Beam energy dependence of the relativistic retardation effects of electrical fields on the ${\pi }^{-}/{\pi }^{+}$ ratio in heavy-ion collisions

Abstract

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.

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

References in corpus (62)

• Determination of the Equation of State of Dense Matter
• Recent Progress and New Challenges in Isospin Physics with Heavy-Ion Reactions
• Isospin Asymmetry in Nuclei and Neutron Stars
• The Nuclear Equation of State and Neutron Star Masses
• Reaction Dynamics with Exotic Beams
• Phase Transitions in Warm, Asymmetric Nuclear Matter
• Circumstantial evidence for a soft nuclear symmetry energy at supra-saturation densities
• Momentum sharing in imbalanced Fermi systems
• Probing the High Density Behaviour of Nuclear Symmetry Energy with High Energy Heavy-Ion Collisions
• A way forward in the study of the symmetry energy: experiment, theory, and observation
• Momentum dependence of symmetry potential in asymmetric nuclear matter for transport model calculations
• Results of the ASY-EOS experiment at GSI: The symmetry energy at suprasaturation density
• Symmetry energy from elliptic flow in 197Au + 197Au
• Neutron and Proton Transverse Emission Ratio Measurements and the Density Dependence of the Asymmetry Term of the Nuclear Equation of State
• Nuclear forces and their impact on neutron-rich nuclei and neutron-rich matter
• Systematics of pion emission in heavy ion collisions in the 1A GeV regime
• On the Lorentz structure of the symmetry energy
• Systematics of central heavy ion collisions in the 1A GeV regime
• Probing high-density behavior of symmetry energy from pion emission in heavy-ion collisions
• Isospin effects in Nuclear Fragmentation
• Probing the Symmetry Energy with Heavy Ions
• Disappearance of Elliptic Flow: A New Probe for the Nuclear Equation of State
• Understanding transport simulations of heavy-ion collisions at 100 and 400 AMeV: Comparison of heavy ion transport codes under controlled conditions
• Comparison of heavy-ion transport simulations: Collision integral in a box
• Momentum dependence of the symmetry potential and nuclear reactions induced by neutron-rich nuclei at RIA
• Isospin effects on sub-threshold kaon production at intermediate energies
• Symmetry Energy of Nucleonic Matter With Tensor Correlations
• Nuclear Isospin Diffusivity
• Subthreshold pion production within a transport description of central Au+Au collisions
• Towards a model-independent constraint of the high-density dependence of the symmetry energy
• Double neutron/proton ratio of nucleon emissions in isotopic reaction systems as a robust probe of nuclear symmetry energy
• The impact of energy conservation in transport models on the ${\pi }^{-}/{\pi }^{+}$ multiplicity ratio in heavy-ion collisions and the symmetry energy
• S$\pi$RIT: A time-projection chamber for symmetry-energy studies
• Neutron-proton effective mass splitting in neutron-rich matter at normal density from analyzing nucleon-nucleus scattering data within an isospin dependent optical model
• Effect of symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei
• Transport Theories for Heavy Ion Collisions in the 1 AGeV Regime
• Relativistic effects in the search for high density symmetry energy
• Magnetic effects in heavy-ion collisions at intermediate energies
• Proton Differential Elliptic Flow and the Isospin-Dependence of the Nuclear Equation of State
• Probing neutron-proton dynamics by pions
• Elliptic flow and the symmetry energy at supra-saturation density
• Medium effects on pion production in heavy ion collisions
• Single and double pi^{-}/pi^{+} ratios in heavy-ion reactions as probes of the high-density behavior of the nuclear symmetry energy
• Effects of short-range correlation reduced kinetic symmetry energy in heavy-ion collisions at intermediate energies
• Probing isospin- and momentum-dependent nuclear effective interactions in neutron-rich matter
• Constraining the density dependence of the symmetry energy using the multiplicity and average $p_T$ ratios of charged pions
• Pion Production in Rare Isotope Collisions
• Observable effects of symmetry energy in heavy-ion collisions at RIA energies
• Covariance Analysis of Symmetry Energy Observables from Heavy Ion Collision
• Extracting the nuclear symmetry potential and energy from neutron-nucleus scattering data
• Isospin-dependent pion in-medium effects on charged pion ratio in heavy ion collisions
• An improved single particle potential for transport model simulations of nuclear reactions induced by rare isotope beams
• Influence of neutron-skin thickness on ${\pi }^{-}/{\pi }^{+}$ ratio in Pb+Pb collisions
• Symmetry potential of $\Delta (1232)$ resonance and its effects on the ${\pi }^{-}/{\pi }^{+}$ ratio in heavy-ion collisions near the pion production threshold
• Cross-checking the symmetry energy at high densities
• Effects of pion potential and nuclear symmetry energy on the ${\pi }^{-}/{\pi }^{+}$ ratio in heavy-ion collisions at beam energies around the pion production threshold
• Role of isospin dependent mean field in pion production in heavy ion reactions
• Effect of Delta potential on the pion-/pion+ ratio in heavy-ion collisions at intermediate energies
• Pre-equilibrium effects in charge-asymmetric low-energy reactions
• Preequilibrium particle emissions and in-medium effects on the pion production in heavy-ion collisions
• Effects of retarded electrical fields on observables sensitive to the high-density behavior of nuclear symmetry energy in heavy-ion collisions at intermediate energies
• Elimination of influence of neutron-skin size difference of initial colliding nuclei in Pb+Pb collisions

Cited by in corpus (7)

• Examination of an isospin-dependent single-nucleon momentum distribution for the isospin-asymmetric nuclear matter in heavy-ion collisions
• Effects of the momentum dependence of nuclear symmetry potential on pion observables in Sn + Sn collisions at 270 MeV/nucleon
• Proton-proton momentum correlation function as a probe of the high momentum tail of the nucleon momentum distribution
• RMF models with $\sigma$-scaled hadron masses and couplings for description of heavy-ion collisions below 2A GeV
• Effects of density-dependent scenarios of in-medium nucleon-nucleon interactions in heavy-ion collisions
• Neutron-proton differential transverse flow in ${}^{132}$Sn + ${}^{124}$Sn collisions at 270 MeV/nucleon
• Necessity of selfconsistent calculations for the electromagnetic field in probing the nuclear symmetry energy using pion observables in heavy-ion collisions