Scatterings, particularly those involving resonances, and other elementary
processes do not happen instantaneously. In the context of semiclassical
nuclear reaction simulations, we consider delays associated with an interaction
for incident quantum wave-packets. As a consequence, we express delays
associated with elementary processes in terms of elements of the scattering
matrix and phase shifts for elastic scattering. We show that, to within the
second order in density, the simulation must account for delays in scattering
consistently with the mean field in order to properly model thermodynamic
properties such as pressure and free-energy density. The delays associated with
nucleon-nucleon and pion-nucleon scattering in free space are analysed with
their nontrivial energy dependence. Finally, an example of s-channel scattering
of massless partons is studied, and scattering schemes in nuclear reaction
simulations are investigated in the context of scattering delays.Comment: 45 pages, 5 uuencoded Postscript figure
