F. Sammarruca, University of Idaho Supported in part by the US Department of Energy. From Neutron Skins to Neutron Stars to Nuclear Reactions with a Self-Consistent and Microscopic Approach International Symposium on Nuclear Symmetry Energy Smith College, June 17-20, 2011

Microscopic calculations of the equation of state (EoS) + Empirical information from EoS-sensitive systems/phenomena = Powerful combination to constrain the in-medium behavior of the nuclear force (Broad-scoped project) 2

Brief overview of our work Nuclear matter predictions within the Dirac-Brueckner-Hartree-Fock method Applications to neutron skins, neutron stars Exploring model dependence Most recent/future work: applications to nuclear reactions (with Larz White, UI) 3

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. 4

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. The isospin dependence of the nuclear force Is constrained at the free-space level. 5 *

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. An efficient alternative to BHF + TBF models. 6

Z-diagram (virtual nucleon-antinucleon excitation) 7

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 8

We obtain the single-particle potentials self-consistently with the effective interaction. For isospin-asymmetric matter: s.p. potentials (by-product of EoS calculation): 9 *

EoS for SNM and NM, an overview: …WHICH LEADS TO: 10

RED: DBHF predictions Black: commonly used parametrizations (consistent with isospin diffusion data) The uncertainty in our knowledge of the EoS is apparent through the symmetry energy: For more recent constraints, see Tsang et al; Trautmann, GSI. 11

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 12

The density-dependence of the symmetry energy and the neutron skin of 208-Pb. Symmetry energy as predicted by DBHF and BHF+TBF calculations. 13 BHF+TBF models from: Li & Schulze, PRC78, (2008)

Neutron skin (208-Pb) vs. symmetry pressure with various microscopic models. L=symmetry pressure Constraints on L: Most recently: (M. Warda et al., PRC80, (2009)) (Chen, Ko, Li) 14 Even more recently (this workshop): L = 60 MeV (20)

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 (PREX??) would definitely be able to discriminate among EoS from microscopic models. 15

We explored the sensitivity of the A-A reaction cross section to medium effects and isospin asymmetries. Collisions of neutron-rich nuclei are useful to investigate, for instance, distribution of nuclear matter in nuclei. The reaction cross section is sensitive to both the nuclear densities and the NN collisions. 16

OPTICAL LIMIT (OLA) of GLAUBER MODEL: NN x-sections Nuclear densities 17

n and p densities in 208-Pb predicted through our EoS Neutron excess parameter S=0.17 fm Next, some sensitivity tests involving 208-Pb 18

40-Ca Pb 1 free-space NN xsections 2 phenomen. formula by Xiangzhou et al. 3 Our microscopic in-medium NN xsections 4 “mass scaling” applied to free-space NN x-sections Fermi momentum = 1.1 (1/fm)Fermi momentum = 1.3 (1/fm) 19

40-Ca+208-Pb E/A=100 MeV Blue: our microscopic in-medium NN cross sections Red: mass scaling applied to NN xsections in vacuum Effects from n/p asymmetry are included in the NN xsections. 20

Data by Licot et al.; E/A between 50 and 70 MeV. Ca and Ar neutron-rich isotopes on a Silicon target. Ca Ar Reaction cross section with neutron-rich isotopes: 21

IN SUMMARY: We performed a sensitivity study of the reaction cross section with a simple reaction model. We observed considerable model dependence of the reaction cross section with respect to medium effects Better data precision required to resolve those differences Important to be selective of an appropriate “laboratory” to discern specific effects 22

MAIN POINT OF THIS EXERCISE Parameter-free continuous pipeline from: Effective NN interaction Nuclear densities The EoS In-medium NN xsections Reaction x-section Free-space NN interaction 23

Main Conclusion USING CONSISTENTLY MICROSCOPIC INGREDIENTS IN THE MANY-BODY THEORY (STRUCTURE AND REACTION) MAXIMIZES THE PREDICTIVE POWER The microscopic approach is more fundamental: Realistic NN interactions reproduce scattering and bound state properties of the free 2N system. In-medium correlations are built-in through many-body techniques. Isospin dependence is included naturally. 24