The ion beam-pellet interaction is investigated by using a time-dependent particle tracking algorithm for the slowing down of the bombarding ions. Model equations for energy and momentum deposition are developed and solved with the aid of a numerical code that describes the beam-pellet interaction as well as the subsequent heating and compression of the target. Results of calculations carried out for solid deuterium-tritium pellets using beams of deuterons, alpha particles, and lithium ions are presented and discussed. Two main conclusions are found to hold, namely: 1. Consideration of the finite thermalization time of the ion in the transport process results in slower heating and compression of the pellet as well as in smaller thermonuclear yield ratios. 2. Taking into account the momentum deposition of the bombarding ions in the pellet also provides different thermonuclear yields for low initial ion energies; for high initial ion energies, the effect of the momentum deposition is negligible.