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

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