Modeling RABITT phases in relativistic regions of heavy atoms

The study of electron dynamics in photoionization has long been, and continues to be, a major scientific frontier. Due to the ultrafast nature of electron-related processes — occurring on the attosecond timescale — their detailed investigation has only become feasible in recent decades. Advances in attosecond science, particularly High Harmonic Generation (HHG), have provided the necessary temporal resolution to explore such phenomena with high precision. Since electrons are described by complex wavefunctions, a complete characterization involves measuring not only the wave amplitudes but also their phases, which often hold crucial information about the underlying physical process. For instance, during photoionization, freed electrons experience a phase shift due to the many-body potential of the parent ion, which can also be understood as an ionization delay. The above-mentioned phase shift (or delay) can be measured using so-called pump-probe experiments, where an electron wave packet, ionized by an extreme ultraviolet (XUV) pulse of the attosecond duration (the ”pump”), is analyzed with a second (”probe”) pulse, often in the infrared (IR) range. A well-known example of such experiments is Reconstruction of Attosecond Beatings by Interference of Two-Photon Transitions (RABITT). In multi-electron systems, accurately modeling RABITT experiments requires advanced theoretical techniques that account for electron correlation. The Random Phase Approximation with Exchange (RPAE) method is an effective approach, applicable to both non-relativistic and, using Relativistic RPAE (RRPAE), relativistic systems. These models are especially crucial near atomic resonances, where complex electron-electron interactions must be captured. In RABITT measurements, such resonances manifest as abrupt phase shifts, which depend on the resonance’s shape and magnitude and may vary with the emission angle of the photoelectron. This thesis employs RRPAE to model RABITT experiments in radon, a heavy atom where relativistic effects — such as the pronounced 6p3/2 – 6p1/2 fine-structure splitting — are clearly evident. Special attention is given to analyzing photoionization phase shifts and their dependence on the emission angle near autoionizing resonances between radon’s first (6p3/2) and second (6p1/2) ionization thresholds. Additionally, an analytical model is developed to predict the shapes and energy positions of these resonant phase shifts.