Calculation of the expansion rate of the three-volume measure in high-energy heavy-ion collisions

TL;DR

This paper calculates the expansion rate of the three-volume measure in high-energy heavy-ion collisions, revealing dependencies on system size and hydrodynamical evolution that influence particle formation and freeze-out conditions.

Contribution

It introduces a method to compute the three-volume expansion rate considering different hydrodynamical solutions in heavy-ion collisions.

Findings

Longitudinal expansion rate is independent of energy density.

Transverse size affects the average expansion rate.

Expansion dynamics influence light nuclei formation and freeze-out temperature.

Abstract

In ultrarelativistic heavy-ion collisions the local three-volume measure is expanding in the longitudinal and transverse directions. This is similar to the Hubble-expansion of the universe, except that the former is not locally isotropic. As an example the expansion rate is calculated assuming that the energy-momentum tensor in the central region is that of an ideal fluid, undergoing Bjorken flow in longitudinal direction, and with initial conditions as expected for BNL-RHIC energy. While the longitudinal expansion of three-volume is independent of the energy density of the fluid, in case of 3+1 dimensional expansion the form of the hydrodynamical solution (rarefaction wave or deflagration shock) affects the three-volume expansion rate on the hadronization hypersurface. As a consequence the average expansion rate on that surface depends on the transverse size of the system. This may reflect in an impact-parameter dependence of the formation probability of light nuclei and of the freeze-out temperature of the strong interactions in the system.