Linear response theory for dissipation in heavy-ion collisions

We formulate a theoretical description appropriate for heavy-ion collisions at large excitation energies. The coupling of the relative motion to the nucleonic degrees of freedom is considered, and seen to be a one-body operator of simple structure in the nucleon coordinates. We then construct a differential equation for the relative motion, in which the nucleonic degrees appear implicitly as simple dissipative and conservative forces, e.g. a friction force proportional to the velocity. We use linear response theory to treat the effect of the coupling on the nucleonic degrees, whose temperature T is supposed to change very little during the nucleonic relaxation time τ. The conditions under which this approach is consistent are discussed. We obtain dispersion formulas to describe which physical processes are responsible for dissipation. Among the implications for heavy-ion collisions are: (i) slow collective motion should be treated explicitly by means of macroscopic variables; (ii) the temperature dependence of the friction coefficient has to be considered.