The Symmetry Energy at Sub- and Supersaturation Densities in … · 2016-07-20 · The Symmetry Energy at Sub- and Supersaturation Densities in Heavy Ion Collisions Hermann Wolter

NuSYM11

Smith College, Northampton, Mass. June 17-20, 2011

The Symmetry Energyat Sub- and Supersaturation Densities in Heavy

Ion CollisionsHermann Wolter

Ludwig-Maximilians-University München

The Symmetry Energyat Sub- and Supersaturation Densities in Heavy

Ion CollisionsHermann Wolter

Ludwig-Maximilians-University München

NuSYM11

Smith College, Northampton, Mass. June 17-20, 2011

Points to discuss

explore the symmetry over a large range of densities with many probes

a satisfactory consistent picture (between different ob servables and betweendifferent groups) has not yet been achieved: it is bette r at subsaturation density butstill lacking at suprasaturation)

the momentum dependence of the symmetry energy (differenc e in neutron and proton effective masses) has to be considered for a reli able interpretation (and isstill controversial)

I report on work of the Catania reaction theory group and associated members:Massimo Di Toro, Maria Colonna, Vincenzo Greco, Joseph Rizzo, Carmelo Rizzo, Valentina Giordano, Lab. Naz. del Sud, CataniaVirgil Baran, University of Bucharest, RomaniaMalgorzata Zielinska-Pfabe, Smith Coll., USATheodoros Gaitanos, Univ. of GiessenVaia Prassa, Georgios Lalazissis, Aristotle Univ. The ssaloniki, GreeceTatiana Mikhailova, Dubna, Russia

Plan:• Relevance of symmetry energy to astrophysics• Overview over different probes at different energies• Analysis of important and illustrative cases

Astrophysical Connection

Hillebrandt, et al., Scient. Americ. 2006

Composition of the matter

collapse

post-bounce

density: log 10n [g/cm 3]entr

opy:

log

10s[

kB/b

aryo

n]

not uniform, but light and heavy clusters(nuclei embedded in the medium)

Symmetry energy plays an essential role in astrophysics

ρρρρ0000

MeV100T0 ≤≤

10/10 08 ≤≤− ρρρρρρρρ

6.0Y0 p ≤≤

Ranges of density, temperature, asymmetry in SN event

Liebendörfer, et al., NIX XI, 2010

EOS for use in Supernovae (and neutron stars): Cf. talk of Maria Voskresenskaya ( + S. Typel, G. Röp ke, et al.)

Parametrization of nuclearsymmetry energy of different stiffness (momentum dependentSkyrme-type) (B.A. Li)

Quantum Statistical model , T=1,4,8 MeV)

Single nucleusapprox. (Wigner-Seitz), RMF

Thermal Green Fct(quantumstatistical) model formedium dependence of clusters

+ gen RMF model (with explicitcluster degrees of freedom)

+ heavy nucleus in the medium (in Wigner-Seitz cell approx)

Comparison to low lowdensitiy SE determined in heavy ioncollisions(Natowitz et al., PRL 104 (2010))

The symmetry energy is finite at low density and temperat ures!

Reaction Mechanisms in Heavy Ion Collisions

Coulomb barrier to Fermi energies

Isospinmigration

Isospinfractionation,multifragm

central

ρρ

ρρ ∇

∂∂

+∇∝− IE

IEjj symsympn

)()(

“Diffusion” “Drift”

Asy-soft

Asy-stiff

Symmetry energy slope

Proton and neutron currents

Sensitive to Sym. Energy and slope depending on observable

peripheral



Isospinmigration


centralperipheral

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

E /

E0

angle

18O + 181Ta, 35 MeV / A

Z = 6

Z = 5

Z = 4

Z = 7

Z = 8

deep-inelastic



Isospinmigration


centralperipheral

deep-inelastic

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

E /

E0

angle

18O + 181Ta, 35 MeV / A

Z = 6

Z = 5

Z = 4

Z = 7

Z = 8

pre-equil. dipole



Isospinmigration


centralperipheral

deep-inelastic

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

E /

E0

angle

18O + 181Ta, 35 MeV / A

Z = 6

Z = 5

Z = 4

Z = 7

Z = 8

pre-equil. dipole

N/Z of PLF residue= isospindiffusion



Isospinmigration


centralperipheral

deep-inelastic

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

E /

E0

angle

18O + 181Ta, 35 MeV / A

Z = 6

Z = 5

Z = 4

Z = 7

Z = 8

pre-equil. dipole


N/Z of neck fragment and velocitycorrelations

Chimera 124Sn + 64N, 35 AMeV

neck fragmentswith largestasymmetry



Isospinmigration


centralperipheral

deep-inelastic

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

E /

E0

angle

18O + 181Ta, 35 MeV / A

Z = 6

Z = 5

Z = 4

Z = 7

Z = 8

pre-equil. dipole



pre-equilibriumlight particles



Isospinmigration


centralperipheral

deep-inelastic

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

E /

E0

angle

18O + 181Ta, 35 MeV / A

Z = 6

Z = 5

Z = 4

Z = 7

Z = 8

pre-equil. dipole



N/Z ratio of IMF‘s

Relativistic energies

Flow: directed and elliptic

p

nasystiffasysoft



Isospinmigration


centralperipheral

deep-inelastic

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

E /

E0

angle

18O + 181Ta, 35 MeV / A

Z = 6

Z = 5

Z = 4

Z = 7

Z = 8

pre-equil. dipole



2. N/Z ratioof IMF‘s



Productionof particles, ππππ,K

pn

asystiffasysoft



Isospinmigration


centralperipheral

deep-inelastic

0 10 20 300.0

0.2

0.4

0.6

0.8

1.0

E /

E0

angle

18O + 181Ta, 35 MeV / A

Z = 6

Z = 5

Z = 4

Z = 7

Z = 8

pre-equil. dipole


5. N/Z of neck fragment and velocitycorrelations

2. N/Z ratioof IMF‘s



Productionof particles, ππππ,K

pre-equilibriumlight particles

pn

asystiffasysoft

one-body pase space density: f(r,p;t)

[ ]σ,fIfUfm

p

t

fcollp =∇∇−∇+

∂∂

r

Vlasov eq.; mean field 2-body hard collisions

[ ])1)(1()1)(1(

)()2(

1

432432

43213412

124322

3

ffffffff

ppppd

dvdpdpdp

−−−−−

−−+Ω

=→

∫∫∫ δσπ

loss term gain term

flucIδ+Fluctuations from higherorder corr.;

stochastic treatment:SMF (stochastic mean field)

fff δ+=

effective mass

Kinetic momentum

Field tensor

Relativistic BUU eq.

[[[[ ]]]] coll*)p(

)r()r( I*)p,r(f*)m*mF*p(*p ====∂∂∂∂∂∂∂∂++++++++∂∂∂∂ µµµµ

µµµµµνµνµνµνννννµµµµ

µµµµ

µµµµµµµµµµµµ ΣΣΣΣΣΣΣΣ

−=

−=

pp

;mm*

s*

µµµµννννννννµµµµµνµνµνµν ΣΣΣΣΣΣΣΣ ∂∂∂∂−−−−∂∂∂∂====F

Quantum molecular dynamics QMD

(stochastic NN collisions)

Transport Description of Heavy Ion Collisions

Isopin diffusion

Imbalance (or Rami, transport) ratio:

ββββ asymmetry of residue (i=PLF,TLF)(also for other isospin sens.quantities) )(

)(R LL

iHHi2

1

LLi

HHi2

1mixi

i β−ββ+β−β=

Limiting values:R=0 complete equilibrationR=+-1, complete transparency

isospin transportthrough „neck“ in peripheral collisions

124Sn(H)+112Sn(L)

J.Rizzo, et al., Nucl. Phys. A806 (2008) 79 more equlibration (lower R) for longer interaction time ~ correlation with total energy loss

Simple equil. model

Ratio det. by interact. and relax. times

Isopin transport

isospin transportthrough „neck“ in peripheral collisions

124Sn(H)+112Sn(L)

experimental data(B. Tsang et al.

PRL 92 (2004) )

J.Rizzo, et al., Nucl. Phys. A806 (2008) 79

points toward a moderately stiff ( γγγγ~1) SE, but disagreement in detail

L.W.Chen, C.M.Ko, B.A.Li, PRL 94, 032701 (2005)

M.B. Tsang, et al., PRL 102 (2008)

Imbalance (or Rami, transport) ratio:

ββββ asymmetry of residue (i=PLF,TLF)(also for other isospin sens.quantities) )(

)(R LL

iHHi2

1

LLi

HHi2

1mixi

i β−ββ+β−β=

Limiting values:R=0 complete equilibrationR=+-1, complete transparency

ImQMD calculations, 112Sn +112Sn, 50 AMeV

Y.Zhang et al., arXiv:1009.1928

SMF

ImQMDLess dependence on impact parameter.

Similar conclusions in comparison with Antisymmetrized Mol. Dynamics (AMD):Colonna, Ono, Rizzo, PRC (2011)

Model dependence of imbalance ratio!

Analysis of differences BNV – QMD

more `explosive´dynamics:more `transparency´

6 fm8 fm

γ = 0.5

γ = 0.5

γ = 2

SMF = dashed linesImQMD = full lines

d<Z

>/dy

(per

eve

nt)

d<N

/Z>/

dy(p

er e

vent

)

Much less isospinmigration in ImQMD, Other sources of dissipation: Fragmentemission, fluctuation?

protons vs. neutrons124Sn + 124Sn 112Sn + 112Sn

asy-soft

asy-stiff

Early emitted neutrons and protons reflect difference in potentials in expanded source, esp. ratio Y(n)/Y(p).

more emission for asy-soft, since symm potential higher

124Sn + 124Sn112Sn + 112Sn

„Double Ratios“

SMF simulations, V.Baran 07

Data: Famiano, et al., PRL 06

asy-soft

asy-stiff

softer symmetryenergy closer to data

Y. Zhang, et al., arXiv (2011)

qualitatively as seenin ImQMD, butquantitatively weakerdependence on SymEn

Central collisions at Fermi energies: Ratios of emitte d pre-equilibrium particles

Momentum Dependence and Effective Mass Splitting

mn*>mp*asysoft (red)asystiff (blue)

asy-softmn*>mp* (red)mn*<mp* (blue)

M. Zielinska-Pfabe, IWM08

Sn+Sn, 50 AMeV

Effect of momentumdependence of symmetrymenergyas large as effect of asy-EOS itself.

Momentumdependence hererather strong

1

2

*

1−

∂∂

+=k

U

k

m

m

m qq

h

Un

,p(k

), ρ

=ρ

0

At high momentum m* splitting effect larger thanasy-stiffness

asy-stiff

asy-soft

Light isobar 3H/3He yields

ObservableObservable veryvery sensitive at high sensitive at high ppTT

to the mass splitting and to the mass splitting and notnot to the to the asyasy --stiffnessstiffness

197Au+197Au600 AMeVb=5 fm, y(0)≤≤≤≤0.3

• m*n>m*p

• m*n<m*p

V.Giordano, M.Colonna et al., PRC 81(2010)

asy-stiff

asy-soft

Crossing of the symmetry potentials fora matter at ρ≈≈≈≈1.7ρρρρ0

n/p ratio yields

Pre-equilibrium nucleon and light cluster emission at h igher energy

npdt3Heαααα7Li7Be

Particle Yields 136Xe + 124Sn, 32 AMeV

asy-soft EOSm*p> m*n (sop )

asy-soft EOSm*n> m*p (son )

asy-stiff EOSm*p> m*n (stp )

asy-stiff EOSm*n> m*p (stn )

Emission of light clusters


n/p and t/ 3He ratios as functions of transverse energy

green asy-soft EOS m* p> m*n (sop ) red asy-stiff EOS m* p>m*n (stp ) blue asy-stiff EOS with m* n>m*p,(stn)yellow asy-soft EOS with m* n>m*p (son )

Transverse energy (MeV/u)

0 0100 100

1

2

3

0

1

2

3

0

32 MeV/u 65 MeV/u

sop and stp n accelerate more than p, the ratio goes up. (There is a limit for first chance emission (be am+ Fermi)).stn and son decrease only. For t/ 3He goes down about beam energy (prob. statistics ).

t/3He ratios

More sensitivity to effective mass than to symmetry energ y!

136Xe+124Sn



0 0100 100

1

2

3

0

1

2

3

0

32 MeV/u 65 MeV/u

n/p ratios


0 0100 100

1

2

3

0

1

2

3

0

32 MeV/u 65 MeV/u

n/p ratiost/3He ratios, energy dependence

Asystiff, mn<mp

E= 32, 45, 65, 100, 150 AMeV

Effect larger at higher energy and high p t

Comparison of results for symmetry energy slope

extracted from Fermi energy collisions

Slope of Symmetry Energy

M.B.Tsang, et al., PRL102,122701(09)

Catania results,qualitativeS0=30 MeV

Agreement in general but differences in detail.

Point to different dynamics in the different approach es which should bebetter understood, as e.g. in Colonna et al., PRC 81 (2011)

Heavy Ion Collisions at Relativistic Energies: “Flow“

GlobalGlobalmomentummomentumspacespace

Fourier analysis of momentum tensor : „flow“

v2: elliptic flowv1: directed flow

..)2cos)b,y(vcos)b,y(v1(N)b,y,(N 210 +++= θθθθθθθθθθθθ

To investigate symmetry energy:

differences of flow ( more sensitive for clusters ):

or differential flow

(analogous for v 1, v2, ..)

FP2 γ=0.98(35)

Russotto, et al., PLB 697, 471 (2011)

Au+Au @ 400 AMeV, FOPI-LAND

stiff

soft

Recent study by Cozma, arxiv 1102.2728

band: soft vs. stiff eos of symmetric matter, robust probe

Differential elliptic flow

asystiff asysoft

m*n>m*p

m*n<m*p

Inversion of elliptic flowsbecause of inversion of potentials with effective mass

W. Reisdorf, ECT*, May 09

Indication of experimental effect

Au+Au, 400 AMeV

t-3He pair similar butweaker

Au+Au, 600 AMeV

Elliptic flow more sensitive, since determined by particl es that are emitted perp to the beam direction

V.Giordano, M.Colonna et al., arXiv 1001.4961, PRC81(2010)

Difference in neutron and proton potentials

1. „direct effects“: difference in proton and neutron (o rlight cluster) emission and momentum distribution

2. „secondary effects“: production of particles, isospin partners ππππ-,+, K0,+

NππππNΛΛΛΛK

ΛΛΛΛK

NN N∆∆∆∆

in-mediumin-elastic σσσσ,,,,

K and ΛΛΛΛpotential (in-medium mass)

∆∆∆∆ in-mediumself-energiesand width

ππππpotential,

G.Ferini et al.,PRL 97 (2006) 202301

asyEOSstifferwithdecrease)(Y)(Y

pn

,

,0

↓↓⇒⇒↓ +

−

+++

−

ππππππππ

∆∆∆∆∆∆∆∆1. Mean field effect: U sym more repulsive

for neutrons, and more for asystiff pre-equilibrium emission of neutron, reduction of asymmetry of residue

2. Threshold effect, in medium effectivemasses: m*

N,, m*∆∆∆∆, , , , contribution of symmetry

energy; m *K, models for K-potentials

( )thin ss −= σσσσσσσσ

stiffnessasywithincrease −↑+

−

ππππππππ

0,K, +±ππππp, n

Particle production as probe of symmetry energy

MDI, x=0, mod. soft Xiao,.. B.A.Li, PRL 102 (09)MDI, x=1, very softNLδδδδ, stiff Ferini, Gaitanos,.. NPA 762 (05)NL, , , , soft, no Esymγγγγ=2, stiff Feng,… PLB 683 (10)SIII, very soft

FOPI, exp

Pion ratios in comparison to FOPI data (W.Reisdorf et al. NPA781 (2007) 459)

Contradictory results of different calculations;

Reason: Treatment of ∆∆∆∆ dynamics?

FromFrom soft to soft to stiffstiff fromfrom lowerlower to to upperupper curvescurves ::Stiffer asy-EOS larger ratio!Threshold dominates mean field effect; largerat lower energies

Kaon ratio still a bit more sensitive probe:~15% difference betw. very soft and stiffsmall but perhaps measurable!double ratio data by FOPI (Lopez, et al.,

PRC75 (07)

Effect reduced in finite nuclei (pre-equilemission reduces asymmetry)

Kaons a good probe for the EOS – also for the Symmetry Ene rgy?

Kaons are a more sensitive and clean probe of the high density EOS. Demonstrated by Fuchs, et al., PRL 86 (01), C.M. Ko & J . Aichelin, PRL55(85) for symmetric matter in comparison with KAOS data.

Kaons are closer to threshold , come only from high density , havelarge mean free path , small width :

Also a probe for the symmetry energy for ratio of differ entcharge states, K 0/K+?

G.Ferini et al.,PRL 97 (2006) 202301, V. Prassa, et al ., NPA 832 (2010)

132Sn+124

Sn

Au+Au, 1 AGeV, central

Inclusive multiplicities

132Sn+124

SnNuclear matter (box calculation)

+

−

ππππππππ

+KK 0

• Investigated different probes for the SymmetryEnergy in heavy ion collisions with transport theoryat different energy (density) ranges

• Explore the sensitivity to the ingredients (asy-EOS, momentum dependence of SymEn, medium, esp. isospin dependence of cross sections)

• Still considerable differences between different codes. Continue code comparison initiative (?)

• Consistent description of many observablesmandatory, also from structure and astrophysics

• Many knotty problems!

• Investigated different probes for the SymmetryEnergy in heavy ion collisions with transport theoryat different energy (density) ranges

• Explore the sensitivity to the ingredients (asy-EOS, momentum dependence of SymEn, medium, esp. isospin dependence of cross sections)

• Still considerable differences between different codes. Continue code comparison initiative (?)

• Consistent description of many observablesmandatory, also from structure and astrophysics

• Many knotty problems!

Summary and Outlook:Summary and Outlook:

Thank you!

Trento, Duomo

Documents

The Symmetry Energy at Sub- and Supersaturation Densities in … · 2016-07-20 · The Symmetry Energy at Sub- and Supersaturation Densities in Heavy Ion Collisions Hermann Wolter