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Within an isospin- and momentum-dependent transport model, we investigate thenecessity of selfconsistent calculations for the electromagnetic field inprobing the nuclear symmetry energy using pion observables in heavy-ioncollisions at intermediate energies. To this end, we perform the $^{96}$Ru +$^{96}$Ru collisions at 400 MeV/nucleon with two calculations scenarios for theelectromagnetic field including the selfconsistent calculation and the mostused Li\'{e}nard-Wiechert formula, while the latter is a simplified one of thecomplete Li\'{e}nard-Wiechert formula by neglecting the radiation field forpractical calculations in heavy-ion collisions at intermediate and/orrelativistic energies. As a comparison, we also consider the static Coulombfield formula for calculations of the electromagnetic field in heavy-ioncollisions. It is shown that the most used simplified Li\'{e}nard-Wiechertformula is not enough for the electromagnetic field calculation because theabsent radiation field in this formula also affects significantly the chargedpions as well as their $\pi^{-}/\pi^{+}$ ratio. Moreover, we also examineeffects of the electromagnetic field in these scenarios on the double$\pi^{-}/\pi^{+}$ ratio of two isobar reaction systems of $^{96}$Ru + $^{96}$Ruand $^{96}$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 theelectromagnetic field calculation scenario and thus can still be an effectiveprobe of the nuclear symmetry energy in heavy-ion collisions. Therefore,according to these findings, it is suggested that the selfconsistentcalculation for the electromagnetic field should be carefully taken intoaccount when using the pion observables to probe the nuclear symmetry energy inheavy-ion collisions.

physical review. c

Necessity of selfconsistent calculations for the electromagnetic field  in probing the nuclear symmetry energy using pion observables in heavy-ion  collisions