outline of talk

Exploring the symmetry energy at sub and supra-saturation

densities

Yu-Gang Ma 马余刚

Shanghai Institute of Applied Physics, Chinese Academy of Science

OUTLINE OF TALK

(1) Brief Introduction from literature (i) symmetry energy, its form and realization in IQMD (ii) Symmetry energy sensitive observables (iii) Main Literature highlights

(2) Work Done (i) Symmetry energy or isospin migration at sub-saturation densities

by using : (a) Single and double n/p ratio; (b) Concept of quasi-participant and quasi-spectator matter; (c) multiplicity of neutrons from high incident energy

(ii) Hint for compressibilities with symmetry energy sensitive and

insensitive observables (iii) sensitive observable from fragmentation at high incident energy (iv) Impact of binding energy clusterization towards isospin physics

and stability of fragments(3) Conclusions

Why intermediate energy heavy-ion collisions? Extreme Conditions Extreme densities and excitation energies

Phase Diagram of Nuclear Matter

What is Symmetry Energy and isospin?Symmetry energy arises due to the isospin parameter of proton

and neutron.Isospin: Isospin is a quantum number related to number of charged states of baryon or meson .Symmetry energy: It is the deviation of the symmetric nuclear matter from pure neutron matter.Bethe Mass Formula

How Symmetry energy depend on the density:

EOS of Isospin Asymmetric Nuclear Matter

s2 4

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

(Parabolic law)

The Nuclear Symmetry Energy2

sym 2

1 ( , )( )

2

EE

The Symmetry Energy

Symmetry energy term(poorly known)

Symmetric Nuclear Matter(relatively well-determined)

Isospin asymmetry

0

2

s

sym

ym

0 0

0 0

sym

sym y 0

0

0s

0

m , ( )3 18

30 MeV (LD mass formula: )

( )3 (Many 50-Bo 2

(

0dy 0 M eTheor

( )

y: : ;

(

)

V Ex

)

p

E My

E

ers & Swiatecki, NPA81; Pomorski & Dudek, PRC67

EEL

L

K

L

0

sy

2sym2

0 sym2m

: ???)

( )9 (Many-Body Theory: : ; Exp: ??700 466 M ?e )V

EK K

Form of Symmetry EnergySymmetry Energy= Kinetic Symmetry energy + Potential Symmetry energySymm. Kin. energy comes from fermi statistics:

But experimental results at u =1So, Sym. Pot. Energy is required

We choose

From S0=30 MeV, CS/2 = 17.5 MeV with F(u)=

The final form for Symm. Energy is:

Linear

IQMD Model

Initialization: In real space: the radial position of n and p are sampled

by using MC method according to the n and p radial density distribution calculated from SHF (or RMF) theory

In momentum space: local Fermi momentum is given by),(,))(3()( 3/12 pnirrp iF

i

Pauli blocking: the Pauli blocking of n and p is treated separately• NN is isospin dependent

np 3nn =3pp

Potentials in IQMD Model:•NUCLEON : As Gaussian Wave Packet

Hamiltonian is given as;

New factor in potential is Vsym, Which is called symmetry energy

Where T3i and T3

j denote the isospin T3 of the particles i and j, i.e ½ for protons and -1/2 for neutrons.

.rprr ipr )(4))((43

2

)2(

1),,( tiLt

iiee

Lt

N

iV

M ii

1 2H

2p

And Potential is as: VVVVVVSymmdiColYukSkyrmeTot

)(1

33

0

6 ji

jisymrrTTtV

Realization of symmetry energy in IQMD

Symmetry potential per nucleon:

Force for the potential is as:

Work-Done

Symmetry energy sensitive observables

Balance energy, ratio and difference of elliptical flow, pionsRatio, kaon ratio, Sigma Ratio, Transverse flow of IMFs

OUTLINE OF TALK



by using (1) Single and double n, p ratio (2) Concept of quasi-participant and

quasi-spectator matter (3) multiplicity of neutrons from high incident energy




Literature Highlights: Esym at low densities- Clustering Effects

S. Kowalski, et al., PRC 75 (2007) 014601.

Horowitz and Schwenk, Nucl. Phys. A 776 (2006) 55

Literature Highlights: Esym at low densities- Clustering Effects

Esym around saturation densities

soft EOS w/o MDI ：• gamma is in [0.61 - 1.22] region and L is in [57 -89.4] MeV, soft EOS with MDI ：•gamma is in [0.78 - 1.22] and L is in [66 - 89.4] MeV

Literature Highlights

Famiano and B. A. LiPRL 97(2006)052701PRL 78 (1997)1644

Catania Group BNV Calc.

Double ratio=

Literature highlights at low energy

Isospin Diffusion

Kinetic Energy Spectra

It is very important to see the distribution of protons and neutrons

0 15 30 45 60 75

0.1

1

0 15 30 45 60 75

0.1

1

0 5 10 15 200.4

0.6

0.81

0 5 10 15 200.4

0.6

0.81

=0.5

b = 2 fmE = 50MeV/A

Free Nucleons

Neutron Protons

Sn132+Sn132 Sn112+Sn112

dN/d

EK

=1.5

b = 2 fm

LCP's

0 4 8 12 16 20

0.1

1

IMF's

EK(MeV/A)

0 4 8 12 16 20

0.1

1

0 15 30 45 60 750.01

0.1

1

0 15 30 45 60 750.01

0.1

1

0 5 10 15 20

0.4

0.60.8

1

0 5 10 15 20

0.4

0.60.81

=0.5

b = 6 fmE = 50 meV/A

Free Nucleons

Neutron Protons

Sn132+Sn132 Sn112+Sn112

dN/d

EK

=1.5

b = 6 fm

LCP's

0 4 8 12 16 200.1

1

IMF's

EK(MeV/A)

0 4 8 12 16 200.1

1

S. Kumar, YGM* et al., Phys. Rev. C 84, 044620 (2011)

Single N/Z RatioExtended the study with impact parameter and more neutron rich system And for the different kind of fragments

N/Z ratio at E = 50 MeV/A

0.7

1.4

2.1

2.8

0 10 20 30 40 50 60 70 800.8

1.6

2.4

3.2

4.0

E = 50 MeV/Ab<5fm

RN/Z

i =0.5

i =1.5

Data

124Sn+124Sn

112Sn+112Sn

EK(MeV/A)

0 14 28 42 56 70

0.6

1.2

1.8

2.4

3.00 14 28 42 56 70

0 14 28 42 56 70

0 14 28 42 56 70

0.6

1.2

1.8

2.4

3.0

0.9

1.2

1.5

0.9

1.2

1.5

b = 2 fmE = 50 MeV/A

Free Nucleons

i=0.5

i=1.5132Sn+132Sn 112Sn+112Sn

RN/Z

b = 6 fm

LCP's

0 4 8 12 16 20

0.6

0.9

1.2

1.5 IMF's

EK(MeV/A)0 4 8 12 16 20

0.6

0.9

1.2

1.5

Double Ratio

Extended the study with impact parameter and more neutron rich systemDR(N/Z) ratio at E = 50 MeV/A

0 17 34 51 68 851.0

1.5

2.0

2.5

3.0

3.5

1.0

1.5

2.0

2.5

3.0

3.5

DR

(N/Z

)

EK(MeV/A)

=0.5 =1.5 (This work) Data MSU(2006) IBUU97_soft Imqmd_Soft(2008-11) BNV-Soft (2007) Data MSU(2006) IBUU04 (x=0)

1.0

1.5

2.0

2.5

3.0

3.5

1.0

1.5

2.0

2.5

3.0

3.5

0 15 30 45 60 751.0

1.5

2.0

2.5

3.0

0 15 30 45 60 751.0

1.5

2.0

2.5

3.0

b= 2 fm = 0.5

E = 50MeV/nucleon

b= 6 fm

DR

[(N

/Z) free]

= 1.5

EK(MeV/A)

Sn132&Sn124

Sn124&Sn112

Sn132&Sn112

Conclusions-1

Comparison with Single and double ratio leads to the prediction of Soft symmetry energy: means that asymmetric matter is soft.

Different fragments are sensitivite to the symmetry energy, but the symmetry energy is found to be weakly affected by the geometry of reaction systems or impact parameter at sub normal densities.

At higher Ek, the exchange between the symmetry energies is observed for the Liquid phase or fragments, but not for the gas state or free particles.


OUTLINE OF TALK








Isospin diffusion

TLF PLFNeck

n/p diffusion

Isospin drift & diffusion

ρ~1/8ρ0

ρ~ρ0

ρ~ρ0

n drift

Isospin drift

TLF PLFNeck

ρ/ρ

Esym vs ρ

Asy-S

tiff

Asy-Soft

Low ρρ0

Isospin equilibration

Long τint

Isospin translucency

Short τint

Proj

Targ

TLF

PLFPLF

TLFTLF

PLF

Colonna et al.; Danielewicz et al.

Participant-Spectator Matter: Symmetry energy and isospin migration

0.0

0.2

0.4

0.6

0.8

1.00 2 4 6 8 101.2 1.3 1.4 1.5 1.6 1.7

0.17

0.34

0.51

0.68

0 2 4 6 8 100.0

0.2

0.4

1.2 1.3 1.4 1.5 1.6 1.70.1

0.2

0.3

0.4

Spec.

/nucl.

b = 8 fm

Total neutrons Protons

i=0.5 i=1.5

Part./nucl.

124Sn+124Sn

b(fm) (N/Z)System

10-4

10-3

10-2

10-4

10-3

10-2

10-4

10-3

10-2

10-4

10-3

10-2

0 15 30 45 60 7510-4

10-3

10-2

0 15 30 45 60 7510-4

10-3

10-2

124Sn+124Snb = 0 fm

112Sn+112Snb= 0fm

b = 4 fm

Yie

ld/n

ucl.

Total Neutrons protons

Part. Spec.

EK (MeV/nucl.)

Yie

ld/n

ucl.

b = 6 fm

132Sn+132Sn

t = 200 fm/c

b = 8 fm

Search Observable for Isospin Migration

10-3

10-2

10-3

10-2

10-3

10-2

10-3

10-2

10-3

10-2

10-3

10-2

0 10 20 30 40 5010-4

10-3

10-2

0 10 20 30 40 5010-4

10-3

10-2

124Sn+124Sn

b = 0 fm

112Sn+112Sn

124Sn+124Sn

132Sn+132Sn

Pp-S

pP

n-S

nS

n-S

p

b = 0fm b = 4 fm b = 6 fm b = 8 fm

EK (MeV/nucl.)

Pn-P

p

10-3

10-2

10-3

10-2

10-3

10-2

10-3

10-2

10-3

10-2

10-3

10-2

0 10 20 30 40 50

10-3

10-2

0 10 20 30 40 50

10-3

10-2

b = 0 fm

112Sn+112Sn

124Sn+124Sn

b =4 fm

i=0.5

i=1.5

Pn+p-S

n+p

EK (MeV/nucl.)

b = 6 fm

b =8 fm

Conclusions-22. Activities…..

The neutrons to protons difference from participant/spectator matter is highly sensitive towards the isospin of the system along the whole geometry of the reaction

participant to spectator matter difference from neutrons/protons is particularly, sensitive towards the density dependence of symmetry energy at semi-peripheral geometry, which can act as a probe for isospin migration.


OUTLINE OF TALK








Experimental data from ALADIN 2000 Collaboration for Projectile spectator fragmentation at 600 MeV/nucleon

Defining the cut for projectile spectator fragmentation and Comparison with data

-2 -1 0 1 20

13

26

39

52

65

0 2 4 6 8 10 120

10

20

30

40

50

(a) Zbound

8 12 21 26 31 35 38 42

124Sn+natSn i=0.5

i =0.5

i=1.5

Zbound

b(fm)

(b)

dNn/

dY

Yred

Wid

thDi

st.

0 2 4 6 8 10

8

9

10

11

b (fm)

4

6

8

10

12

3

4

5

6

7

4

6

8

10

3

4

5

6

7

Mp

(a) 124Sn+natSn

data i =0.5

i =1.5

Mn

(b)

(c) 124La+natSn

(d)

0 10 20 30 40 504

6

8

10(e) 124Sn+124Sn

Zbound

0 10 20 30 40 503

4

5

6(f)

Checking the sensitivity with other Observables at PSF at 600 MeV/nucleon

1.0

1.2

1.4

1.6

1.8

0 10 20 30 40 501.0

1.2

1.4

1.6

Zbound

(a) 124Sn+natSn

i=0.5

i=1.5

R(n

/p)

(b) 124La+natSn

0 9 18 27 36 451.0

1.1

1.2

1.3

1.4

i = 0.5

i = 1.5

RD(n

/p)

Zbound

0 10 20 30 40 500

9

18

27

36

45(a) 124Sn

Mn

R(n/p) RD(n/p)

St

Zbound

0 10 20 30 40 500

9

18

27

36

45

(b) 124La Mn

R(n/p) RD(n/p)


soft symmetry energy from projectile spectator fragmentation (means Sub-saturation density), Which took place at 600 MeV/nucleon or high density zone.

Single ratio is more sensitive compared to multiplicity as well as double ratio, when isobars are studied, however, for isotopes, it was Double ratio.

Single ratio obtained the maxima or minima trend like multiplicity, But not from double ratio study.

S. Kumar, YGM, Phys. Rev. C 86, 051601R (2012)

OUTLINE OF TALK








K_asy is poorly known till date at Sub as well as supra saturation density, some Clue near -550 MeV from diffusion study

K_0 is well known near the saturation Density235+14, while varies vastly at high Densities from the study of collective flow, Multifragmentation, KAOS Collaboration, neutron star studies

Review is available in Kumar and Ma, NPA 898, 57 (2013)

Determination of K_asy

Z_bound dependence for LCPs and IMFs including neutronsand protons between them

LCPs IMFs

Z_bound dependence for free nucleons and LCPs including neutronsand protons between them

free nucleons LCPs

Determination of K_0

IMFs: HMD


Soft symmetry energy from isospin sensitive observable M_n with the Isospin part isobaric compressibility K_asy=-372 to -530 MeV from projectile spectator fragmentation region.

Hard momentum dependent equation of state with K= 380 MeV from Isospin insensitive observable M_imfs from projectile fragmentation region.

In projectile spectator fragmentation region, universal Z_bound dependence for free, LCPS and IMFs, while from projectile fragmentation region, no universality is maintained.

In projectile spectator fragmentation region, M_n are most sensitive to symmetry energy, while in PF region, LCPS are most sensitive.

Correlation is maintained between the free M_n from PSF with soft EOS and soft Symmetry energy with M_n within IMFs with Hard EOS and any symmetry energy.

S. Kumar, YGM*, Nucl. Phys. A 898, 57 (2013).

OUTLINE OF TALK








Pions ratio at high incident energies

Elliptical flow at high energy

0

50

100

150

200

0

10

20

30

IMF's

Fre

e n

ucleons

LCP's

(a)

(b)

0 20 40 60 80 100-2

0

2

4

6(c)

Time(fm/c)

0 20 40 60 800.0

0.6

1.2

1.8

Time (fm/c)

E = 50 MeV/nucl. E = 100 MeV/nucl. E = 200 MeV/nucl. E= 400 MeV/nucl. E = 600 MeV/nucl.

132Sn+132Sni= 0.5

b=2 fm

</ >

Specifying Observable for Supra-saturation density region during Fragmentation

0.8

1.2

1.6

2.0

2.4

0.8

1.2

1.6

2.0

2.4

0 200 400 6000.4

0.5

0.6

0.7

0.8

0 200 400 6000.8

0.9

1.0

1.1

(a-i) t = t@(./0)max

Free Nucleons

(a-ii) t = 200 fm/c

(b-i)

LCP's

Ebeam (MeV/nucleon)

R(N

/Z)

(b-ii)

1.2

1.4

1.6

1.8

0 200 400 6001.0

1.1

1.2

Free Nucleons

DR(N

/Z)

(a)

(b)

Ebeam (MeV/nucleon)

LCP's

Beam energy dependence of Single and Double Ratio

0 100 200 300 400 500 6000.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

Par

amet

er

Ebeam(MeV/nucleon)

i = 0.5

i = 1.5

Power law dependence of double ratio study

1.0

1.2

1.4

1.6

1.81.0 1.1 1.2 1.3 1.0 1.1 1.2 1.3

1.0

1.2

1.4

1.6

1.8

1.0

1.2

1.4

1.6

1.0

1.2

1.4

1.6

E = 50 MeV/nucl.

Free Nucleons

DR(N

/Z)

(a) (b)E = 100 MeV/nucl.

(c)E = 150 MeV/nucl.

(d)

E = 200 MeV/nucl.

1.0 1.1 1.2 1.31.0

1.2

1.4

1.6(e)E = 400 MeV/nucl.

DR(N/Z)System

1.0 1.1 1.2 1.31.0

1.2

1.4

1.6(f)E = 600 MeV/nucl.


The double neutron-to-proton ratio from free nucleons is highly sensitive to the symmetry energy, incident energy, and isospin asymmetry of the system.

The sensitivity of the neutron-to-proton double ratio from LCPs to the nuclearsymmetry energy is almost beam-energy independent above 200 MeV/nucleon. The same trend is observed for the single Pions ratio above 1 GeV/nucleon.

The sensitivity of the soft symmetry energy to the ratio parameter is strongly affected by the choice of times, which is not true for the stiff symmetry energy.

neutron-to-proton double ratio from free nucleons can act as a useful probe to constrain the high-density behavior of the symmetry energy. Experiments are planned at MSU, GSI, RIKEN, and FRIB to determine the high-density behavior ofthe symmetry energy by using the neutron-to-proton ratio.


OUTLINE OF TALK








Literature review with different clusterization methods

In order to study the NEOS of symmetric nuclear matter:Spatial Coelesence Method (famous as MST)-Most commonly usedSpatial Coelsence method with Binding energy cut (MSTB) PRC 83, 047601 (2011)Energy Minimization technique (SACA). J. of Comp. Phys. 162, 245 (2000)Early cluster recognization Algorithm (ECRA). PLB 301, 328 (1993)

RI

RJ

DMIN P

IP

JP

MIN

Effect on the symmetric matter NEOS

Different calescence method found to affect drastically the symmetric Matter equation of state. The binding energy effects were found Uniquely important

PRC 83, 047601 (2011)

PR

C 83, 047601

(2011)

JPG

37, 015105 (2010)

Literature review with different clusterization methods

In order to study the NEOS of asymmetric nuclear matter:Spatial Coelesence Method (famous as MST)-Most commonly used Isospin_MST Method is used. PRC 85, 051602 (2012).

RI

RJ

DMIN

PI

PJ

PMIN

In Iso-MST, the relative difference was nn,pp, pn dependent:

Effect of Iso-MST on isospin sensitive observablesP

RC

85, 051602 (2012)

Iso-MST found to affect the yield of isospin sensitive particles as Well as their ratios and isoscaling also.

Problems with simple MST and Iso-MST method Can not answer the time evolution of formation of fragments: It

gives a single large fragment in high density region. Light and medium mass fragments are formed after several hundred fm/c.

This is due to the formation of artificial unstable fragments only due to the cut on position and momentum of nucleons.

In order to check the stability of fragments and to check the effect on isospin physics, in addition to position and momentum cut, we have tried to apply the binding energy cut as follow:

with E_bind= -4.0 MeV if Nf > 3 (One can also use the realistic binding energy for more accuracy) = 0.0 otherwise The method will help to break the loosely bound fragments in high density region.

To check the effect of MSTB towards the isospin physics:

First we compared the results with experimental findings available in the literature and then

The effect is studied on the isospin sensitive particles n, p, 3H, 3He yield and directed flow.

Comparison with Experiments

0 2 4 6 8 1010-4

10-2

100

102

104

0 5 10 15 20 25

10-2

10-1

100

101

0 10 20 30 400.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.3 0.6 0.90.0

0.3

0.6

0.9

197Au+197Au 400 MeV/nucleonData-1997

MST MSTB Data

Z

dN/d

Z

ZM

ax/ZPro

jectile

MIM

Fs

Zbound

124Sn+124Sn50 MeV/nucleon,b =2 fm Data-2003

Z

124Sn+natSn600 MeV/nucleon Data-2011

Zbound/ZProjectile

No significant improvement is observed from the fragment spectra.

Importance of MSTB can be seen clearlyFrom bottom two panles, where MSTB is able to explain the data upto 70% region point to point, however little deflection in 30%region, while Simple MST failed badly throughout all The Zbound region. By assessing the importance of MSTB method In intermediate energies, it is important to check its Sensitivity towards the isospin physics.

Effect on Time Evolution of different kind of fragments

0

60

120

180

240

0 90 1802703604500 90 180270360450

0

60

120

180

240

0

5

10

15

20

0

5

10

15

20

IMFs

LCPs

i = 0.5

b = 2 fmE = 50 MeV/A

124Sn+

124Sn

FN

112Sn+

112Sn

0 90 1802703600

2

4

6 MST MSTB

Time(fm/c)0 90 180270360450

0

2

4

6

In MSTB, free nucleons becomesstable as early as 100 fm/c, which is quit good compared to MST.

Enhanced production of free Nucleons and reduced productionof fragments with MSTB.

Free nucleons and LCPs are mostsensitivity to MSTB method.

MSTB is sensitive with isospin of the reaction system.

We decided to study the effect of binding energy clusterization method on the isospin in term of n, p, 3H, 3HeParticles.

Effect on rapidity distribution of isospin sensitive particles

-2 -1 0 1

0

3

6

9

-2 -1 0 1 20.0

0.2

0.4

0.60

1

2

3

4

5

-2 -1 0 10.0

0.1

0.2

0.3

d(3 H

-3 He)/dy

d(n

-p)/dy1H

Yie

ld (arb

. units

)

Sn112 Sn124

MST MSTB

3He

1n

3H

Yred

Neutrons and 3H production with MSTB is more sensitive compared to protons and 3He with the isospin of the system.

Mid-rapidity region is more sensitive to MSTB method.

MSTB affect the production of particles more compared to Iso-MST.

Differential rapidity distribution of particles is affected more for neutron rich System 124Sn+124Sn.

Effect on kinetic energy spectra of isospin sensitive particles

0 10 20 30 40 50 60

1E-3

0.01

0.1

0 10 20 30 40 50 60 701E-4

1E-3

0.01

0.1

0.1

1

0 10 20 30 40 50 601E-3

0.01

0.1

d(3 H

-3 He)/dE K

d(n

-p)/dE K

1H

Yie

ld (arb

. units

)

Sn112 Sn124

MST MSTB

3He

1n

3H

EK (MeV/nucleon)

Kinetic energy spectra of neutrons and differential (n-p) is most sensitive to MSTB and isospin physics collectively at lower kinetic energy, however, at high kinetic energy, spectra is more sensitive towards the isospin physics compared to MSTB method.

Even low yield of 3H and 3He at incident energy of 50 MeV/nucleon, the Binding energy effects are significantly visible at low kinetic energy, but, it is Hard to separate the isospin effects.

Indicating free particles spectra at low incident energy can affect the isospin physics in the presence of MSTB method.

Effect on kinetic energy spectra of Single ratio

1.0

1.2

1.4

1.6

1.8

1.0

1.2

1.4

1.6

1.8

0 14 28 42 560.5

1.0

1.5

2.0

0 14 28 42 56 700.5

1.0

1.5

2.0

3 H/3 H

e

EK(MeV/nucleon)

i=0.5

b = 2 fm

n/p

112Sn+112Sn

MST MSTB

124Sn+124Sn

More isospin and MSTB method effectfor neutron rich system through out the Kinetic energy spectra are observed.

The higher single ratio with simple MST method is due to the decreased production of Protons and not much neutrons due to the symmetry energy. The binding energy Method enhanced the production of Neutrons to greater extent. So, it is important to include the binding energy effects for proper understanding of isospin effects due to the symmetry energy.

No any systematic is observed from 3H/3He ratio due to the less production of particles at 50 MeV/nucleon Incident energy.

Effect on kinetic energy spectra of Double ratio

The double ratio is affected greatly in low and intermediate kinetic energy region.

As we have seen from the rapidity distribution figure, the MST method yields different protons yields for 112Sn and 124Sn with MST method, while with MSTB method, the yield of protons production is least affected for 112Sn and 124Sn. So even by taking the Double ratio with MST method, one can not cancel completely the Coulomb effects, which can be easily done by using the yield of Protons with MSTB. This can help to deal the Isospin effects in term of symmetry energy with Accuracy.

In actually practice, the MSTB method suggests the decrease in the DR(n/p) compared to MST.

0 10 20 30 40 50 60 701.0

1.2

1.4

1.6

1.8

DR (n/p

)

EK(MeV/nucleon)

MST MSTB

b= 2 fm

E = 50 MeV/nucleon

N/Z dependence of different particles at 50 MeV/nucleon

All the lines are fitted with power law aX^b. In the figures, the values are slope b, which are used to check sensitivity.

With increase in N/Z, neutrons are more sensitive And protons are less sensitive to MSTB compared to MST, which is logicallytrue as in the reaction systems neutrons are increasing and protons are constant.

Some of the 3H (3He) produced with MST were greatly unstable and hence the yield is decreased with MSTB. 3He is found more unstable that 3H.

n/p is more sensitive to N/Z of the systemand MSTB method compared to 3H/3He at 50 MeV/nucleon.

20

30

40

50

1.0

1.5

2.0

2.5

3.0

1.2 1.3 1.4

1.2

1.4

1.6

1.2 1.3 1.4 1.5

1.4

1.6

1.8

2.03H

/3He

n/p

N P

MST MSTB

-0.20

-0.72

1.24

N/Z

i=0.5

b = 2 fm

Yie

ld

1.20

3H 3He

MST MSTB

-1.06

-0.92

0.93

1.035

MST MSTB

1.45

1.94

1.81

1.88

Slope parameter with incident energy for n/p and 3H/3He

The fitted parameter is plotted with incident Energy. The sensitivity of n/p is smoothly decreasing with incident energy as well as with MST and MSTB method.

The sensitivity of 3H/3He has a zig zag behavior with MST and MSTB along the incident energy.

The sensitivity between MST and MSTB results of 3H/3He is increasing with incident energy.

0 100 200 300 400 500 600

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Para

mete

r

Ebeam(MeV/nucleon)

n/p 3h/3he

MST MSTB

Sensitivity of MST and MSTB towards Flow parameter

-1.5 -1.0 -0.5 0.0 0.5 1.0-20

-15

-10

-5

0

5

10

15

-1.5 -1.0 -0.5 0.0 0.5 1.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-20

-15

-10

-5

0

5

10

15

Yred

i=0.5100 MeV/nucleon124Sn+124Sn

b = 2 fm

PX/A

(M

eV/c)

1n 1H

3H

The rapidity distribution of Px/A for different particles is shown at 100 MeV/nucleon for 124Sn+124Sn system.

The slope of the plot between -0.5 to 0.5 acts as a flow parameter.At 100 MeV/nucleon, 3H are found to affect more by the MSTB method of clusterization.

Conclusions-6

From the physics point of view, stability of fragments is an important issue.

The advantage of stability of free nucleons at relatively early time i.e. 100 fm/c.

The multiplicity of isospin sensitive particles pair n-p, 3H-3He is greatly influenced by the binding energy cut in the clusterization method.

The binding energy clusterisation method is important when we study the isospin effects from mid-rapidity region, low kinetic energy region.

The single ratio is significantly affected by the MSTB method. The sensitivity is increased towards the more neutron rich system. This is clearly indicating the importance of binding energy in clusterization for the study of isospin physics.

The double ratio with the MSTB method is more accurate for the study of isospin effects due to symmetry energy as compared to MST method. MSTB is affecting the results of flow also with N/Z of the system for the isospin sensitive particles n,p, 3H, 3He, showing its important in determining the asymmetric matter equation of

state. (submitted)

Summary

The soft symmetry energy is realized from two different experimental studies of 2009 and 2012.

The new observable for the study of isospin migration as well as observables for the experimental study is introduced.

The new debate on the compressibility of isospin symmetric and asymmetricnuclear matter sensitive observables is explored.

The detailed analysis of neutrons to protons ratio towards the supra saturation density is presented.

Importance of binding energy in clusterization method for the stability of fragments and isospin physics importance is elaborated.

outline of talk

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