Symmetry potential of $\Delta (1232)$ resonance and its effects on the ${\pi }^{-}/{\pi }^{+}$ ratio in heavy-ion collisions near the pion production threshold

Abstract

Effects of the completely unknown symmetry (isovector) potential of the \D on the total and differential \rpi in heavy-ion collisions at beam energies from 100 to 1000 MeV/A are explored within an isospin-dependent transport model IBUU. The effects are found to be negligible at beam energies above the pion production threshold due to the very short lifetimes of less than 2 fm/c for $\Delta$ resonances with masses around $m_{\Delta }=1232$ MeV, leaving the ${\pi }^{-}/{\pi }^{+}$ ratios of especially the energetic pions still a reliable probe of the high-density behavior of nuclear symmetry energy $E_{sym}(\rho )$. However, as the beam energy becomes deeply sub-threshold for pion production, effects of the $\Delta$ symmetry potential becomes appreciable especially on the \rpi of low-energy pions from the decays of low-mass $\Delta$ resonances which have lived long enough to be affected by their mean-field potentials, providing a useful tool to study the symmetry potential and spectroscopy of $\Delta$ resonances in neutron-rich nuclear matter. Interestingly though, even at the deeply sub-threshold beam energies, the differential \rpi of energetic pions remains sensitive to the \esym at supra saturation densities with little influence from the uncertain symmetry potential of the $\Delta$ resonance.

Version to appear in PRC (2015)

References in corpus (4)

• Symmetry energy from elliptic flow in 197Au + 197Au
• Systematics of pion emission in heavy ion collisions in the 1A GeV regime
• Critical Density and Impact of $\Delta (1232)$ Resonance Formation in Neutron Stars
• Effects of short-range correlation reduced kinetic symmetry energy in heavy-ion collisions at intermediate energies

Cited by in corpus (24)

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• Probing neutron-proton dynamics by pions
• $\Delta$ (1232) effects in density-dependent relativistic Hartree-Fock theory and neutron stars
• 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
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• Effects of energy conservation on equilibrium properties of hot asymmetric nuclear matter
• Effect of Delta potential on the pion-/pion+ ratio in heavy-ion collisions at intermediate energies
• Collective flows of pions in Au+Au collisions at energies 1.0 and 1.5 GeV/nucleon
• The effect of internal magnetic field on collective flow in heavy ion collisions at intermediate energies
• Effect of energy conservation on in-medium $\mbox{NN}\to \mbox{N}Δ$ cross section in isospin-asymmetric nuclear matter
• Examination of an isospin-dependent single-nucleon momentum distribution for the isospin-asymmetric nuclear matter in heavy-ion collisions
• Nucleon Effective E-Mass in Neutron-Rich Matter from the Migdal-Luttinger Jump
• Effects of retarded electrical fields on observables sensitive to the high-density behavior of nuclear symmetry energy in heavy-ion collisions at intermediate energies
• Determination of the density region of the symmetry energy probed by the ${\pi }^{-}/{\pi }^{+}$ ratio
• Beam energy dependence of the relativistic retardation effects of electrical fields on the ${\pi }^{-}/{\pi }^{+}$ ratio in heavy-ion collisions
• Deep crustal heating by neutrinos from the surface of accreting neutron stars
• Effects of density-dependent scenarios of in-medium nucleon-nucleon interactions in heavy-ion collisions
• Necessity of selfconsistent calculations for the electromagnetic field in probing the nuclear symmetry energy using pion observables in heavy-ion collisions
• Pion production and absorption in heavy-ion collisions
• Effects of an induced electric field on π^{-}/π^{+} ratio in heavy-ion collisions