The proposed work has four aims: (1) to use the mathematical scheme of orthogonal operators to analyze experimental data on energy levels of atoms, identifying the effects that atomic states belonging to different configurations have on one another; (2) to use group theory methods to develop higher dimensional analogs of angular momentum, so that N electron systems can be treated as through they consisted of four quasi-particles with no statistical constraints; (3) to develop a self-consistent complex coordinate method to study lifetimes of decaying atomic states; and (4) to study non-linear processes in the interactions of intense electromagnetic fields and atoms.
