A new and finite family of solutions of hydrodynamics: Part III: Advanced estimate of the life-time parameter

We derive a new formula for the longitudinal HBT-radius of the two particle Bose-Einstein correlation function from a new family of finite and exact, accelerating solution of relativistic perfect fluid hydrodynamics for a temperature independent speed of sound. The new result generalizes the Makhlin-Sinyukov and Herrmann-Bertsch formulae and leads to an advanced life-time estimate of high energy heavy ion and proton-proton collisions.