Extending closed-orbit theory using quantum-defect ideas: Basic concepts and derivations

High-resolution spectra of complex atoms and molecules have been described efficiently in the energy domain using quantum-defect methods. At the same time, the coarser modulations in energy associated with external field effects such as quasi-Landau phenomena have been most fruitfully described in the framework of semiclassical closed-orbit theory, which relates the short-time quantum-mechanical behavior to the classical orbits of the system. In this paper, we demonstrate a unified theory based on semiclassical scattering matrices that adds to the power and generality of both methodologies.