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On the isospin effects in flow, its disappearance

and other related phenomena

Sakshi GautamSakshi Gautam

Department of PhysicsPanjab University

Chandigarh-160014INDIA

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Density Dependence of the Nuclear Symmetry Energy

HIC’s induced

by neutron-

rich nuclei

Most uncertain property of an asymmetric

nuclear matter

What is the isospin dependence of the in-medium nuclear effective interactions???

Isospin Physics

Neutron Stars …

Structures of Radioactive Nuclei, SHE …

Isospin Effects in HIC’s …

Nuclear Force

EOS for Asymmetric

Nuclear Matter

Terrestrial labs… In Heaven…

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Equation of State of symmetric nuclear matter is relatively well determined

K0=231±5 MeV

P. Danielewicz, R. Lacey and W.G. Lynch Science 298, 1592 (2002)

J. Aichelin and C.M. Ko PRL55, (1985) 2661

D. H. Youngblood, H. L. Clark and Y. W. Lui

PRL 82, 691 (1999)

2ρ0< ρ < 5ρ0 using flow data from BEVALAC, SIS/GSI and AGS

EOS of symmetric matter for 1ρ0< ρ < 3ρ0 from K+ production KaoS Collab.

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Liquid-drop model

Symmetry energy term

The Nuclear Symmetry Energy

EOS of Asymmetric Nuclear Matter

s2 4

ym ( )( , ) ( ), ( ),0) /( n pE OE E

Symmetric nuclear matter

Symmetry energy term

2

sym 2

1 ( , )( )

2

EE

Esym (ρ0)≈ 30 MeV

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Symmetry Energy Esym and dependence on density, takes some form:

Esym() C(/0)

= 1.5 suggests stiff S() = 0.5 suggests soft S()

Using data as input to transport

models helps constrain

Asy-stiff

Asy-soft

PRL 102, 062502 (2009)

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Promising Probes of the Esym(ρ) in Nuclear Reactions

At sub-saturation densities

At supra-saturation densities

Sizes of neutron-skinn/p ratio of pre-equ. nucleons Isospin fractionationIsospin scalingIsospin diffusiont/He3 ratio………

π-/π+, K+/K0 ratioNeutron-proton differential transverse flown/p ratio at mid-rapidityElliptic flow at high ptn/p ratio of squeeze out nucleons

Esym (ρ)γ γ ???

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Isospin-dependent quantum molecular dynamics model

Initialization of coordinates and momentum by Monte Carlo method of simulation.

Nucleons of P/T are initializedNucleons propagate under the mean fieldNucleons scatter if they come too close

ijsym

ijmdi

ijCoul

ijYukawa

ijSkyrme

ij VVVVVV

γ

oo

Skyrme

ρ

ρ

1γ

β

ρ

ρ

2

αV

jij, ji

ji

3ij

Yukawaμrr

μrrexptV

C. Hartnack et al., Eur. Phys. J A 1, 151 (1998).

Skyrme potential Coulomb potentialYukawa potential Symmetry potential

jij, ji

2jiij

Coulrr

eZZV )(

1V 33

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ijSym jiji rrTTt

Momentum –dependent interactions nn cross section

Isospin dependentIsospin independent

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Isospin effects in density

Not significant isospin effects and effect of symmetry energy

Sakshi Gautam, Phys. Rev. C 83, 064604 (2011)

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Behavior of transverse flow for different forms of

symmetry energy Sensitive to

symmetry energy

Insensitive tosymmetry energy

Mean fielddominance

collisionsdominance

S. Gautam et al., Phys. Rev. C 83, 034606 (2011).

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At the start larger no. of particles lie in BIN 1

As nuclei overlap particles increases

in BIN 2 at midrapidity

Expansion phase begins and Particles increases in BIN 1

Most of the particles lie in BIN 1

Attractive mean fieldwill push the particles

to participant zone

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Behavior of flow for diff. Esym

forms

In spectator regionrepulsive symmetry

energy will accelerate

particles away from overlap zone Attraction

towards Central densezoneParticles

enteringBIN2 have

high +ve value

of flow, mean field has to

deacc., stop andacc. backtowards overlap

zone.

BIN2 flowbehaves similarly

for all forms b/w 0-10 fm/c

b/w 10-25 fm/cdecrease is more

for F3 and F4S. Gautam et al., Phys. Rev. C 83, 034606 (2011).

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P

T

Low E

nergy

High Energy

QP

QT

QT

QP

<p x/

A>

yc.m./ybeam

0

0yc.m./ybeam

0

0

<p x/

A>

yc.m./ybeam

0

0

<p x/

A>

Balance Energy

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Isospin effects in disappearance of flow

S. Gautam et al, J. Phys. G :Nucl. Part. Phys. 37, 085102 (2010).

neutron-rich has higher EVF

Coulomb is less Cross-section is less

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Isospin effects in mass dependence of balance energy

S. Gautam and A. D. Sood, Phys. Rev. C 82, 014604 (2010).S. Gautam et al., Phys. Rev. C 83, 014603 (2011).

Symmetry energy

dominates

Coulomb dominates

15Sensitive to density dependence

of symmetry energy

Insensitive to isospin dependence of nn cross-section

N/Z dependence of EVFDifferent forms of symmetry energy and nn

cross section

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Participant matterdecreases slightly with

neutron contentof the colliding pairs

N/Z dependence of participant matter

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Participant matter becomes

almostconstant

of the neutroncontent

of the collidingpair

Repulsive innature

Esym = 0

Symmetryenergy effects

are dominating the mass effects

MDI

Participant matter decreases

with the neutron

content of the

colliding pair

Throw the matter away from the central

dense zone during theinitial stage of the reaction

Sakshi Gautam, Eur. Phys. J A 48, 3 (2012)

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System size dependence of participant/spectator matter

Power law behaviour is observed

with system mass

Mass independent behaviour

of participant/spectator

matterSakshi Gautam and R. K. Puri, Phys. Rev. C (communicated)

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• Transverse directed flow- sensitive to symmetry energy and its density dependence.

• Dominance of Coulomb potential in isospin effects in EVF of isobaric pairs

• N/Z dependence of EVF– a probe of symmetry energy and its density dependence.

• Participant/spectator matter behaves in a similar way for n-rich colliding pairs as for stable systems.

Conclusive remarks…

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and to my collaborators

Dr. Aman D. Sood, P.U. IndiaProf. Rajeev K. Puri, P.U. IndiaProf. C. Hartnack, SUBATECH, FranceProf. J. Aichelin, SUBATECH, France

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2

22

2 z

yx

ap

ppR

1aR

equlibriumglobalFull

/),(),( ttK TRR rPrP

Anisotropy ratio

Indicator of global equilibriumas doesn’t

depend on local positions

Relative momentum

Equilibrium

Indicator of local equilibrium

as itdepend on local positions

),(

),()(

),( 1

tr

trtP

trPj

A

jjj

i

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Saturates after high dense phase

indicating nn collisions

after high density

phase don’t change p-space much

Better thermalization

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Directed Transverse flow

Elliptic flow

Squeeze out

Types of flows .….

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Role of colliding geometry in isospin effects for

ISOTOPIC PAIRS

40

60

80

100

120

40

60

80

100

120

40 120 200 28036040

80

120

160

40 120 200 28036040

80

120

160200240280

N/Z 1.16 1.33

BIN 2

Eba

l (M

eV/n

ucle

on)

System Size (A)

1.16

= -0.44 ± 0.01

1.33

= -0.42 ± 0.01

1.16

= -0.32 ± 0.04

1.33

= -0.32 ± 0.04

BIN 1

1.16

= -0.58 ± 0.05

1.33

= -0.58 ± 0.05

BIN 3 BIN 4

1.16

= -0.82 ± 0.05

1.33

= -0.78 ± 0.05

n-rich has lower

Ebal

No isospin effects

throughout b

System size effects dominate throughout colliding geometry

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Role of colliding geometry in isospin effects for ISOBARIC PAIRS

With A = 48 Without A = 48

n-rich has higher Ebal

Isospin effects enhance

at higher b

Coul. Red.

n-rich has

lower Ebal

Symmetry energy role is uniform

Decrease in EVF

is much steeper

Coulomb is responsible

for steep

decrease

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τ1 increases more sharply

No diff. with and

without A =48

Steep rise withoutA =48

τ1 and τ1.4 almostsame.

Role of isospin-dependent

cross sectionand symm. energy

is independentof N/Z on

mass dep. of Ebal throughoutcolliding geom.

Variation of tau

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Effect of collisions Ebal increases

on switching off thecollisions

Roleof Coulomb

S. Gautam, A. D. Sood, R. K. Puri, and J. Aichelin, Phys. Rev. C 83, 014603 (2011).

Magnitude of risein Ebal

is almost samefor both

themasses

Significantrise in

Ebal

showsimportanceof collisionsat peripheral

geometry

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Ebal diff. constantSymm. energy: uniform in

mass, geometry

Impact parameter dependence of Ebal

N/Z =1 N/Z =1.4

All: EbalLighter: Ebal

Heavier: Ebal

N/Z =1,1.4

Coulomb full

Coulomb reduced

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Central

Peripheral

Effects is strong formedium and heavy masses

Effects is strong forheavy masses

Effect of Coulomb on collision rate

Coulomb reduces

CollisionRate !!!

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N/Z dependence of EVF

Ebal decreases with N/Z:Increase in massIncreased role of symmetry energy

Relative importance not

clear

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Sensitive to symmetry energyInsensitive to isospin dependence

of nn cross-section

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Mean field and collisions contribution to the transverse flow

The difference is reflected in

flow due to mean field

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Time evolution of spectator/participant matter at balance energies

Transition fromspectator to

participant matter is swift

and sudden for lightersystems

Lighter systems react

at higher incident energies

At the end of the reaction,

nearly same participant

matter indicating

universality in balancing

attractive andrepulsive forces.

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Increase in density of

neutron-rich systems

MDI Esym

Density decreases

withinclusion of MDI because

of repulsive

nature

Repulsive nature of symmetry

energy

Sakshi Gautam, Eur. Phys. J A 48, 3 (2012)

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Isospin effects in disappearance of flow

S. Gautam et al, J. Phys. G :Nucl. Part. Phys. 37, 085102 (2010).

neutron-rich has higher EVF

Coulomb is less Cross-section is less