Time dependent models for the interaction of energetic particles in the ISM

We present a general model allowing one to calculate the distribution function of energetic particles in the interstellar medium, and hence any relevant nuclear reaction rate, for any given time-dependent injection function, as well as in situations when the propagation coefficients themselves are non stationary. We review and provide physical interpretation of general formal solutions of a propagation equation taking into account energy losses, nuclear destruction and escape. Both one-zone and extended models are investigated. Our main goal is to provide standard and general tools for subsequent use in nuclear astrophysics, notably to calculate the gamma-ray emission and spallation rates associated with energetic events and specific acceleration mechanisms. Considering the stationary limit of the model, we show that only time-dependent calculations can probe the density dependence of the physical processes under study, while steady-state models can \emph{in principle} only give information about density-independent processes.