CAUSAL VIOLATION OF THE SPEED OF SOUND AND THE EQUATION OF STATE OF NUCLEAR-MATTER

The causal violation of the adiabatic speed of sound in nuclear matter at high density and/or high temperature is studied with phenomenologi cal density-dependent effective interactions within the framework of t he density matrix expansion and the non-relativistic Fermigas model. T his study shows that the causal violation is essentially governed by t he range of the exchange component and the nature of the density depen dence of the effective interaction used to derive the equation of stat e (EOS) of nuclear matter as a function of density and temperature. Wi th a model effective interaction consisting of a short-range density-d ependent part of delta-function form and a long-range density-independ ent part of Gaussian form, it is observed that the causal violation ca n be completely avoided if the long-range part of the exchange compone nt of the interaction has a range mu(ex) greater than or equal to 1.2f and if the density dependence of the interaction is chosen in the for m (rho/1 + c(3) rho)(g)amma with (1 + 1/c(3) rho(nm))(gamma+1) less th an or equal to mc(2)/(T-F/5 - epsilon(nm)) instead of the Skyrme appro ximation rho(g)amma. The implications of these restrictions on the eff ective interaction imposed by causality are also discussed.