Toward a model-independent constraint of the high-density dependence of the symmetry energy

Abstract

Neutron-proton elliptic flow difference and ratio have been shown to be promising observables in the attempt to constrain the density dependence of the symmetry energy above the saturation point from heavy-ion collision data. Their dependence on model parameters like microscopic nucleon-nucleon cross-sections, compressibility of nuclear matter, optical potential, and symmetry energy parametrization is thoroughly studied. By using a parametrization of the symmetry energy derived from the momentum dependent Gogny force in conjunction with the T\'{u}bingen QMD model and comparing with the experimental FOPI/LAND data for 197Au+197Au collisions at 400 MeV/nucleon, a moderately stiff, x=-1.35 +/- 1.25, symmetry energy is extracted, a result that agrees with that of a similar study that employed the UrQMD transport model and a momentum independent power-law parametrization of the symmetry energy. This contrasts with diverging results extracted from the FOPI $\pi^{-}/\pi^{+}$ ratio available in the literature

Effects of the symmetry energy on the isovector properties of neutron-rich nuclei within a Thomas-Fermi approach

“…Actually there is a variety of neutron star properties which are sensitive to SE, that is the maximum mass value and the corresponding radius, the onset of the direct Urca process, the crust-core transition density and pressure e.t.c. [2,9] Recently, there is an extended theoretical [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,57,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,…”

Cross-checking the symmetry energy at high densities

“…Fig. 10 shows predicted neutron and proton elliptic flows in Au + Au reaction under the FOPI-LAND experimental conditions (here we use the data with b = 7.2 fm case) and geometry [20]. The experimental data was multiplied by a factor 1.15 owing to dispersion of the reaction plane [55].…”

“…To unscramble symmetry energy related experimental data, various isospin-dependent transport models are frequently used to probe the symmetry energy below and above saturation density [1,2]. With great efforts, the nuclear symmetry energy and its slope around saturation density of nuclear matter from 28 analysis of terrestrial nuclear laboratory experiments and astrophysical observations have been roughly pinned down [15], while recent interpretations of the FOPI and FOPI-LAND experimental measurements by different groups made the symmetry energy at supra-saturation densities fall into chaos [16][17][18][19][20][21][22]. It does not seem to be clarified why the nuclear symmetry energy at supra-saturation densities is so uncertain, maybe the effects of pion inmedium effects [23][24][25], the isospin dependence of inmedium nuclear strong interactions [26], the short-range tensor force [27,28] are some factors.…”

“…Unfortunately, effects of the above isospin-dependent SRC were seldom taken into account in most of currently used isospin-dependent transport models, while the latters have been frequently used to unscramble symmetry energy related experimental data [17,20,[39][40][41][42]. To extract information on the symmetry energy from experimental data, in this study, by considering both the effects of the isospin-dependent SRC and the important but often-overlooked in-medium baryon-baryon inelastic cross section in the isospin-dependent transport model, two unrelated experimental measurements are simultaneously re-analyzed.…”

Symmetry potential of theΔ(1232)resonance and its effects on theπ−/π+ratio in heavy-ion collisions near the pion-prod

“…Among the potential probes of the high-density symmetry energy, the π − /π + ratio in heavy-ion collisions has attracted much attention since it was first proposed [12]. Unfortunately, several model analyses [13][14][15][16][17][18] of some existing data have so far been inconclusive. Realizing the importance of thoroughly understanding all aspects of the π − N − ∆ dynamics in isospin-asymmetric matter especially since several experiments measuring the π − /π + ratio are cur- * Email: Bao-An.Li@Tamuc.edu rently underway at RIKEN [19] and NIRS [20] besides those planned at other facilities [21,22], significant efforts have been made recently in studying effects of the in-medium pion production threshold [23], pion meanfield [24][25][26][27], electromagnetic field [28], neutron-skin [29] and nucleon-nucleon short-range correlation [30,31] on pion production mostly at intermediate energies above the pion production threshold of about 300 MeV/A.…”