Date post: | 17-Jan-2016 |
Category: |
Documents |
Upload: | lisa-atkins |
View: | 215 times |
Download: | 0 times |
Constraints on the Symmetry Energy from Heavy Ion Collisions
Hermann WolterLudwig-Maximilians-Universität München
44th Karpacz Winter School of Theoretical Physics, and 1st ESF CompStar Workshop,
„The Complex Physics of Compact Stars“, Ladek Zdroj, Poland, 25.-29.2.08
Outline:
- the symmetry energy and its role for neutron stars
- knowledge of the symmetry energy
- Investigation in heavy ion collisions
- below saturation density: Fermi energies, diffusion, fragmentation
- high densities: relativistic energies; flow, particle production
- summary
Punchline:
- we identify several observables in heavy ion collisions which are sensitive to the symmetry energy
- however, the situation is not yet at a stage (experimentally and theoretically) to fix the symmetry energy
Collaborators:
M. Di Toro, M. Colonna, LNS, Catania
Theo Gaitanos, U. Giessen
C. Fuchs, U. Tübingen;
S. Typel, GANIL
Vaia Prassa, G. Lalazissis, U. Thessaloniki
Schematic Phase Diagram of Strongly Interacting Matter
Liquid-gas coexistence
Quark-hadron coexistence
SIS
Schematic Phase Diagram of Strongly Interacting Matter
Liquid-gas coexistence
Quark-hadron coexistence
Z/N
1
0
SIS
neutron stars
...)()()(/),( 42 IOIEEAIE BsymBB ZN
ZNI
Symmetry Energy: Bethe-Weizsäcker MassenformelE
sym
MeV
)
1 2 30
Asy-st
iff
Asy-soft
Asy-su
persti
ff
pairICsv AZNaAZZaAaAaZAE /)()1(),( 23/13/2
High density: Neutron stars
Around normal density:
Structure, neutron skins
heavy ion collisions in the Fermi energy regime
Theoretical Description of Nuclear Matter
Vij
Non-relativistic:
Hamiltonian H = S Ti + S Vij,; V nucleon-nucleon interaction
Relativistic:
Hadronic Lagrangian
y, nucleon, resonances
s,w, p,.... mesons 0
,...),,,,;(
,
ii
L
dx
dL
L
phenomenological microscopic
(fitted to nucl. matter) (based on realistic NN interactions
non-relativistic Skyrme-type Brueckner-HF (BHF)
(Schrödinger)
Relativistic Walecka-type Dirac-Brueckner HF (DB)
(Quantumhadrodyn.)
Density functional theory
Decomposition of DB self energy
...),(
ˆˆ2
1ˆˆ4
1ˆˆˆ2
1
ˆˆ
222
mesonsisovector
VVmWWΦmΦΦ
ΦgmVgiL
Density (and momentum) dependent coupling coeff.
,,,
),(),( 2
1
2
2
i
k
m
gk
i
i
i
ii
Dirac-Brueckner (DB) Density dep. RMF
(alternative: non-linear model (NL)
meson self interactions)
BF
Fsym E
Mff
E
kE
2
*
*
2*
2
2
1
6
1
No f 1.5 fFREE
f2.5 fm2 f 5f
FREE
PRC65(2002)045201
RMF Symmetry Energy: .contrib
28÷36 MeV
NL
NLρ
NLρδ
The Nuclear Symmetry Energy in different Models
The symmetry energy as the difference between symmetric and neutron matter:
stiff
soft
iso-stiff
iso-soft
empirical iso-EOS‘s cross at about
06.0
microscopic iso-EOS`s soft at low densities but stiff at high densities
C. Fuchs, H.H. Wolter, EPJA 30(2006)5,(WCI book)
Uncertainities in optical potentials
Isoscalar Potential Isovector (Lane) Potential
data
GSI SIS
LNS, GANIL, MSU
Incident energy of Heavy Ion Collision:
Low energy (Fermi regime):
Fragmentation, liquid-gas phase transition,
Deep inelastic
High energy (relativistic):
Compression, particle production, temperature.
Modificaion of hadron properties
Transport description of heavy ion collisions:For Wigner transform of the one-body density: f(r,p;t)
,fIfUfm
p
t
fcollp
Vlasov eq.; mean field 2-body hard collisions
AN
iii tppgtrrg
Ntprf
1
))((~))((1
);,(
Simulation with Test Particles:
effective mass
Kinetic momentum
Field tensor
Relativistic BUU eq.
)1)(1()1)(1(
)()2(
1
432432
43213412
124322
3
ffffffff
ppppd
dvdpdpdp
loss term gain term
11 1
12
3 4
flucIFluctuations from higher
order corr.;
stochastic treatment
fff
Data: Famiano et al. PRL 06Calc.: Danielewicz, et al. 07
soft
stiff
SMF simulations, V.Baran 07
Central Collisions at Fermi energies:
Investigation of ratio of emitted pre-equilibrium neutrons over protons
124Sn + 124Sn112Sn + 112Sn
Peripheral collision at Fermi energies: Schematic picture of reaction phases and possible observables
pre-equilibrium emission:
Gas asymmetry
Proton/neutron ratios
Double ratios
binary events:
asymmetry of PLF/TLF
transport ratios
ternary events:
asymmetry of IMF
Velocity corr.
isospin diffusion/transport
npnp
npnpnp
DD
j
//
// ),(Isospin current due to density and isospin gradients:
drift coefficients
diffusion coeffients
npD /
npD /
symIp
In
sympn
CDD
CIDD
4
4
Differences in tranport coefficients simply connected to symmetry energy
MeVA
Esym 32)( 0
asy-stiff
asy-soft
Density range in peripheral collisions
Opposite effects on drift and diffusion for asy-stiff/soft
Isospin Transport through Neck:
Imbalance (or Rami, transport) ratio:(i = proj/targ. rapidity)(also for other isospin sens.quantities) )(
)(
21
21
LLi
HHi
LLi
HHi
mixi
iR
Limiting values: R=0 complete equilibration
R=+-1, complete trasnparency
Discussed extensively in the literature, and experimental data (MSU)
e.g. L.W.Chen, C.M.Ko, B.A.Li, PRL 94, 032701 (2005)
V. Baran, M. Colonna, e al., PRC 72 (2005)
Momentum dependence important
Isospin Transport through Neck:
exp. MSU
Asymmetry of IMF
in symm. Sn+Sn collisions
Asymmetry of IMF in symm. Sn+Sn collisions I
MF MD
MI
Stiff-soft, 124
Stiff-soft, 112
Stiff-soft, 124
Stiff-soft, 112
Asymmetry of IMF in peripheral collision rather sensitive to symmetry energy, esp. for
1. MD interactions
2. when considered as ratio relative to asymmetry of residue
3. Effects of the order of 30%, sensitive variable!
Results from Flow Analysis (P. Danielewicz, R. Lynch,R.Lacey, Science)
Flow and elliptic flow described in a model which allows to vary the stiffness (incompressibility K), and has a momentum dependence
Deduced limits for the EOS (pressure vs. density) for symmetric nm (left).
The neutron EOS (i.e. the symmetry energy) is still uncertain, thus two areas are given for two different assumptions.
v2: Elliptic flowv1: Sideward flow
...2cos),(cos),(1(),,;(: 210 ttt pyvpyvNbpyNFlow
Asymmetric matter: Differential directed and elliptic flow132132Sn + Sn + 132132Sn @ 1.5 AGeV b=6fmSn @ 1.5 AGeV b=6fm
p
n
differential directed flow
differential elliptic flow
Difference at high pt first stage
Dynamical boosting of thevector contribution
T. Gaitanos, M. Di Toro, et al., PLB562(2003)
Proton-neutron differential flow
and analogously for elliptic flow
)()1(1
,)()()(
1)(
1
protonneutronforw
wpyF
i
yN
ii
xiyN
xpn
Pion production: Au+Au, semicentral
Equilibrium production (box results)
Finite nucleus simulation:
Tpnabs
abs
/)(2exp
~ 5 (NLρ) to 10 (NLρδ)
+
+
-
-
+
+
-
-W.Reisdorf et al. NPA781 (2007) 459
Transverse Pion Flows
Simulations:V.Prassa Sept.07
Antiflow:Decoupling of thePion/Nucleon flows
OK general trend. but:- smaller flow for both - and +-not much dependent on Iso-EoS
Kaon Production:
A good way to determine the symmetric EOS (C. Fuchs, A.Faessler, et al., PRL 86(01)1974)
Also useful for Isovector EoS?
-charge dependent thresholds
- in-medium effective masses
-Mean field effects
Main production mechanism: NNBYK, pNYK
Effect of Medium-Effects on Pion (left) and Kaon (right) Ratios
Inelastic cross section
K-potential (isospin independent)K-potential (isospin dependent)
Astrophysical Implications of Iso-Vector EOS
Neutron Star Structure
Constraints on the Equation-of-state
- from neutron stars: maximum mass
gravitational mass vs.
baryonic mass
direct URCA process
mass-radius relation
- from heavy ion collisions: flow constraint
kaon producton
Equations of State tested:
Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802
Neutron star masses and cooling and iso-vector EOS
Tolman-Oppenheimer-Volkov equation to determine mass of neutron star
Proton fraction and direct URCA
cooling neutrinofast %,11 :ld thresho
:processURCA direct
)( :neutrality charge and mequilibriu
y
enp
yZ
N y
e
sym
Onset of direct URCA
Forbidden by Direct URCA constraint
Typical neutron stars
Heaviest observed neutron star (now retracted)
Dir
ect
Urc
a C
oo
lin
g l
imit
Mas
s-R
adiu
s R
elat
ion
s
Gra
vita
tio
nal
vs.
Bar
yon
M
ass
Hea
vy I
on
Co
llis
ion
o
bse
vab
les
Constraints of different EOS‘s on neutron star and heavy ion observables
Max
imu
m m
ass
Summary:
•While the Eos of symmetric NM is fairly well determined, the isovector EoS is still rather uncertain (but important for exotic nuclei, neutron stars and supernovae)
•Can be investigated in HIC both at low densities (Fermi energy regime, fragmentation) and high densities (relativistic collisions, flow, particle production)
•Data to compare with are still relatively scarce; it appears that the Iso-EoS is rather stiff.
•Effects scale with the asymmetry – thus reactions with RB are very important
•Additional information can be obtained by cross comparison with neutron star observations