmetry energy on HIC at subnormaland supra-normal densities – to map out the densitydependence of symmetry energy term in a broad range of densities

G.A.Souliots, M.Veselsky, G.Chubarian, et.al., PR L. 91 022701(2003)

2005.8 CCAST 18

0

upn

pn

np

symsymnp

vV

,,

np

np

u

,,

,

emission rate of protons and neutrons

motion of protons and neutrons

2

2

1 uCv ssym

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124Sn+86Kr peripheral reactions @25AMeV

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emission time for neutrons and protons

neutron

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mass and charge distribution

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Time evolution of N/Z ratio for particles at neck region

Neutron skin effectN/Z increases with b

plateau

matter at neck area is neutron -rich

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The spectrum of N/Z ratio

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N/Z ratio of free nucleons as function of impact

parameters for

KrSn 86124,112

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Yields of 3H and 3He as function of b

stiff

soft

stiff

soft

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)(

)(3

3

HeY

HY

124Sn+86Kr

112Sn+86Kr

Soft-sym Stiff-sym

2.33 1.86

1.85 1.4

36Ar+58Ni

exp

1.4

central reactions

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Conclusions I

1) Strong effect of symmetry potential on the slope of the N/Z ratio of free nucleons vs impact parameters in peripheral reactions is explored . The slope is strongly enhanced with stiff symmetry potential .

2) The yield of 3H and the ratio Y(3H)/Y(3He) in peripheral reactions depend on Esym(ρ) strongly. The reducing slope of yield of 3H with impact parameters for peripheral reactions is very sensitive to the Esym(ρ) and isospin asymmetry of the reaction system, while that of 3He is not.

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In order to map out the density dependence of the symmetry energy at subnormal and supra-normal densities

We make a simultaneous study of the effects of different symmetry energies at sub- and supra-normal densities. 208Pb+208Pb @0.4AGeV

UrQMD+Vsym is adopted

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Symmetry potential for resonances (Δ,N*) and Σ

For resonances: are determined by isospin C-G coef. in B*

For Σ+-,0, assuming charge independence of the baryon-baryon interaction

V1 Lane potential pn

pn

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1

2

3

4

2)(2

)( uFC

v ssym

T.Gaitanos,et.al.

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Dmax=D23

1

2

3

4

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208Pb+208Pb @0.8AMeV@7-9fm

- differential elliptic flow

Proton-neutron differential collective flow

T. Gaitanos,et. al.Nucl-th 0402041

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and ratio by UrQMD + symmetry potential

F1(a) Fa3(b)

1.5AGeV

3.5AGeV

Sensitivity to Esym (ρ) reduces as energy increase for -/+

2.5AGeV

ba

a

b

b

a

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diff

diff

similar with -/+

without the symmetry potential of Σ

(a)(b)

b

ab

a

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Conclusion II

we have investigated the influence of different forms of symmetry energies on various observables proposed to be sensitive to the symmetry energy at subnormal and superanomal densities.

We have shown that the differences between the values of observables predicted with different symmetry potentials has a close correspondence with the different behavior of the density dependence of the symmetry energies at certain region of densities. It will help us to map out the density dependence of the symmetry energy term at a broad densities and to extract the knowledge of the isospin dependent part of the effective interaction.

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Thanks for the patience

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Stiff symmetry potential

B.A. Li, NPA,2002

Soft symmetry potential

The density dependence ofEsym strongly influence the structure of neutron star

Direct URCL limitProton fraction 1/9

2005.8 CCAST 41B.A. Li, NPA 2002

π-/π+ ratio is sensitive to the Esym at ρ>ρ0

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The production rate of and at different densities

UrQMDwithoutsymmetry potential

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At low energy case pions are produced mainly through , the ratio is determined by the ratio of N/P.

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Δ+ +, Δ+, Δ0 , Δ– production strongly depends on ρn/ρp

For E~1AGeV or less pions are mainly produced by Δ therefore π-/π+~ (N/Z)2

For E>>1AGeV many channels open. The situation becomes more complicatedΣ-/ Σ+ is more complicated than π-/π+

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Σ is baryon, as soon as it is produced it will be under of the mean field of nuclear matter.

The ratio of Σ+/ Σ- therefore is also depends on the symmetry potential of Σ in nuclear matter, in addition to those of particles which produce Σ

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Soft-sym

Stiff-sym

similar with -/+

without the symmetry potential of Σ

b

ab

a

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The effect of the symmetry potential of Σ in nuclear matter can not be neglected! The strength of this effect depends on V1

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Conclusions II(high densities)

1) A strong dependence of the ratios of -/+ and Σ -/ Σ + on Esym(ρ) which provide good means for st

udy Esym at ρ> ρ0 .

2) The ratio of -/+ n/ p for E=1.5 AGeV case but not 3.5 AGeV case. The sensitivity of -/+ ratio to Esym(ρ) reduced as energy increases.

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3) The ratio depends on the symmetry potential of in addition to those of particles which produce ’s.

Therefore a more complicated situation appears for the ratio, a reversion is appeared from E= 1.5 AGeV to E=3.5 AGeV, which may provide a useful probe to obtain the information of Lane potential V1.

/

/

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Thanks for the patience

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II) In-Medium Nucleon-Nucleon Elastic Scattering cross Section

The dynamics in heavy ion collisions at Fermi energies is

dominated by both mean field and collision terms. The isospin dependence of two-body scattering cross s

ections and its medium correction plays an important role in the reaction dynamics.

Empirically, the form of medium correction is taken as: σ= σ0 (1-αρ/ρ0), α is taken as a parameters and is isospin independent

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Our study is based on the formalism of the closed time Green’s function . With this approach, both mean field and two-body scattering cross sections can be obtained with the same effective interactions (self-consistently).The analytical expressions of the in-medium two-body scattering cross sections are obtained by computing the collisional self-energy part up to Born terms.Refs: Mao, Li, Zhuo, et.al, PRC.49(1994), Phys.lett. B327(1994)183, PRC53(1996), PRC55(1997)387, … Li, Li, Mao, PRC 64(2001)064612 Li, Li, PRC , accepted

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The effective Lagrangian density of density dependentrelativistic hadron field theory:

The energy density is:

The coupling constants are of the functional of densityRef: PRC64(2001)034314

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M*(x)=M0+ΣHσ(x)+ Σ Hδ(x)

Mp

Mn

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(Mao,Li, et.al, PRC.49(1994), Li,Li,Mao, PRC 64(2001)064612)

The Feynman diagrams for computing the in-medium nucleon-nucleon elastic scattering cross section

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The isospin dependence of in-medium cross sections is contributed from ρ and δ meson

The contributions from σ and ω exchange

The density dependence of σn

p,

σnn(pp) at Yp=0.5 and Yp=0.3

σnp

σnn(pp)

σnp

σpp

σnn

σnp/σnn(pp)

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The contributions to σnn(pp), σnpfrom the ρ and δ related terms(total 7 terms)

There exist strong cancellation effect. The final results are the delicate balance between 7 terms

σ-δ

σρ

σρ

σρ

ωρ

ωδ

ωδ

ωρ

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The density and temperature dependence of σnn,σpp,σnp for Y=0.3 Ek=10MeV

Clear isospin dependence for in-medium cross section is seen. The density dependence is stronger than temperature dependence. The isospin dependence of cross section will influence the reaction dynamics strongly.

Y=Z/A

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III. Isospin effect in HIC Multifragmentationmultifragmentation in intermediate HIC relating to possible liquid-gas phase transition (M.Fisher,Physics(N.Y.)3(1967)255,PRL88,042701,PRL88,022701, PRC52,2072,…) We study multifragmentation through central collisions in intermediate HIC. isospin distillation ,isoscaling effect, …..N/Z of free nucleons, IMF, light charged particlesstrongly depends on the symmetry energy Flow effectsneutron,proton flow, light charged particle flow, differential flow,… (various kind flow)

Probing the density dependence of Esym at ρ<ρ0

2005.8 CCAST 62

The momentum distribution of Nnpof nucl. and IMF

a)The effect of Cs on Nnp of nucleons is more pronounced at large momentum and that of is more pronounced at small momentum (because nucleons with large momentum mainly emitted at early time and that of small momentum emitted at later stage) .b) Nnp(IMF) for =0.5 enhances at p/pproj<0.25 (Coulomb effect) and at large p/pproj >1.0 ( density dependence of symmetry pot. ?) comparing with sym- stiff case.

0.5 1.0 1.50.0

0.1

0.2

0.3

0.4

0.5 1.0 1.5

0.9 1.00.00

0.05

0.10

Nucleons

CS=0 MeV

CS=35 MeV :

=0.5 =1.0 =1.5

96Zr+96ZrE=100 AMeV, b=0 fm

Nn

p

IMF

=1.0 : C

S=27 MeV

CS=50 MeV

p/pproP/Ppro

j

2005.8 CCAST 63

Probing the equilibrium with respect to isospin sensitive observables in HIC

-1.0 -0.5 0.0 0.5 1.0-1.0

-0.5

0.0

0.5

1.0

Exp.

Zr+Ru Ru+Zr E(AMeV) b(fm) 100 0 400 0 400 5

RZ

Y

The normalized proton counting number as function of rapidity.Rz=1, for Zr+Zr,Rz=-1, for Ru+Ru,Rz=0, for Zr+Ru and Ru+Zr, if equilib.is reached

Results show protons are not from an equilibrium source and the reaction is half transparent

Li, Li,PRC64(01)064612

2005.8 CCAST 64

Density dependence of the mean field contributing from symmetry potential

2/ 122

uuC

U Spnsym

When > 0 neutrons are more bound for =0.5 than for symmetry-stiff case. When < 0 neutrons are less bound for =0.5 than for symmetry-stiff case.It is just opposite for protons

np

symsymnp

VU

,,