The scattering of atoms, molecules, and radiation are the most fundamental mechanisms of energy-momentum transfer in nature. Fluxes of particles and radiation may deposit energy into a system as well as be emitted, giving deep insight into fundamental processes occurring within the system. Astrophysics, in particular, may benefit from collisional modeling and transport as remote viewing of distant objects is the only option for the vast majority of astrophysical objects. Practically all interaction processes between atoms, molecules, and radiation require a quantum mechanical description. Using well known quantum analysis as well as newly developed methods, scattering parameters have been obtained over important astrophysical energy ranges not previously investigated. The newly calculated parameters have been used to model transport, collisional heating, and thermalization in a variety of astrophysical systems including the atmosphere of Mars, cometary atmospheres, and the interstellar gas and plasmas. Results of the collisional simulations allow for better understanding of current observational data as well as predictions for next generation in situ measurements.