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Quantum and Semiclassical Scattering Matrix Theory for Atomic Photoabsorption in External Fields

TitleQuantum and Semiclassical Scattering Matrix Theory for Atomic Photoabsorption in External Fields
Publication TypeThesis
Year of Publication2001
AuthorsGranger, BE

The photoabsorption spectra of Rydberg atoms in static, external electric and magnetic fields

provide an excellent opportunity to study the properties of a nonintegrable physical system. This thesis
develops a general theory for predicting and interpreting the photoabsorption spectra of these systems.
Using ideas from both quantum-defect theory and semiclassical approximations, such as closed-orbit
theory, I introduce scattering matrices to describe the final state of an electron in a photoabsorption
experiment. The scattering matrices encapsulate all of the important physics of the system, and are
related to important observables of the system, such as the bound state spectrum and the photoabsorption
cross section.
Initially, the framework for calculating the photoabsorption cross section is presented in complete
generality. An exact expression for the energy smoothed photoabsorption cross section is derived and
is shown to provide a useful link between quantum-defect theory and semiclassical approximations.
Although the formula is an exact result, it already contains many of the physical insights of semiclassical
approximations about the time (or action) domain physics of the electron. Both the complications of
multielectron atoms and arbitrary configurations of static, electromagnetic fields are included in the
After the basic framework has been developed, semiclassical approximations are introduced for
the specific case of an alkali-metal atom in an external magnetic field. I derive a semiclassical S-matrix to
describe the scattering of the electron off the combined Coulomb and diamagnetic long-range potentials.
The relationship of the semiclassical approximation to accurate quantum calculations is then explored.
Finally, the semiclassical S-matrix is used to construct a semiclassical formula for the photoabsorption
cross section. Here, the focus is on the Fourier transformed cross section, or recurrence spectrum,
which shows sharp peaks that correspond to certain quantum mechanical paths of the electron as
it scatters off the long-range potentials. The semiclassical approximation of the cross section interprets
these quantum paths by correlating them with classical closed orbits of the electron. By taking a surprising
cancellation between ghost and core-scattered orbits into account, a resumed semiclassical cross
section is derived. This formula gives a convergent, semiclassical theory for the recurrence spectra of
nonhydrogenic atoms. Results are presented for diamagnetic lithium and rubidium.