Delays associated with elementary processes in nuclear reaction simulations

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, 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. Delays associated with nucleon-nucleon and pion-nucleon scattering in free space are analyzed 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.