Calculating the initial energy density in heavy ion collisions by including the finite nuclear thickness

Abstract

The initial energy density produced in heavy ion collisions can be estimated with the Bjorken energy density formula after choosing a proper formation time $\tau {}_{\mathrm{F}}$. 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 $\tau {}_{\mathrm{F}}$ 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 $\tau {}_{\mathrm{F}}$ and/or high-enough energies our result approaches the Bjorken formula. We also find a qualitative difference in that our maximum energy density ${\epsilon }^{\max }$ at $\tau {}_{\mathrm{F}}=0$ is finite, while the Bjorken formula diverges as $1/\tau {}_{\mathrm{F}}$ and the previous result diverges as $\ln (1/\tau {}_{\mathrm{F}})$ at low energies but as $1/\tau {}_{\mathrm{F}}$ at high energies. Furthermore, our solution of the energy density approximately satisfies a scaling relation. As a result, the $\tau {}_{\mathrm{F}}$-dependence of ${\epsilon }^{\max }$ determines the $A$-dependence, and the weaker $\tau {}_{\mathrm{F}}$-dependence of ${\epsilon }^{\max }$ in our results at low energies means a slower increase of ${\epsilon }^{\max }$ with $A$.

arXiv comment10 pages, 8 figures, 1 table; typos in Eq.(19) and Fig.8 corrected; final published version

References in corpus (27)

• Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
• Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration
• Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment
• The PHOBOS Perspective on Discoveries at RHIC
• A Multi-Phase Transport Model for Relativistic Heavy Ion Collisions
• New Forms of QCD Matter Discovered at RHIC
• HIJING 1.0: A Monte Carlo Program for Parton and Particle Production in High Energy Hadronic and Nuclear Collisions
• Bulk Properties of the Medium Produced in Relativistic Heavy-Ion Collisions from the Beam Energy Scan Program
• Thermalization of gluons in ultrarelativistic heavy ion collisions by including three-body interactions in a parton cascade
• Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan
• On the sign of kurtosis near the QCD critical point
• Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC : An Overview
• Baryon Stopping and Charged Particle Distributions in Central Pb+Pb Collisions at 158 GeV per Nucleon
• Systematic Studies of the Centrality and sqrt(s_NN) Dependence of dE_T/deta and dN_ch/deta in Heavy Ion Collisions at Mid-rapidity
• Nuclear Stopping in Au+Au Collisions at sqrt(sNN) = 200 GeV
• Longitudinal Flow of Protons from 2-8 AGeV Central Au+Au Collisions
• STAR experiment results from the beam energy scan program at RHIC
• Evolution of transverse flow and effective temperatures in the parton phase from a multi-phase transport model
• $\Lambda$ and $\bar{\Lambda }$ Production in Central Pb-Pb Collisions at 40, 80, and 158 A$\cdot$GeV
• Proton and Pion Production in Au+Au Collisions at 10.8A GeV/c
• Modelling J/psi production and absorption in a microscopic nonequilibrium approach
• Baryon Stopping as a new Probe of Geometric Scaling
• The kurtosis of net baryon number fluctuations from a realistic Polyakov--Nambu--Jona-Lasinio model along the experimental freeze-out line
• New approach to initializing hydrodynamic fields and mini-jet propagation in quark-gluon fluids
• Hybrid model with dynamical sources for heavy-ion collisions at BES energies
• A hybrid approach to relativistic heavy-ion collisions at the RHIC BES energies
• Extension of the Bjorken energy density formula of the initial state for relativistic heavy ion collisions

Cited by in corpus (10)

• Status and initial physics performance studies of the MPD experiment at NICA
• Further developments of a multi-phase transport model for relativistic nuclear collisions
• Hyperon Polarization from the Vortical Fluid in Low Energy Nuclear Collisions
• Collision energy dependence of the critical end point from baryon number fluctuations in the Linear Sigma Model with quarks
• Phase diagram determination at fivefold nuclear compression
• Thermodynamics of partonic matter in relativistic heavy-ion collisions from a multiphase transport model
• A method for probing the formation of quark matter
• Elliptic Flow of Heavy-Flavor Decay Electrons in Au+Au Collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}$ = 27 and 54.4 GeV at RHIC
• Left-right splitting of elliptic flow due to directed flow in heavy ion collisions
• Calculating QCD Phase Diagram Trajectories of Nuclear Collisions using a Semi-analytical Model