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

2. Equation-of-State and Symmetry Energy
BW mass formula
symmetry energy
density-asymmetry dep. of nucl.matt.
neutron matter EOS
Symmetry energy:
Diff. neutron and symm matter
asy-stiff
asy-soft
rB/r0
stiff
soft
Fairly well fixed! Soft
EOS of symmetric nuclear matter
density r
asymmetry d
Investigate dependence in large part of (r,d)-plane
Rather uncertain!
esp. at high density
Isovector tensor correlations?

3. Constraints on EoS via Astrophysical Observation and Laboratory Experiments
Model for structure of NS
Heavy ion collisions

4. Constraints on EoS via Astrophysical Observation and Laboratory Experiments
Model for structure of NS
Trümper Constraints (Universe Cluster, Irsee 2012)
Hadronic EoS‘s
Strange and Quark EoS‘s
Observations of:
masses
radii (X-ray bursts)
rotation periods
etc

5. Heavy ion collisons Levels of description of evolution
non-equilibrium
Levels of description of evolution
from initial to final state:
initial final
thermal
Thermal expansion
hydrodynamics
transport theory

6. BUU transport equation
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
Spectral fcts, off-shell transport, quasi-particle approx.
QPA
Transport theory is on a well defined footing, in principle

7. 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 one-body 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)

8. Present constraints on the symmetry energy from heavy ion collisions
p+/p- ratio,
Feng, et al.
Au+Au, elliptic flow, FOPI
Esym(r) [MeV]
Fermi energy HIC, various observables
r/r0
p+/p- ratio
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.

9. Investigations on the Nuclear Symmetry Energy
Hadronic
EoS‘s
Neutron star
Constraints;
allowed region
Neutron star Mass-Radius relation
heavy ion collisions in the Fermi energy regime
Isospin Transport properties, (Multi-)Fragmentation
Esym (rB) (MeV)
rB/r0 1 2 3
Asy-stiff
Asy-soft
M. Colonna, A. Chbihi
S. Typel, M. Oertel, N. Chamel
G. Baym (ECT* Colloquium)
p, n
rel. heavy ion collisions
Isotopic ratios of
flow, particle production
Nuclear structure
(neutron skin thickness, Pygmy DR, IAS)
Slope of Symm Energy
D. Roissy,
An interesting day !
P. Russoto

11. Constraints on the slope of the symmetry energy from Structure and reactions
A. Carbone, et al., PRC81, (2010)
heavy ion collisions

12. 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 many-body approaches
C. Fuchs, H.H. Wolter, EPJA 30(2006)5
The symmetry energy (at T=0) as the difference between symmetric and neutron matter: SE
Different proton/neutron effective masses
Isovector (Lane) potential: momentum dependence
SE ist also momentum dependent  effective mass
data
m*n < m*p
m*n > m*p
r/r0
k [fm-1]
Why is symmetry energy so uncertain in microscopic models?
 In-medium r mass, and short range isovector tensor correlations (e.g. B.A. Li, PRC81 (2010))

13. Constraints on EoS via Astrophysical Observation and Laboratory Experiments
Model for structure of NS
Liquid-gas
phase transition
Quark-hadron
SIS
Z/N 1
neutron stars
Supernovae IIa
Isospin degree of freedom