Extension of the Bjorken energy density formula of the initial state for relativistic heavy ion collisions

Abstract

For relativistic heavy ion collisions, the Bjorken formula is very useful for estimating the initial energy density once an initial time ${\tau }_0$ is specified. However, it cannot be trusted at low energies, e.g. well below $\sqrt{s_{{}_{\mathrm{NN}}}}\approx 50$ GeV for central Au+Au collisions, when ${\tau }_0$ is smaller than the finite time it takes for the two nuclei to cross each other. Here I extend the Bjorken formula by including the finite time duration of the initial energy production. Analytical solutions for the formed energy density in the central spacetime-rapidity region are derived for several time profiles. Compared to the Bjorken formula at low energies, the maximum energy density reached is much lower, increases much faster with the collision energy, and is much less sensitive to the uncertainty of the formation time, while the energy density time evolution is much longer. Comparisons with results from a multi-phase transport confirm the key features of these solutions. The effect of the finite longitudinal width of the initial energy production, which is neglected in the analytical results, is investigated with the transport model and shown to be small. This work thus provides a general model for the initial energy production of relativistic heavy ion collisions that is also valid at low energies.

6 pages, 6 figures, added new figures and discussions, corrected typos in and below Eq.(13); final version to appear on Phys Rev C

References in corpus (6)

• Evolution of transverse flow and effective temperatures in the parton phase from a multi-phase transport model
• Collision Energy Dependence of Viscous Hydrodynamic Flow in Relativistic Heavy-Ion Collisions
• Quark-antiquark production from classical fields in heavy ion collisions: 1+1 dimensions
• New approach to initializing hydrodynamic fields and mini-jet propagation in quark-gluon fluids
• A hybrid approach to relativistic heavy-ion collisions at the RHIC BES energies
• Systematic Investigation of Negative Cooper-Frye Contributions in Heavy Ion Collisions Using Coarse-grained Molecular Dynamics

Cited by in corpus (9)

• Further developments of a multi-phase transport model for relativistic nuclear collisions
• Hyperon Polarization from the Vortical Fluid in Low Energy Nuclear Collisions
• Calculating the initial energy density in heavy ion collisions by including the finite nuclear thickness
• Constraining the Particle Production Mechanism in Au+Au Collisions at $\sqrt{s_{NN}}=$ 7.7, 27, and 200 GeV Using A Multi Phase Transport Model
• Thermodynamics of partonic matter in relativistic heavy-ion collisions from a multiphase transport model
• Anti-flow of Mesons in the High Baryon Density Region
• Reaction plane correlated triangular flow in Au+Au collisions at $\sqrt{s_{NN}}=3$ GeV
• Left-right splitting of elliptic flow due to directed flow in heavy ion collisions
• Measurement of Kaon Directed Flow in Au+Au Collisions in the High Baryon Density Region