Rapidity distribution of secondaries in ultra-relativistic heavy ion collisions using Landau's hydrodynamic model

Abstract

Pion rapidity density distributions for ultra-relativistic heavy ion collisions at 14.6 GeV/ A, 60 GeV/ A and 200 GeV/ A are analysed using the exact solutions for Landau's hydrodynamics. The data can be described properly only if the velocity of sound is taken to be very small. This may be interpreted to imply that the collision history of the matter is dominated by a mixed phase. Curiously, the approximate solution of Landau's hydrodynamics popularly used in the literature also describes the data equally well but with a velocity of sound about 1 3 , even though the numerical approximations leading to the final result are not at all valid for the temperatures and rapidities over which the results are used. We also point out that it is not essential to identify the initial volume of the matter as the Lorentz contracted volume normally used in Landau's model. We argue that the initial temperature of the thermalized plasma can be obtained directly if the total energy of the secondaries and their multiplicity is known and thus we can evaluate the initial volume if we know the state of the matter. This leads to much smaller energy densities and much larger initial volumes, than hitherto believed to be attained in Landau's hydrodynamics.