F. Sammarruca, University of Idaho Supported in part by the US Department of Energy. From neutron skins to neutron stars with a microscopic equation of state 10 th International Spring Seminar on Nuclear Physics Vietri sul Mare, May 21-25, 2010

Microscopic predictions of the energy/A in nuclear matter (EoS) are now especially important and timely. They support the rich experimental effort presently going-on to constrain the less known aspects of the nuclear EoS (in particular, IANM) The Facility for Rare Isotope Beams (FRIB) was recently approved. This program will have widespread impact, ranging from the physics of exotic nuclei to nuclear astrophysics (

Our project fits within this program and is broad-scoped: EoS (for SNM or IANM) Mean field Effective masses/effective cross sections, mean free path.. Properties of exotic nuclei…….. are all sensitive to different aspects of the same nuclear interaction and must be handled consistently.

Ab initio : realistic free-space NN forces, potentially complemented by many-body forces, are applied in the nuclear many-body problem. Most important aspect of the ab initio approach: No free parameters in the medium.

Our present knowledge of the nuclear force is the results of decades of struggle. QCD and its symmetries led to the development of chiral effective theories. But, ChPT is unsuitable for applications in dense matter. Relativistic meson-theory is a better choice. Our starting point : a realistic NN potential developed within the framework of a relativistic scattering equation (Bonn B). Also, pv coupling for pseudoscalar mesons.

The many-body framework: The Dirac-Brueckner-Hartree-Fock (DBHF) approach to (symmetric and asymmetric) nuclear matter. DBHF allows for a better description of nuclear matter saturation properties as compared with conventional BHF.

The typical feature of the DBHF method: Via dressed Dirac spinors, effectively takes into account virtual excitations of pair terms in the nucleon selfenergy. Repulsive, density-dependent saturation effect Z-diagram

Red: nuclear matter Dash: neutron matter Dash-dot: matter in beta equilibrium (n, p, ) EoS’s for stellar matter available at: arXiv: [nucl-th] (International Journal of Modern Physics E, in press) A quick overview of our EoS:

An overview of saturation observables:

RED: DBHF predictions Black: commonly used parametrizations B.A. Li and L.W. Chen. PRC72, (2005) The uncertainty in our knowledge of the EoS is apparent through the symmetry energy: For more recent constraints, see Tsang et al. (MSU), Trautmann, GSI.

From the theoretical standpoint, we must ask the following questions: What is the best way to proceed? Mean field models are popular. But the microscopic approach is more fundamental  higher predictive power. What about three-body forces? Should additional degrees of freedom be included at high density? Most likely yes, e.g. hyperons. But, NS maximum masses are reported to become (unrealistically?) small when strange baryons are included.

Z-diagram (virtual nucleon-antinucleon excitation)

A popular three-nucleon force diagram (attractive) But, consistency then requires: Two-meson exchange diagram involving the Delta isobar in the NN force (repulsive medium effect) Cancellation!

To explore how different handlings of TBF impact predictions of EoS-sensitive “observables”, we have looked at several microscopic “BHF + TBF” models from the work of Li, Lombardo, Schulze, Zuo. They are: BOB=Bonn B + micro. TBF N93=Nijmegen 93 + micro TBF V18= Argonne V18 + micro TBF UIX=Argonne V18 + phen. UIX vs. DBHF

The density-dependence of the symmetry energy and the neutron skin of 208-Pb. Symmetry energy as predicted by DBHF and BHF+TBF calculations.

Neutron skin (208-Pb) and symmetry pressure correlation with various microscopic models. L=symmetry pressure Constraints on L: Most recently: (M. Warda et al., arXiv: ) (Chen, Ko, Li, 2005)

What we have learnt from this exercise: Although microscopic models do not display as much spreading as phenomenological ones, there are large variations in the density dependence of the symmetry energy (and related observables.) A measurement of the neutron skin of 208-Pb with an accuracy of 0.05 fm (as it has been announced) would definitely be able to discriminate among EoS from microscopic models.

Moving to a system 18 orders of magnitudes larger and 55 orders of magnitude heavier… Neutron stars: BOB and DBHF share the same NN potential (Bonn B). Stronger repulsion in BOB comes from non-linear terms in TBF.

Present constraints cannot pin down the high-density behavior of the EoS. Nevertheless, we suggest that microscopic models allow for a deeper insight and should be pursued along with more stringent constraints.

Another link between IANM and the physics of neutron-rich nuclei: The close connection between the symmetry potential and the isovector part of the nuclear optical potential.

In transport models of HIC, particles drift in the presence of an average potential while undergoing two-body collisions. Isospin-dependent collision dynamics is included through the symmetry potential (and also Isospin-dependent effective cross sections (ECS)) Symmetry potential single p/n potential in iso-asymmetric matter.

Isospin-asymmetry dependence of single-n/p potentials: will separate n/p dynamics

Momentum dependence of single-neutron, single-proton potential in isospin-asymmetric nuclear matter:

Should be comparable with the isovector part of the optical potential: Shaded area:

In conclusion: Microscopic calculations of the EoS and stringent constraints from EoS-sensitive observables can reveal information about the nature of the underlying nuclear force and its behavior in the medium. With the wealth of experiments/analyses going on or planned for the near future, and coherent effort from theory, the prospects of a significant improvement in our knowledge of nuclear matter (especially its isospin asymmetries) are very good.

Our project is broad-scoped, in that it reaches out to a variety of systems Advancing our understanding of dense nuclear systems requires coherent effort from: Experiment Theory Observations Phenomenology