Transcript Folie 1

Workshop on
Nuclear Structure and Astrophysical Applications
„EOS day“ (Thursday, July 11)
Convenors: F. Gulminelli (Caen), Y. Leifels (GSI)
 chairpersons: H. Wolter (LMU Munich), H. Leeb (TU Wien)
Workshop on Nuclear Structure and Astrophysical Application,
3nd Thexo meeting, ECT*, Trento, July 8-12, 2013
Equation-of-State and Symmetry Energy
BW mass
formula
densityasymmetry dep.
of nucl.matt.
E ( A , Z ) / A  av  a s A
1 / 3
 aC Z ( Z  1 ) A
E (  B ,  ) / A  E nm (  B )  E sym
4 / 3
 a s ( N  Z ) /( N  Z )   pair
2
symmetry energy
2
4
(  B )  O (  )  ...
2
 
n  p
n  p
neutron matter EOS
Symmetry energy:
Diff. neutron and symm matter
EOS of symmetric
nuclear matter
asy-soft
B/0
Fairly well fixed! Soft
Investigate dependence
in large part of (,)-plane
Rather uncertain!
esp. at high density
Isovector tensor correlations?
Constraints on EoS via Astrophysical Observation and Laboratory Experiments
Model for structure of NS
Heavy ion collisions
Constraints on EoS via Astrophysical Observation and Laboratory Experiments
Model for structure of NS
Trümper Constraints (Universe Cluster, Irsee 2012)
Hadronic EoS‘s
Observations of:
masses
radii (X-ray bursts)
rotation periods
etc
Strange and Quark EoS‘s
Heavy ion collisons
non-equilibrium
Levels of description of evolution
from initial to final state:
initial
final
thermal
Thermal expansion
hydrodynamics
transport theory
BUU transport equation


 (p)  
p  (r )

 f  U ( r )  f ( r , p; t ) 
t
m
f
f



3
d
v
d
v
d
v
v

(

)
(
2

)
 ( p 1  p 2  p 1'  p 2 ' )
2
1
'
2
'
21
12

1'
f 2 ' ( 1  f1 )( 1  f 2 )  f1 f 2 ( 1  f1' )( 1  f 2 ' )

Can be derived:
 Classically from the Liouville theorem
collision term added
 Semiclassically from THDF
(and fluctuations)
 From non-equilibrium theory (Kadanoff-Baym)
collision term included
mean field and in-medium cross sections
consistent, e.g. from BHF
T
T
T
Spectral fcts, off-shell transport, quasi-particle approx.
A( x , p ) 
2 ( x ,p )
( p * m * )   ( x , p )
2
2
2

 ( x , p )  m * Im  s  p  * Im 
QPA
  ( p * m * )  ( p * )
2
2

Transport theory is on a well defined footing, in principle
0
T
Code Comparison Project:
Workshop on Simulations of Heavy Ion Collisions at Low and Intermediate
Energies, ECT*, Trento, May 11-15, 2009
 using same reaction and physical input (not neccessarily very realistic, no symm energy))
 include major transport codes
 obtain estimate of „systematic errors“
transverse
flow
 agreement for flow and other onebody observables reasonable,
but perhaps not really good enough to
make detailed conclusions
 symmetry effects are order of
magnitude smaller: hope that
differences are less sensitive (?)
 origin of differences: collisions ?
time
distribution of
collisions
(energy
integrated)
Present constraints on the symmetry energy from heavy ion collisions
+/- ratio,
Au+Au,
elliptic flow,
FOPI
Fermi energy HIC,
various observables
Esym() [MeV]
Feng, et al.
+/- ratio
/0
B.A. Li, et al.
Moving towards a determination of the symmetry energy in HIC
but at higher density few data
and some difficulty with consistent results of simulations for
pion observables.
Investigations on the Nuclear Symmetry Energy
E (  B , I ) / A  E (  B )  E sym (  B ) I  O ( I )  ...
2
heavy ion collisions in the Fermi energy
regime
4
I 
Isospin Transport properties,
(Multi-)Fragmentation
Neutron star
Constraints;
allowed region
N Z
N Z
Asy-stiff
Esym (B) (MeV)
Neutron star Mass-Radius relation
M. Colonna, A. Chbihi
Hadronic
EoS‘s
S. Typel, M. Oertel, N. Chamel
G. Baym (ECT* Colloquium)
Asy-soft
0
1
B/0
2
Nuclear structure
(neutron skin
thickness, Pygmy DR,
IAS)
Slope of Symm Energy
D. Roissy,
An interesting day !
rel. heavy ion collisions
p, n

 ,0
3
 ,K
Isotopic ratios of
flow, particle production
P. Russoto
Constraints on the slope of the symmetry energy from Structure and reactions
A. Carbone, et al., PRC81, 043101 (2010)
heavy ion collisions
L  60  25 MeV
The Nuclear Symmetry Energy in different „microscopic“ models
Rel, Brueckner
Nonrel. Brueckner
Variational
Rel. Mean field
Chiral perturb.
The EOS of symmetric and pure
neutron matter in different manybody approaches
C. Fuchs, H.H. Wolter, EPJA 30(2006)5
The symmetry energy (at T=0) as the
difference between symmetric and
neutron matter:
E sym  E neutr . matt  E nucl
SE
. matt
SE ist also momentum dependent  effective mass
Different
proton/neutron
effective masses
m*n < m*p

m U q 
 1  2

m
 k k 

*
mq
datam*n > m*p
k [fm-1]
1
Isovector (Lane)
potential: momentum
dependence
U Lane ( k ) 
1
2
( U neutr  U prot )
/0
Why is symmetry energy so uncertain in microscopic models?
 In-medium  mass, and short range isovector tensor correlations (e.g. B.A. Li, PRC81 (2010))
Constraints on EoS via Astrophysical Observation and Laboratory Experiments
Model for structure of NS
Quark-hadron
phase
transition
Liquid-gas
SIS
phase
transition
1
0
Supernovae
IIa
Z/N
Isospin degree of
freedom
neutron stars