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Register a new userThe ASY-EOS experiment at GSI: investigating the symmetry energy at supra-saturation densities
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The elliptic-flow ratio of neutrons with respect to protons in reactions of neutron rich heavy-ions systems at intermediate energies has been proposed as an observable sensitive to the strength of the symmetry term in the nuclear Equation Of State (EOS) at supra-saturation densities. The recent results obtained from the existing FOPI/LAND data for $^{197}$Au+$^{197}$Au collisions at 400 MeV/nucleon in comparison with the UrQMD model allowed a first estimate of the symmetry term of the EOS but suffer from a considerable statistical uncertainty. In order to obtain an improved data set for Au+Au collisions and to extend the study to other systems, a new experiment was carried out at the GSI laboratory by the ASY-EOS collaboration in May 2011.
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Directed and elliptic flows of neutrons and light charged particles were measured for the reaction 197Au+197Au at 400 MeV/nucleon incident energy within the ASY-EOS experimental campaign at the GSI laboratory. The detection system consisted of the Large Area Neutron Detector LAND, combined with parts of the CHIMERA multidetector, of the ALADIN Time-of-flight Wall, and of the Washington-University Microball detector. The latter three arrays were used for the event characterization and reaction-plane reconstruction. In addition, an array of triple telescopes, KRATTA, was used for complementary measurements of the isotopic composition and flows of light charged particles. From the comparison of the elliptic flow ratio of neutrons with respect to charged particles with UrQMD predictions, a value gamma = 0.72 pm 0.19 is obtained for the power-law coefficient describing the density dependence of the potential part in the parametrization of the symmetry energy. It represents a new and more stringent constraint for the regime of supra-saturation density and confirms, with a considerably smaller uncertainty, the moderately soft to linear density dependence deduced from the earlier FOPI-LAND data. The densities probed are shown to reach beyond twice saturation.
Motivated by the historical detection of gravitational waves from GW170817, the neutron star and the neutron drop, i.e., a certain number of neutrons confined in an external field, are systematically investigated by ab initio calculations as well as the nonrelativistic and relativistic state-of-art density functional theories. Strong correlations are found among the neutron star tidal deformability, the neutron star radius, the root-mean-square radii of neutron drops, and the symmetry energies of nuclear matter at supra-saturation densities. From these correlations and the upper limit on the tidal deformability extracted from GW170817, the neutron star radii, the neutron drop radii, and the symmetry energy at twice saturation density are respectively constrained as $R_{1.4M_{odot}}leqslant 12.94$ km, $R_{rm nd} leqslant 2.36$ fm, and $E_{mathrm{sym}}(2rho_0) leqslant 53.2$ MeV.
Nuclear symmetry energy $E_{rm{sym}}(rho)$ at density $rho$ is normally expanded or simply parameterized as a function of $chi=(rho-rho_0)/3rho_0$ in the form of $E_{rm{sym}}(rho)approx S+Lchi+2^{-1}K_{rm{sym}}chi^2+6^{-1}J_{rm{sym}}chi^3+cdots$ using its magnitude $S$, slope $L $, curvature $K_{rm{sym}}$ and skewness $J_{rm{sym}}$ at the saturation density $rho_0$ of nuclear matter. Much progress has been made in recent years in constraining especially the $S$ and $L$ parameters using various terrestrial experiments and astrophysical observations. However, such kind of expansions/parameterizations do not converge at supra-saturation densities where $chi$ is not small enough, hindering an accurate determination of high-density $E_{rm{sym}}(rho)$ even if its characteristic parameters at $rho_0$ are all well determined by experiments/observations. By expanding the $E_{rm{sym}}(rho)$ in terms of a properly chosen auxiliary function $Pi_{rm{sym}}(chi,Theta_{rm{sym}})$ with a parameter $Theta_{rm{sym}}$ fixed accurately by an experimental $E_{rm{sym}}(rho_{rm{r}})$ value at a reference density $rho_{rm{r}}$, we show that the shortcomings of the $chi$-expansion can be completely removed or significantly reduced in determining the high-density behavior of $E_{rm{sym}}(rho)$. In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher $chi$-order contributions and converges to the same $E_{rm{sym}}(rho)$ much faster than the conventional $chi$-expansion at densities $lesssim3rho_0$. Several quantitative demonstrations using Monte Carlo simulations are given.
Within an isospin- and momentum-dependent hadronic transport model it is shown that the recent FOPI data on the $pi^-/pi^+$ ratio in central heavy-ion collisions at SIS/GSI energies (Willy Reisdorf {it et al.}, NPA {bf 781}, 459 (2007)) provide circumstantial evidence suggesting a rather soft nuclear symmetry energy esym at $rhogeq 2rho_0$ compared to the Akmal-Pandharipande-Ravenhall prediction. Some astrophysical implications and the need for further experimental confirmations are discussed.
Methods of extraction of the symmetry energy (or enthalpy) coefficient to temperature ratio from isobaric and isotopic yields of fragments produced in Fermi-energy heavy-ion collisions are discussed. We show that the methods are consistent when the hot fragmenting source is well characterized and its excitation energy and isotopic composition are properly taken into account. The results are independent of the mass number of the detected fragments, which suggests that their fate is decided very early in the reaction.
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