Zhuxia Li (China Institute of Atomic En ergy) Collaborators: Yinxun Zhang (CIAE), Qingfen Li (ITP), Ning Wang(ITP) Probing the density dependenc e of the symmetry potentia l
Jan 14, 2016
Zhuxia Li (China Institute of Atomic Energy)
Collaborators: Yinxun Zhang (CIAE), Qingfen Li (ITP),
Ning Wang(ITP)
Probing the density dependence of the symmetry potential
2004.8 Weihai 2
Outline
1) Equation of state for asymmetric nuclear matter2) Probing the density dependence of the symmetry potential at low densities3) Probing the density dependence of the symmetry potential at high densities
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I. Equation of State for asymmetry nuclear matter
)0,(),( 0 EE ),()( 42 OEsym
Empirical parabolic law:
Esym(ρ)=E(ρ,neutron matter) -E(ρ,symmetric matter)
MeV
MeVEK symsym 460
400)(9
0
2
222
icrelativistMeV
icrelativistnonMeVEa sym
4035
3827
2
1
0
2
22
4
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)
Esym(ρ)<0 when ρ>3ρ0
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.
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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 potential is highly requisite
By nuclear structure:the accurate measurements of of Pb,Snisovector giant resonance…
pn rr
MeVaMeV 3634 4
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Find sensitive observables to the density dependence of symmetry potential
Study dynamical effect of symmetry potentialon the reaction mechanism
By heavy ion collisions: The matter of
various density and isospin asymmetry are
produced---test the density dependence of
the symmetry potential
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II. Probing the symmetry potential at low densities
Central collisions at intermediate energies :multifragmentation- isospin distillationin L-G phase transition
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Isoscaling effect (Tsang,et.al, PRL,2001)
Nucl-ex/0406008
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M.B.Tsang,et.al.PRL 92 (2004)
Peripheral reaction ----Isospin diffusion
α
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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
) /( ) 2(1 1 2 2 1 1 2 2 2 1 Z Z Z Z Z Rz
2004.8 Weihai 12
Probing the symmetry potential at low densities by peripheral HIC
Products in peripheral collisions at Fermi energies : Calculations are performed by means of ImQMD model (Wang,Li,et.al., PRC, 65(2002)064648, 69(2004)034608)
2
2
1 uCv ssym 0/ u
nuclear potential energy density functional :
2004.8 Weihai 13pn
pn
0
u
0 1 2-20
-10
0
10
20
e (
Me
V)
u
?
0
0.20.40.60.8
1.0
uuF For low densities we take the density dependence ofSymmetry potential:
2)(2
)( uFC
v ssym
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Density dependence of the mean field contributing from symmetry potential
2/ 122
uuC
U Spnsym
0 1 2-20
0
20
=0. 5 =1. 0 =1. 5
Pr ot ons
Neut r ons
Usym
u
When > 0 neutrons are more bound for =0.5 than for stiff symmetry pot. When < 0 neutrons are less bound for =0.5 than for stiff symmetry pot.It is just opposite for protons
np
symsymnp
VU
,,
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0.0 0.5 1.0 1.5-35
-30
-25
-20
-15
-10
-5
0C
S:
:
Dash Dotted CS=27 MeV
Line: =0.5
u(=/0)
Pure Line: =1.5Dashed Line: =0.5
Protons
Neutrons
=16/96 p
,n (
MeV
)
Density dependence of chemical pot.
)
,(
,,
npnp
u
Cs=35MeV
Esym-stiff.
Esym-soft
ε is the energy density
μn(ρ)-μp(ρ)=4Esym(ρ)δ
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neutrons move to the neck region faster than protons, neck area experiences weakcompression, expansion and finally rupturesPLF and TLF are at normal densitynucleons and light charged particles are emitted from neck
)(symv directly influences the motion of nucleons towards to neck region influences the emission rate of the neutrons and protons
)(, pnsym
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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 peripheral reactions of
KrSn 86124,112
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Yields of and3H 3He
EES model
Ni/Zi ,N/Z ratio of particles at neck area(emission source)
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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
2.5 1.9
1.98 1.54
36Ar+58Ni
exp
1.4
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Conclusions I(low densities)
1) The N/Z ratio of emitted nucleons is enhanced with soft symmetry potential, while the slope of N/Z ratio of free nucleons vs impact parameters is enhanced with stiff symmetry potential for peripheral reactions.
2) The yields of H3 ,He3 and the ratio depend on Esym(ρ) sensitively. The reducing slope of yield of H3 with impact parameters for peripheral reactions is very sensitive to the Esym(ρ) and asymmetry of the reaction system, while that of He3 is not.
)(
)(3
3
HeY
HY
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III. Study the density dependence of the symmetry potential at high density
π-/π+ ratio is sensitive to the Esym(ρ) at ρ>ρ0 B.A. Li, NPA
2002
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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
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π-/π+ ratio is sensitive to the Esym at ρ>ρ0
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Probing the density dependence of symmetry potential by -/+ and Σ-Σ + ratio by means of UrQMD-V1.3
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The production rate of and at different densities
UrQMDwithoutsymmetry potential
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Symmetry potential for resonances
(Δ++,+,0,-,N*) and ,Σ+-,0
For resonances: are determined by isospin C-G coef. in B*+N
For Σ+-,0, assuming charge independence of the baryon-baryon interaction, in the linear approximation in y= (Z-N)/A
V (Σ+-)=V0 (Σ+-)12V1 (Σ+-) y
V1, Lane potential
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-/+ and Σ-Σ + ratio by UrQMD with symmetry potential
Stiff Esym(a)
Soft Esym(b)
1.5AGeV
3.5AGeV
Sensitity to Esym (ρ) reduces as energy increase for -/+
2.5AGeV
b aa
b
b
a
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At low energy case pions are produced mainly through , the -/+ ratio is determined by n/ p.
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N/Z|132Sn
=1.64
Red lines for soft-Esym and black lines for stiff-Esym
b
a
b
a
ba
b
a
ba
ba
ba
ba
b
a
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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.
2004.8 Weihai 42
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
2004.8 Weihai 45
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
2004.8 Weihai 46
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
2004.8 Weihai 53
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
2004.8 Weihai 54
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
2004.8 Weihai 55
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
,,