This is the manuscript of my "Habilitation à diriger des recherches", where I present the research work that I have done after my PhD, defended in 2009. The manuscript is divided in two parts. The first one is dedicated to atomic-structure calculations with neutral and trivalent lanthanides, in the contexts of ultracold gases and rare-earth doped solids. The second part deals with long-range interactions in ultracold gases of alkali-metal atoms and diatomic molecules, as well as lanthanide atoms. The detailed description of long-range interactions serves to characterize ultralow-temperature phenomena, like photoassociation and collisional shielding.
Charge-dipole interactions are very common interactions among atoms and molecules, especially materials that can emit light or contain free charges. The second-order charge-dipole interactions, proportional to
R41, are stronger than the second-order dipole-dipole interactions or van der Waals interactions, proportional to
R61, at longer distances. In reality, there is more than one atom or charge; therefore, we focus on few-body charge-dipole interactions, such as charge-dipole-dipole interactions. Laser cooling and trapping allow us to study such interactions with much higher precision. In this article, charge-dipole interactions will be investigated in ultracold gases. To increase the interaction strength, we excite the ultracold atoms to highly excited states, Rydberg states. Here, we treat one Rydberg atom as a dipole, the excited electron and the ion core are the two poles of an electric dipole. Specifically, we study charge-atom interactions in ultracold Rydberg gases.