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

Understand

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 $\sqrt{s_{_{\rm NN}}} \approx 50$ 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.