Based on the isospin-dependent Boltzmann-Uehling-Uhlenbeck(IBUU) transport model, effects of ∆ resonance potential on the free n/p and π − /π + ratios in the central collision of 197 Au + 197 Au at beam energies of 200 and 400 MeV/A are studied. It is found that the effect of ∆ potential on the ratio of pre-equilibrium free n/p is invisible. The effect of ∆ isovector potential on the kinetic energy integrating ratio of π − /π + may be observable only at lower incident beam energies and with stiffer symmetry energy. The strength of the ∆ isoscalar potential affects the height of the π − /π + ratio around the Coulomb peak but does not affect the kinetic energy integrating ratio of π − /π + . In heavy-ion collisions at intermediate energies, relating to the question of non-conservation of energy on ∆ or π productions, one can replace the ∆ potential by nucleon isoscalar potential especially a soft symmetry energy is employed.
I. MOTIVATIONSIn recent years, the research of the density dependent symmetry energy is still one of the hot topics in nuclear physics and astrophysics communities. This is simply because the symmetry energy governs many nuclear and astrophysical phenomena, such as the cooling of neutron stars [1], the mass-radius relations of neutron stars [2], the study of Gravitational waves [3], properties of nuclei involved in r-process nucleosynthesis [4], and observables in heavy-ion collisions at intermediate energies [5,6]. While significant progress has been made in constraining the symmetry energy around saturation density [6][7][8][9], it is rather uncertain at supra-saturation densities. . It thus provides more opportunities and enhances our confidences to study the symmetry energy although there are still many uncertain factors, such as the effects of pion potential [15,16], the isospin dependence of inmedium nuclear strong interactions [17], the short-range tensor force [18,19] and the π − N − ∆ dynamics [20][21][22].It is noted that the sensitivities of the π − /π + ratio to the symmetry energy shown in Ref. [16,20] is quite different from that shown in Ref. [15]. The discrepancies observed among the results of different models may be * Electronic address: yonggaochan@impcas.ac.cn because the latter uses a momentum-dependent nucleon symmetry potential while the previous two studies use a momentum-independent nucleon symmetry potential. The momentum-dependent nucleon symmetry potential could increase the sensitivity of dense neutron to proton ratio (thus the π − /π + ratio) to the symmetry energy [23]. While in this study, we use a modified symmetry potential which including the effects of the short-range correlations of neutron and proton [24]. The short-range correlations of neutron and proton reduce the kinetic symmetry energy, the strength of the modified symmetry potential is thus increased [24]. The effects of such modified symmetry potential on the π − /π + ratio may be also enlarged. In the following studies, we confirmed the above deduction.In Refs. [20][21][22] it is argued that due t...