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Within an isospin- and momentum-dependent transport model by including the kaon production, we study the kaon prodution in heavy-ion collisions (HICs) at SIS (Darmstadt Schwerionen Synchrotron, GSI) energies. Based on simulations of a centrality of 0-40\% Au + Au collision at $\sqrt{s_{NN}}=2.4$ GeV, a typical reaction that has been carried out by the HADES Collaborator, we find that the medium modification of kaon masses plays a vital role in studying the kaon productions in HICs, and is also unavoidable for the successful interpretation of the HADES data on kaon rapidity distributions and transverse mass spectra. Moreover, we also find that the kaon transverse and directed flows are affected significantly by both the kaon potential or dispersion relation and medium modification of kaon masses, and thus could be used in HICs as the sensitive probes to detect the kaon potential or dispersion relation as well as the medium modification of kaon masses., Comment: 8 pages, 6 figures, submitted for publication

Within the possible least uncertainty on the nuclear incompressibility $K_{0}$, we examine effects of $K_{0}$ in heavy-ion collisions at intermediate energies. Based on simulations of Au + Au collision at 400 MeV/nucleon using an isospin- and momentum-dependent transport model, we find that the incompressibility $K_{0}$ indeed affects significantly the attainable density in central regions, and thus the particle productions and/or distributions at final states, e.g., nucleon rapidity distributions and yields of charged pions. Nevertheless, through examining the free neutron over proton ratios $n/p$, the neutron-proton differential transverse and directed flows as well as the charged pion ratio $\pi^{-}/\pi^{+}$ and its kinetic energy distribution, we find that these observables are less affected by the uncertainty of $K_{0}$, but mainly sensitive to the slope of symmetry energy at the saturation density. We also compare and discuss our results with the corresponding data., Comment: 7 pages, 8 figures. Accepted for publication in Physical Review C

Within a transport model coupled with a microscopic coalescence model, the directed and elliptic flows of protons and deuterons as well as their scalling properties are studied in the centrality of 20-30% Au+Au collisions at $\sqrt{s_{\rm NN}}=2.4$ GeV. It is found that the flows as well as their scaling properties simulated with the isospin- and momentum-dependent nuclear mean field with an incompressibility $K_{0}=230$ MeV fit fairly the HADES data, while those simulated with the commonly used momentum-independent nuclear mean field with an incompressibility $K_{0}=380$ MeV can only fit partially the HADES data. Moreover, by checking the rapidity distributions of both protons and deuterons in the centrality of 0-10% Au+Au collisions at $\sqrt{s_{\rm NN}}=2.4$ GeV, we find that the rapidity distributions of deuterons are underestimated while those of protons are overestimated by the simulations with the momentum-independent nuclear mean field. In contrast, the rapidity distributions of both protons and deuterons simulated with the isospin- and momentum-dependent nuclear mean field are in good agreement with the HADES data. Our findings imply that the momentum dependence of nuclear mean field is an unavoidable feature for a fundamental understanding of nuclear matter properties and for the successful interpretation of the HADES data., Comment: 7 pages, 5 figures. Accepted for publication in Physics Letters B

Within a transport model, we study the neutron-proton differential transverse flow and its excitation function in central $^{132}$Sn + $^{124}$Sn collisions at 270 MeV/nucleon. To more accurately evaluate effects of the high-density behavior of symmetry energy \esym on this observable, we also consider the uncertainties of \esym around the saturation density $\rho_{0}$. It is shown that the neutron-proton differential transverse flow and its excitation function are mainly sensitive to the slope $L$ of \esym at $\rho_{0}$. However, the effects of low-density behavior of \esym on this observable should also be considered. Therefore, it is suggested that measurements of the neutron-proton differential transverse flow and its excitation function may provide useful complements to the constraints on $L$ extracted from the spectral pion ratio in S$\pi$RIT experiments., Comment: 6 pages, 7figures.Accepted for publication in Physical Review C

Within a transport model, we study effects of the momentum dependence of nuclear symmetry potential on pion observables in central Sn + Sn collisions at 270 MeV/nucleon. To this end, a quantity $U_{sym}^{\infty}(\rho_{0})$, i.e., the value of nuclear symmetry potential at the saturation density $\rho_{0}$ and infinitely large nucleon momentum, is used to characterise the momentum dependence of nuclear symmetry potential. It is shown that with a certain $L$ (i.e., slope of nuclear symmetry energy at $\rho_{0}$) the characteristic parameter $U_{sym}^{\infty}(\rho_{0})$ of symmetry potential affects significantly the production of $\pi^{-}$ and $\pi^{+}$ as well as their pion ratios. Moreover, through comparing the charged pion yields, pion ratios as well the spectral pion ratios of theoretical simulations for the reactions $^{108}$Sn + $^{112}$Sn and $^{132}$Sn + $^{124}$Sn with the corresponding data in S$\pi$RIT experiments, we find that our results favor a constraint on $U_{sym}^{\infty}(\rho_{0})$, i.e., $-160^{+18}_{-9}$~MeV, and the $L$ is also suggested within a range, i.e., $62.7

Within an isospin- and momentum-dependent transport model, we investigate the necessity of selfconsistent calculations for the electromagnetic field in probing the nuclear symmetry energy using pion observables in heavy-ion collisions at intermediate energies. To this end, we perform the $^{96}$Ru + $^{96}$Ru collisions at 400 MeV/nucleon with two calculations scenarios for the electromagnetic field including the selfconsistent calculation and the most used Li\'{e}nard-Wiechert formula, while the latter is a simplified one of the complete Li\'{e}nard-Wiechert formula by neglecting the radiation field for practical calculations in heavy-ion collisions at intermediate and/or relativistic energies. As a comparison, we also consider the static Coulomb field formula for calculations of the electromagnetic field in heavy-ion collisions. It is shown that the most used simplified Li\'{e}nard-Wiechert formula is not enough for the electromagnetic field calculation because the absent radiation field in this formula also affects significantly the charged pions as well as their $\pi^{-}/\pi^{+}$ ratio. Moreover, we also examine effects of the electromagnetic field in these scenarios on the double $\pi^{-}/\pi^{+}$ ratio of two isobar reaction systems of $^{96}$Ru + $^{96}$Ru and $^{96}$Zr + $^{96}$Zr at 400 MeV/nucleon. It is shown that the double $\pi^{-}/\pi^{+}$ ratio of two reactions tends to be less affected by the electromagnetic field calculation scenario and thus can still be an effective probe of the nuclear symmetry energy in heavy-ion collisions. Therefore, according to these findings, it is suggested that the selfconsistent calculation for the electromagnetic field should be carefully taken into account when using the pion observables to probe the nuclear symmetry energy in heavy-ion collisions., Comment: 7 pages, 6 figures. Accepted for publication in Physical Review C

Using a more reasonable separate density-dependent scenario instead of the total density-dependent scenario for in-medium $nn$, $pp$ and $np$ interactions, we examine effects of differences of in-medium nucleon-nucleon interactions in two density-dependent scenarios on isospin-sensitive observables in central $^{197}$Au+$^{197}$Au collisions at 400 MeV/nucleon. Moreover, to more physically detect the differences between the nucleon-nucleon interactions in two density-dependent scenarios, we also map the nucleon-nucleon interaction in the separate density-dependent scenario into that in the total density-dependent scenario through fitting the identical constraints for symmetric nuclear matter as well as the identical slope parameter of nuclear symmetry energy at the saturation density. It is shown that two density-dependent scenarios also lead to essentially different symmetry potentials especially at high densities although they can lead to the identical equation of state for the symmetry nuclear matter as well as the identical symmetry energy for the isospin asymmetric nuclear matter. Consequently, these isospin-sensitive observables are also appreciably affected by the different density-dependent scenarios of in-medium nucleon-nucleon interactions. Therefore, according to these findings, it is suggested that effects of the separate density-dependent scenario of in-medium nucleon-nucleon interactions should be taken into account when probing the high-density symmetry energy using these isospin-sensitive observables in heavy-ion collisions., Comment: 8 pages, 6 figures. Abbreviated abstract to meet the criterion of arXiv platform. Accepted for publication in Physical Review C

Within an improved transport model, we examine effects of the high momentum tail of the nucleon momentum distribution induced by short-range correlations on the proton-proton momentum correlation function in $^{197}$Au+$^{197}$Au collisions at 400 MeV/nucleon. It is found that the proton-proton momentum correlation function from preequilibrium emissions responds sensitively to the presence as well as fraction of nucleons in the high momentum tail of the nucleon momentum distribution, but is almost robustly insensitive to other factors including the symmetry energy and the uncertainty of cutoff value of nucleon effective high momentum. In terms of the sensitivity and clearness, we propose that the proton-proton momentum correlation function from preequilibrium emissions can be as an effective probe of the high momentum tail of the nucleon momentum distribution., Comment: 7 pages, 6 figures. Accepted for publication in Physical Review C

Within a transport model using as the input nucleon momentum profiles from a parameterized isospin-dependent single-nucleon momentum distribution with a high momentum tail induced by short-range correlations, we employ the $^{197}$Au + $^{197}$Au collisions at 400 MeV/nucleon to examine on one hand effects of the short-range correlations on the pion and flow observables in probing the nuclear symmetry energy, and on the other hand how reliable are this isospin-dependent single-nucleon momentum distribution as well as the corresponding parameter settings. Besides significant effects of the short-range correlations on the pion and flow observables are observed, we also find that the theoretical simulations of $^{197}$Au + $^{197}$Au collisions with this momentum distribution using two sets of parameters extracted from the experimental analysis and the self-consistent Green's function prediction, respectively, can reproduce the neutron elliptic flows of the FOPI-LAND experiment and the $\pi^{-}/\pi^{+}$ ratios of the FOPI experiment under the symmetry energy setting in a certain range. Therefore, we conclude that this parameterized isospin-dependent single-nucleon momentum distribution is reliable for the isospin-asymmetric nuclear matter, correspondingly, two sets of parameters extracted from both the experimental analysis and the self-consistent Green's function prediction can not be ruled out according to the available experimental information at present., Comment: 10 pages, and 9 figures, published version to meet the journal's style

In this article we investigate the beam energy dependence of relativistic retardation effects of electrical fields on the single and double $\pi^{-}/\pi^{+}$ ratios in three heavy-ion reactions with an isospin- and momentum-dependent transport model IBUU11. With the beam energy increasing from 200 to 400 MeV/nucleon, effects of the relativistically retarded electrical fields on the $\pi^{-}/\pi^{+}$ ratio are found to increase gradually from negligibly to considerably significant as expectedly; it is however, the interesting observation is the relativistic retardation effects of electrical fields on the $\pi^{-}/\pi^{+}$ ratio are becoming gradually insignificant as the beam energy further increasing from 400 to 800 MeV/nucleon. Moreover, we also investigate the isospin dependence of relativistic retardation effects of electrical fields on the $\pi^{-}/\pi^{+}$ ratio in two isobar reaction systems of $^{96}$Ru+$^{96}$Ru and $^{96}$Zr+$^{96}$Zr at the beam energies from 200 to 800 MeV/nucleon. It is shown that the relativistic retardation effects of electrical fields on the $\pi^{-}/\pi^{+}$ ratio are independent of the isospin of reaction. Furthermore, we also examine the double $\pi^{-}/\pi^{+}$ ratio in reactions of $^{96}$Zr+$^{96}$Zr over $^{96}$Ru+$^{96}$Ru at the beam energies from 200 to 800 MeV/nucleon with the static field and retarded field, respectively. It is shown the double $\pi^{-}/\pi^{+}$ ratio from two reactions is still an effective observable of symmetry energy without the interference of electrical field due to using the relativistic calculation compared to the nonrelativistic calculation., Comment: 8 pages, 7 figures. Abbreviated abstract to meet the criterion of arXiv platform. Accepted for publication in Physical Review C. An extended but necessary complementary study to arXiv:1709.09127

Within the isospin- and momentum-dependent transport model IBUU11, we examine the relativistic retardation effects of electrical fields on the $\pi^{-}/\pi^{+}$ ratio and neutron-proton differential transverse flow in heavy-ion collisions at intermediate energies. Compared to the static Coulomb fields, the retarded electric fields of fast-moving charges are known to be anisotropic and the associated relativistic corrections can be significant. They are found to increase the number of energetic protons in the participant region at the maximum compression by as much as 25\% but that of energetic neutrons by less than 10\% in $^{197}$Au+$^{197}$Au reactions at a beam energy of 400 MeV/nucleon. Consequently, more $\pi^{+}$ and relatively less $\pi^{-}$ mesons are produced, leading to an appreciable reduction of the $\pi^{-}/\pi^{+}$ ratio compared to calculations with the static Coulomb fields. Also, the neutron-proton differential transverse flow, as another sensitive probe of high-density symmetry energy, is also decreased appreciably due to the stronger retarded electrical fields in directions perpendicular to the velocities of fast-moving charges compared to calculations using the isotropic static electrical fields. Moreover, the retardation effects on these observables are found to be approximately independent of the reaction impact parameter., Comment: 10 pages, 9 figures

The studies, from several independent methods, consistently show that $\pi^-/\pi^+$ ratio in the $^{132}$Sn+$^{124}$Sn reaction at 300 MeV/nucleon, which is being carried out at Radioactive Isotope Beam Facility (RIBF) in Japan, just probes the symmetry energy around saturation density., Comment: 6 pages, 6 figures, accepted by Journal of Physics G: Nuclear and Particle Physics

Using an isospin- and momentum-dependent transport model, we examine the effects of an electric field induced by a variable magnetic field on the \pi^{-}/\pi^{+} ratio in central to peripheral heavy-ion collisions at beam energies of 400 and 1500MeV/nucleon. It is shown that while the induced electric field does not affect the total multiplicities of both $\pi^{-}$ and $\pi^{+}$ mesons at both the lower beam energy of 400MeV/nucleon and the higher beam energy of 1500MeV/nucleon, it reduces (enhances) the emission of $\pi^{-}$ ($\pi^{+}$) mesons in midrapidity, but enhances (reduces) the emission of $\pi^{-}$ ($\pi^{+}$) mesons in forward and backward rapidities especially for the more peripheral collisions at the lower beam energy because of the rapidly transient variable magnetic field at more peripheral collisions and longer reaction duration time at the lower beam energy. These findings indicate that the total \pi^{-}/\pi^{+} ratio is still a precisely reliable probe of symmetry energy at both the lower and higher beam energies, but one should consider the induced electric field when using the differential \pi^{-}/\pi^{+} ratio to probe the symmetry energy especially for the lower beam energy and more peripheral collisions. Finally, the relative suppression factor based on the ratio of \pi^{-}/\pi^{+} in different rapidities is proposed to be an effective probe of the induced electric field generated in heavy-ion collisions due to its maximizing effects of induced electric fields on the differential \pi^{-}/\pi^{+} ratio but minimizing effects of some uncertainty factors in heavy-ion collisions., Comment: 7 pages, 15 figures, Accepted for publication in Physical Review C

The impact parameter dependence of \rpi ratio is examined in heavy-ion collisions at 400MeV/nucleon within a transport model. It is shown that the sensitivity of \rpi ratio on symmetry energy shows a transition from central to peripheral collisions, i.e., the stiffer symmetry energy leads to a larger \rpi 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 \rpi ratio, we found this transition of sensitivity of \rpi ratio to symmetry energy is mainly from less energetic pions, i.e., the softer symmetry energy gets the less energetic pions to form a smaller \rpi ratio in peripheral collisions while these pions generate a larger \rpi ratio in central collisions. Undoubtedly, the softer symmetry energy can also lead more energetic pions to form a larger \rpi ratio in peripheral collisions. Nevertheless, considering that most of pions are insufficient energetic at this beam energy, we therefore suggest the \rpi 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 \rpi ratio from peripheral collisions., Comment: 5 pages, 6 figures, accepted for publication in Adv. in High Energy Phys

Photon from neutron-proton bremsstrahlung in p+Pb reactions is examined as a potential probe of the neutron-skin thickness in different centralities and at different proton incident energies. It is shown that the best choice of reaction environment is about 140MeV for the incident proton and the 95\%-100\% centrality for the reaction system since the incident proton mainly interacts with neutrons inside the skin of the target and thus leads to different photon production to maximal extent. Moreover, considering two main uncertainties from both photon production probability and nucleon-nucleon cross section in the reaction, I propose to use the ratio of photon production from two reactions to measure the neutron-skin thickness because of its cancellation effects on these uncertainties simultaneously, but the preserved about 13\%-15\% sensitivities on the varied neutron-skin thickness from 0.1 to 0.3fm within the current experimental uncertainty range of the neutron-skin size in $^{208}$Pb., Comment: Accepted version for publication. To appear in Physical Review C

Within an isospin- and momentum-dependent transport model using as an input nucleon density profiles from Hartree-Fock calculations based on a modified Skyrme-like (MSL) model, we study how to eliminate the influence of neutron-skin size difference of initial colliding nuclei in probing the nuclear symmetry energy. Within the current experimental uncertainty range of neutron-skin size of $^{208}$Pb, the Pb+Pb collisions are performed in semicentral and peripheral collisions with impact parameters of 5 and 9fm and at beam energies from 50 MeV/nucleon to 1000 MeV/nucleon, respectively. It is shown that combination of neutron and proton collective flows, i.e., neutron-proton differential elliptic flow, neutron-proton elliptic flow difference, neutron-proton differential transverse flow and neutron-proton transverse flow difference, can effectively eliminate the effects of neutron-skin size difference and thus can be as useful sensitive observables in probing nuclear matter symmetry energy in heavy-ion collisions. Moreover, the combined neutron-proton stopping power including the neutron-proton differential stopping power and neutron-proton stopping power difference can also eliminate the effects of neutron-skin size difference and shows some sensitivities to symmetry energy especially at the lower beam energy., Comment: Accepted for publication by Physical Review C

Within an isospin- and momentum-dependent transport model IBUU11 using as an input nucleon density profiles from Hartree-Fock calculations based on a modified Skyrme-like (MSL) model, we study the influence of the uncertainty of the neutron skin thickness on the $\pi^{-}/\pi^{+}$ ratio in both central and peripheral Pb+Pb collisions at beam energies of 400 MeV/nucleon and 1000 MeV/nucleon. Within the current experimental uncertainty range of neutron skin in $^{208}$Pb, while the neutron skin effect on the \rpi ratio is negligible in central reactions at both energies, it increases gradually with increasing impact parameter and becomes comparable with or even larger than the symmetry energy effect in peripheral collisions especially at 400 MeV/nucleon. Moreover, we found that while the \rpi ratio is larger with a softer \esym in central collisions, above certain impact parameters depending on the size of the neutron skin, a stiffer \esym can lead to a larger \rpi ratio as most of the pions are produced at densities below the saturation density in these peripheral reactions. Thus, a clear impact parameter selection is important to extract reliable information about the \esym at suprasaturation densities (size of neutron skin) from the $\pi^-/\pi^+$ ratio in central (peripheral) heavy-ion collisions., Comment: 8 pages including 9 figures