Two-photon processes are atomic processes in which an atom interacts simultaneously with two photons. Such processes describe a wide range of phenomena, such as two-photon decay \nand elastic or inelastic scattering of photons. In recent years two-photon processes involving highly charged heavy ions have become an active area of research. Such studies do not only consider the total transition or scattering rates but also their angular and polarization dependence. To support such examinations in this thesis I present a theoretical framework to describe these properties in all two-photon processes with bound initial and final states \nand involving heavy H-like or He-like ions. I demonstrate how this framework can be used in some detailed studies of different two-photon processes. Specifically a detailed analysis of two-photon decay of H-like and He-like ions in strong external electromagnetic fields shows the importance of considering the effect of such fields for the physics of such systems. Furthermore I studied the elastic Rayleigh as well as inelastic Raman scattering by heavy H-like ions. I found a number of previously unobserved phenomena in the angular and polarization dependence of the scattering cross-sections that do not only allow to study interesting details of the electronic structure of the ion but might also be useful for the measurement of weak physical effects in such systems.
We theoretically investigate a two-photon process via molecular internal conversion, driven by correlated photons with time delay. As an example, a molecular system approximated by Morse oscillators is used in order to evaluate the efficiency of the process, in terms of how the efficiency changes with the nonadiabatic coupling rate of vibronic states. We show that an efficient two-photon process requires two different correlated photon pairs with positive and negative energy correlations, depending on the value of the nonadiabatic coupling rate.