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 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?

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 Strange and Quark EoS‘s Observations of: masses radii (X-ray bursts) rotation periods etc

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

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

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)

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.

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

Constraints on the slope of the symmetry energy from Structure and reactions A. Carbone, et al., PRC81, 043101 (2010) heavy ion collisions

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))

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