Workshop on Nuclear Structure and Astrophysical Application, 3nd Thexo meeting, ECT*, Trento, July 8-12, 2013

Workshop on

Nuclear Structure and Astrophysical Applications

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)

...)(O)(E)(EA/),(E 42BsymBnmB

pn

pn

Equation-of-State and Symmetry Energy

pair22

s3/4

C3/1

sv )ZN/()ZN(aA)1Z(ZaAaaA/)Z,A(E BW mass formula

density-asymmetry dep. of nucl.matt.

stiff

soft

Fairly well fixed! Soft

EOS of symmetric nuclear matter

symmetry energy

asymmetry density

neutron matter EOS

Rather uncertain!esp. at high densityIsovector tensor correlations?

Investigate dependence in large part of -plane

Symmetry energy: Diff. neutron and symm matter

asy-

stiff

asy-soft

Model for structure of NS

Constraints on EoS via Astrophysical Observation and Laboratory Experiments

Heavy ion collisions

Model for structure of NS

Constraints on EoS via Astrophysical Observation and Laboratory Experiments

Observations of:massesradii (X-ray bursts) rotation periodsetc

Hadronic EoS‘s Strange and Quark EoS‘s

Trümper Constraints (Universe Cluster, Irsee 2012)

Heavy ion collisons

Levels of description of evolution from initial to final state:

initial final

thermal

Thermal expansion

hydrodynamics

transport theory

non-equilibrium

)'f1)(f1(ff)f1)(f1(ff

)pppp()2()(vvdvdvd)t;p,r(f)r(Ufm

p

t

f

2'12121'2'1

'2'1213

1221'2'12)p()r(

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 T

)p,x()*m*p(

)p,x(2)p,x(A

222

Im*pIm*m)p,x( s

)*p()*m*p( 022 QPA

Spectral fcts, off-shell transport, quasi-particle approx.

BUU transport equation

Transport theory is on a well defined footing, in principle

time distribution of collisions (energy integrated)

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 ?

Present constraints on the symmetry energy from heavy ion collisions

+/- ratioB.A. Li, et al.

Fermi energy HIC, various observables

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.

Esy

m(

) [M

eV]

Au+Au, elliptic flow, FOPI

+/- ratio,Feng, et al.

...)()()(/),( 42 IOIEEAIE BsymBB

Esy

m

M

eV)

1 2 30

Asy-stiff

Asy-soft

heavy ion collisions in the Fermi energy regime

Isospin Transport properties, (Multi-)Fragmentation

Investigations on the Nuclear Symmetry Energy

ZN

ZNI

Hadronic EoS‘s

Neutron star Constraints;allowed region

Neutron star Mass-Radius relation

Nuclear structure(neutron skin thickness, Pygmy DR, IAS)Slope of Symm Energy

0,K, p, nrel. heavy ion collisions

Isotopic ratios offlow, particle production P. Russoto D. Roissy,

S. Typel, M. Oertel, N. Chamel G. Baym (ECT* Colloquium)

M. Colonna, A. Chbihi

An interesting day !

A. Carbone, et al., PRC81, 043101 (2010)

Constraints on the slope of the symmetry energy from Structure and reactions

MeV2560L

heavy ion collisions

The symmetry energy (at T=0) as the difference between symmetric and neutron matter:

C. Fuchs, H.H. Wolter, EPJA 30(2006)5

matt.nuclmatt.neutrsym EEE

Rel, BruecknerNonrel. BruecknerVariationalRel. Mean fieldChiral perturb.

The Nuclear Symmetry Energy in different „microscopic“ models

The EOS of symmetric and pure neutron matter in different many-body approaches

SE

1

q

2

*q

k

U

k

m1

m

m

Different proton/neutron effective masses

Isovector (Lane) potential: momentum dependence

)UU()k(U protneutr21

Lane

SE ist also momentum dependent effective mass

data

m*n < m*p

m*n > m*p

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))

k [fm-1] 0

Model for structure of NS

Constraints on EoS via Astrophysical Observation and Laboratory Experiments

Liquid-gasphase transition

Quark-hadron phase transition

SIS

Z/N

1

0neutron stars

Supernovae IIa

Isospin degree of freedom