Advances in High Energy Physics

Volume 2016 (2016), Article ID 9317873, 8 pages

http://dx.doi.org/10.1155/2016/9317873

## Impact Parameter Dependence of Ratio in Probing the Nuclear Symmetry Energy Using Heavy-Ion Collisions

^{1}Shaanxi Key Laboratory of Surface Engineering and Remanufacturing, School of Mechanical and Material Engineering, Xi’an University, Xi’an 710065, China^{2}Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, TX 75429-3011, USA^{3}School of Electronic Engineering, Xi’an Shiyou University, Xi’an 710065, China

Received 18 August 2015; Revised 12 December 2015; Accepted 14 December 2015

Academic Editor: Frank Filthaut

Copyright © 2016 Gao-Feng Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

The impact parameter dependence of ratio is examined in heavy-ion collisions at 400 MeV/nucleon within a transport model. It is shown that the sensitivity of ratio on symmetry energy shows a transition from central to peripheral collisions; that is, the stiffer symmetry energy leads to a larger ratio in peripheral collisions while the softer symmetry energy always leads this ratio to be larger in central collisions. After checking the kinematic energy distribution of ratio, we found this transition of sensitivity of ratio to symmetry energy is mainly from less energetic pions; that is, the softer symmetry energy gets the less energetic pions to form a smaller ratio in peripheral collisions while these pions generate a larger ratio in central collisions. Undoubtedly, the softer symmetry energy can also lead more energetic pions to form a larger ratio in peripheral collisions. Nevertheless, considering that most of pions are insufficiently energetic at this beam energy, we therefore suggest the ratio as a probe of the high-density symmetry energy effective only in central at most to midcentral collisions, thereby avoiding the possible information of low-density symmetry energy carried in ratio from peripheral collisions.

The determination of density-dependent nuclear symmetry energy is one of the hot topics in isospin physics due to its importance in understanding the structure of radiative nuclei in nuclear physics [1–5] and the evolution of massive stars and properties of neutron stars in nuclear astrophysics [6–10]. Presently, although many useful experimental observables [11–20] have been proposed to determine the nuclear symmetry energy, the knowledge regarding the nuclear symmetry energy is still far lacking except for the relative determination of nuclear symmetry energy at saturation density from empirical liquid-drop mass formula [14, 21]. For example, by comparing the ratio with the FOPI experimental data [22], the Boltzmann-Uehling-Uhlenbeck (BUU) [23] and Boltzmann-Langevin (BL) [24] communities favor a supersoft symmetry energy, but the quantum molecular dynamics (QMD) [25] community suggests a superstiff symmetry energy. Therefore, much more efforts need to be made to better determine the nuclear symmetry energy at both supersaturation and subsaturation densities.

Heavy-ion collisions induced by neutron-rich nuclei as an important tool are commonly used to study the density dependence of nuclear symmetry energy [26–31]. Usually, a higher compressive density formed in central heavy-ion collisions with the softer symmetry energy gets the ratio to be larger compared to the case of stiffer symmetry energy. However, the densities formed in heavy-ion collisions always experience a broad range from subsaturation to supersaturation densities. Therefore, one has to evaluate the influence of the high-density (low-density) matter phase on observable when probing the symmetry energy at subsaturation (supersaturation) density using heavy-ion collisions due to the formation of supersaturation (subsaturation) density matter. Certainly, the influence of low-density matter phase is inevitable using heavy-ion collisions to probe high-density symmetry energy due to the densities formed at the final reaction stage always lower than the saturation density; therefore, one has to select those of reaction production without experiencing the final reaction stage such as preequilibration neutron-proton ratio. On the other hand, as shown recently, the pion potential has opposite effects on ratio compared to the effect of symmetry energy on it and thus decreases the sensitivity of ratio to symmetry energy [32, 33]. Moreover, the modification of pion production threshold can even invert the sensitivity of ratio to symmetry energy [34]. Actually, impact parameter as a factor can also influence the compressive density of participating region and thus may even invert the sensitivity of ratio to symmetry energy in peripheral collisions as mentioned in our recent work about the influence of neutron-skin thickness on the ratio in heavy-ion collisions [35]. Therefore, it is necessary to systematically check the impact parameter dependence of ratio in probing the symmetry energy using heavy-ion collisions and show the corresponding reasons and which energy range of pion does get the sensitivity of ratio to symmetry energy reversal. This is the main purpose of the present study.

The present study is based on an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model [36]. In this model, an isospin-dependent mean-field is used to model the nuclear interaction; its expression is defined as follows:In the above, is the nucleon number density and is the isospin asymmetry of the nuclear medium; denotes the neutron (proton) density, the isospin is for neutrons and for protons, and is the local phase space distribution function. The expressions and values of the parameters , , , , , , and can be found in [37, 38], and they lead to the binding energy of −16 MeV, incompressibility 212 MeV for symmetric nuclear matter, and symmetry energy MeV at saturation density , respectively, while parameter is used to mimic the different forms of symmetry energy predicted by various many-body theories without changing any properties of symmetric nuclear matter and the value of symmetry energy at saturation density . Shown in Figure 1 is the density dependence of symmetry energy with a softer setting and stiffer one .