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Register a new userNecessity of selfconsistent calculations for the electromagnetic field in probing the nuclear symmetry energy using pion observables in heavy-ion collisions
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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.
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Based on the ultrarelativistic quantum molecular dynamics (UrQMD) model, the effects of the density-dependent symmetry potential for baryons and of the Coulomb potential for produced mesons are investigated for neutron-rich heavy ion collisions at intermediate energies. The calculated results of the $Delta^-/Delta^{++}$ and $pi ^{-}/pi ^{+}$ production ratios show a clear beam-energy dependence on the density-dependent symmetry potential, which is stronger for the $pi ^{-}/pi ^{+}$ ratio close to the pion production threshold. The Coulomb potential of the mesons changes the transverse momentum distribution of the $pi ^{-}/pi ^{+}$ ratio significantly, though it alters only slightly the $pi^-$ and $pi^+$ total yields. The $pi^-$ yields, especially at midrapidity or at low transverse momenta and the $pi^-/pi^+$ ratios at low transverse momenta, are shown to be sensitive probes of the density-dependent symmetry potential in dense nuclear matter. The effect of the density-dependent symmetry potential on the production of both, K$^0$ and K$^+$ mesons, is also investigated.
Using covariance analysis, we quantify the correlations between the interaction parameters in a transport model and the observables commonly used to extract information of the Equation of State of Asymmetric Nuclear Matter in experiments. By simulating $^{124}$Sn+$^{124}$Sn, $^{124}$Sn+$^{112}$Sn and $^{112}$Sn+$^{112}$Sn reactions at beam energies of 50 and 120 MeV per nucleon, we have identified that the nucleon effective mass splitting are most strongly correlated to the neutrons and protons yield ratios with high kinetic energy from central collisions especially at high incident energy. The best observable to determine the slope of the symmetry energy, L, at saturation density is the isospin diffusion observable even though the correlation is not very strong ($sim$0.7). Similar magnitude of correlation but opposite in sign exists for isospin diffusion and nucleon isoscalar effective mass. At 120 MeV/u, the effective mass splitting and the isoscalar effective mass also have opposite correlation for the double n/p and isoscaling p/p yield ratios. By combining data and simulations at different beam energies, it should be possible to place constraints on the slope of symmetry energy (L) and effective mass splitting with reasonable uncertainties.
The in-medium color potential is a fundamental quantity for understanding the properties of the strongly coupled quark-gluon plasma (sQGP). Open and hidden heavy-flavor (HF) production in ultrarelativistic heavy-ion collisions (URHICs) has been found to be a sensitive probe of this potential. Here we utilize a previously developed quarkonium transport approach in combination with insights from open HF diffusion to extract the color-singlet potential from experimental results on $Upsilon$ production in URHICs. Starting from a parameterized trial potential, we evaluate the $Upsilon$ transport parameters and conduct systematic fits to available data for the centrality dependence of ground and excited states at RHIC and the LHC. The best fits and their statistical significance are converted into a temperature-dependent potential. Including nonperturbative effects in the dissociation rate guided from open HF phenomenology, we extract a rather strongly coupled potential with substantial remnants of the long-range confining force in the QGP.
The initial energy density produced in heavy ion collisions can be estimated with the Bjorken energy density formula after choosing a proper formation time $tau{_{rm F}}$. However, the Bjorken formula breaks down at low energies because it neglects the finite nuclear thickness. Here we include both the finite time duration and finite longitudinal extension of the initial energy production. When $tau{_{rm F}}$ is not too much smaller than the crossing time of the two nuclei, our results are similar to those from a previous study that only considers the finite time duration. In particular, we find that at low energies the initial energy density has a much lower maximum value but evolves much longer than the Bjorken formula, while at large-enough $tau{_{rm F}}$ and/or high-enough energies our result approaches the Bjorken formula. We also find a qualitative difference in that our maximum energy density $epsilon^{rm max}$ at $tau{_{rm F}}=0$ is finite, while the Bjorken formula diverges as $1/tau{_{rm F}}$ and the previous result diverges as $ln (1/tau{_{rm F}})$ at low energies but as $1/tau{_{rm F}}$ at high energies. Furthermore, our solution of the energy density approximately satisfies a scaling relation. As a result, the $tau{_{rm F}}$-dependence of $epsilon^{rm max}$ determines the $A$-dependence, and the weaker $tau{_{rm F}}$-dependence of $epsilon^{rm max}$ in our results at low energies means a slower increase of $epsilon^{rm max}$ with $A$.
We introduce isospin dependence in the cluster recognition algorithms used in the Quantum Molecular Dynamics model to describe fragment formation in heavy ion collisions. This change reduces the yields of emitted nucleons and enhances the yields of fragments, especially heavier fragments. The enhancement of neutron-rich lighter fragments mainly occurs at mid-rapidity. Consequently, isospin dependent observables, such as isotope distributions, yield ratios of $n/p$, $t/^3He$, and isoscaling parameters are affected. We also investigate how equilibration in heavy ion collisions is affected by this change.
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