HYDRODYNAMICS NEAR THE QCD PHASE-TRANSITION - LOOKING FOR THE LONGEST-LIVED FIREBALL

We propose a new strategy for the experimental search of the QCD phase transition in heavy ion collisions: One may tune collision energy to the point where the lifetime of the fireball is the longest. Using hyd rodynamical description of space-time evolution and assuming Landau-li ke initial conditions, we show that this longest lifetime corresponds to the initial energy density being at the ''softest point'' (where th e pressure to energy density ratio reaches its minimum), epsilon(i) ap proximate to 1.5 GeV/fm(3) for our choice of equation of state. The pl asma lifetime is effectively increased by about a factor of 3. We sugg est distinct changes in various observables which may help to locate t he softest point.