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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

A simple high-performance liquid chromatography (HPLC) method coupled with principal component analysis (PCA) and hierarchical cluster analysis (HCA) was developed for distinguishing Astragali Radix from its adulterants. Five species, including A. membranaceus var. mongolicus, A. membranaceus, H. polybotrys, A. chrysopterus and A. ernestii, were analyzed by this method. At the same time, four major bioactive isoflavonoids, namely calycosin-7-O-D-glucopyranosidc, ononin, calycosin and formononetin, were simultaneously determined in Astragali Radix. This method was proven to have good precision, repeatability, stability and recovery. It was successfully applied to distinguish Astragali Radix from its adulterants species and can be used for the quality control of Astragali Radix.

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

The impact parameter dependence ofπ-/π+ratio is examined in heavy-ion collisions at 400 MeV/nucleon within a transport model. It is shown that the sensitivity ofπ-/π+ratio on symmetry energy shows a transition from central to peripheral collisions; that is, the stiffer symmetry energy leads to a largerπ-/π+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 ofπ-/π+ratio, we found this transition of sensitivity ofπ-/π+ratio to symmetry energy is mainly from less energetic pions; that is, the softer symmetry energy gets the less energetic pions to form a smallerπ-/π+ratio in peripheral collisions while these pions generate a largerπ-/π+ratio in central collisions. Undoubtedly, the softer symmetry energy can also lead more energetic pions to form a largerπ-/π+ratio in peripheral collisions. Nevertheless, considering that most of pions are insufficiently energetic at this beam energy, we therefore suggest theπ-/π+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 inπ-/π+ratio from peripheral collisions.

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

Using an isospin- and momentum-dependent transport model, we examine the effects of an electric field induced by a variable magnetic field on the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio in central to peripheral heavy-ion collisions at beam energies of 400 and 1500 MeV/nucleon. It is shown that while the induced electric field does not affect the total multiplicities of both ${\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\ensuremath{\pi}}^{+}$ mesons at both the lower beam energy of 400 MeV/nucleon and the higher beam energy of 1500 MeV/nucleon, it reduces (enhances) the emission of ${\ensuremath{\pi}}^{\ensuremath{-}}\phantom{\rule{0.16em}{0ex}}({\ensuremath{\pi}}^{+})$ mesons in midrapidity, but enhances (reduces) the emission of ${\ensuremath{\pi}}^{\ensuremath{-}}\phantom{\rule{0.16em}{0ex}}({\ensuremath{\pi}}^{+})$ 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 the longer reaction duration time at the lower beam energy. These findings indicate that the total ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio is still a precisely reliable probe of symmetry energy at both the lower and the higher beam energies, but one should consider the induced electric field when using the differential ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ 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 ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ 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 ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio but minimizing effects of some uncertainty factors in heavy-ion collisions.

The impact parameter dependence of π-/π+ ratio is examined in heavy-ion collisions at 400 MeV/nucleon within a transport model. It is shown that the sensitivity of π-/π+ ratio on symmetry energy shows a transition from central to peripheral collisions; that is, the stiffer symmetry energy leads to a larger π-/π+ 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 π-/π+ ratio, we found this transition of sensitivity of π-/π+ 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 π-/π+ ratio in peripheral collisions while these pions generate a larger π-/π+ ratio in central collisions. Undoubtedly, the softer symmetry energy can also lead more energetic pions to form a larger π-/π+ ratio in peripheral collisions. Nevertheless, considering that most of pions are insufficiently energetic at this beam energy, we therefore suggest the π-/π+ 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 π-/π+ ratio from peripheral collisions.