Isospin breaking quark condensates in Chiral Perturbation Theory
On the isospin effects in flow, its disappearance and other related phenomena
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Transcript of On the isospin effects in flow, its disappearance and other related phenomena
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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
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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