Quark-gluon-plasma evolution in scaling hydrodynamics

The relation between the rapidity density of produced particles in ultrarelativistic nuclear collisions and the maximum proper energy density ${\epsilon }_0$ is derived. The new scaling hydrodynamic equations of Bjorken, Kajantie, and McLerran are employed. The results exceed earlier estimates obtained with inside-outside cascade models and provide an independent estimate of ${\epsilon }_0$ from collision data. We also derive a lower bound on ${\epsilon }_0$ incorporating viscous heating and the first-order phase transition between the quark and hadronic phases. We infer that ${\epsilon }_0>2\mathrm{}$ GeV/${\mathrm{fm}}^3$ can indeed be reached in the collision of heavy nuclei at cosmic-ray energies.