Studies of the high density behavior of nuclear symmetry energy by using the

triton-3He relative and differential flows

Gao-Chan YongIMP, China

Collaborators: Bao-An Li, Lie-Wen Chen,Zhi-Gang Xiao,Ming Zhang, Xun-

Chao ZhangAug. 24, IWND09

EoS of nuclear matter

pn

pn2sym ,)(E)0,(E),(E

B.A. Li , L.W. Chen, Che Ming Ko, Phys. Rep. 464, 113 (2008).

W.G. Lynch, et al., arXiv: 090.0412, [nucl-ex]

poorly known especially at high densitiesConstraints at high densities have been extracted

HF with a modified Gogny force:HF with a modified Gogny force:

0 1 2 30

20

40

60

80x= -2

x= 0

x= 1

Esy

m(

)/M

eV

/0

MDI interaction

C.B. Das, S. Das Gupta, C. Gale and B.A. Li, PRC 67, 034611 (2003)

)(xUU Single particle potential

soft

stiff

X is induced to mimic

different symmetry energies

Momentum dependent symmetry potential

consistent with the

existing experimental

data !

Effect of the momentum dependent symmetry potential

Phys.Rev. C69 (2004) 011603

Related probes

①Single/double /

②Single/double n-p differential flow

③Squeezed-out n/p

④Hard photon emissions Phys. Lett. B661 (2008) 82

Phys. Lett. B650 (2007) 344

Phys. Rev. C74 (2006) 064617

Phys. Rev. C73 (2006) 034603

Ratio_neutron-rich / Ratio_neutron_deficient

Flow_neutron-rich / Flow_neutron_deficient

Nucleons emitted perpendicular to the reaction plane

Photon_neutron-rich / Photon_neutron_deficient

For more : Tsang, Lynch, Di toro, Q.Li, Y.X. Zhang, et al.

Phase space Coalescence after-burner+Coulomb after-burner

1, R_0=3 fm, P_0=263 MeV/c,

2, our predictions on the Au+Au@200MeV/nucleon

Z=1,Z=2 flows are consistent with the experimental data.

Li,Q: arXiv:0808.0624

Yields of triton and 3He

132Sn+124Sn@400MeV/A, b=5 fm

(1) The yields are not sensitive to

the symmetry energy.

(2) More tritons are produced than

the 3He.

(3) both mostly at mid-rapidities

from the participant ragion.

arXiv: 0906.0939

Ratio of triton and 3He yields

(1) The (n/p)_free/ (n/p)_bound is

higher/lower than the (n/p)_system

due to isospin fractionation.

(2) t/3He ratio is much higher than the

(n/p)_free, maybe due to Coulomb.

(3) All are insensitive to the symmetry

energy.

Triton and 3He flows

(1) 3He clusters show a stronger flow than triton clusters, due to the stronger Coulomb force

(2) 3He flow shows more effects of symmetry energy than the triton flow.

(3) Both are insensitive to the symmetry energy

n-p differential and relative flows

Hep

tn

pN

pN

PP

ppNN

P

pn

pn

N

iix

p

N

iix

n

px

nx

N

iix

N

iix

pn

pnx

3

11

11

11

:flownucleon of difference

1

:flow e transversaldifferenti p-n

To reduce the isoscalar potential while enlarge the isovector potential

Neutrons are hard to probe delicately,

it is thus necessary to see cluster’s flow

t-3He differential and relative flows

Het

Het

N

iix

He

N

iix

t

Hex

tx

Hex

Het

Hetx

Het

t

N

iix

N

iix

Het

Hetx

ApN

ApN

APAP

APNN

NAP

NN

N

ApApNN

AP

3

3

3

3

3

3

3

3

3

3

11

3

11

3

/1

/1

//

:flow relative He-t

//

//1

/

:flow aldifferenti He-t

To reduce the isoscalar potential while enlarge the isovector potential

n-p differential and relative flows

(1)The larger symmetry energy effects

at positive rapidities are due to the

more neutron-rich of projectile.

(2) n-p relative flow:

F(x = 1) = -53 MeV/c,

F(x = -1) = -25 MeV/c,

(3) n-p differential flow:

F(x = 1) = 20 MeV/c,

F(x = -1) = 36 MeV/c,

t-3He differential and relative flows(1)The triton-3He relative flow is very

sensitive to the symmetry energy

than the triton-3He differential flow

(2) The larger slope of the 3He flow cause the triton-3He relative flow shows a negative slope at mid-rapidity.

(3) The The triton-3He differential flow is dominated by triton clusters, thus exhibit a positive slope at mid-rapidity.

(3) t-3He relative flow:

F(x = 1) = -74 MeV/c,

F(x = -1) = -22 MeV/c,

(4) t-3He differential flow:

F(x = 1) = 21 MeV/c,

F(x = -1) = 42 MeV/c,

(5) Similar behavior to the n-p flow !Not very sensitive to the R_0,P_0

Summary

1. the t-3He relative and differential flows have similar behaviors to the n-p’s.

2. the t-3He relative and differential flows are powerful probes of nuclear symmetry energy at supra-saturation densities.