Photoionization, Photodissociation, and Long-Range Bond Formation in Molecular Rydberg States

The Rydberg spectra of atoms and small molecules offers an experimentally convenient
probe for exploring the exchange of energy between Rydberg electrons and other
forms of electronic, vibrational, and rotational excitation. This thesis investigates a series
of special topics in the field of molecular Rydberg spectra, using a diverse set of
theoretical techniques all designed to take advantage of the computational efficiency of
the sorts of scattering parameterizations commonly associated with the field of quantum
defect theory. In particular, I consider various mechanisms by which Rydberg electrons
participate in the formation (bonding) and destruction (dissociation) of molecular states.

First, I review the methodology of multichannel quantum defect theory in molecular
systems, demonstrating its versatility in reducing a complicated set of channel-coupled
solutions into a physically observable photoionization spectrum with exceptionally
high resolution, even in regions characterized by complex resonant structures with
strong energy dependence. The utility of the Fano frame transformation is discussed,
two approaches to the problem of extracting resonant effects via the delay of asymptotic
boundary conditions are presented, and a case study featuring the molecular hydrogen
isotopomer HD is examined in detail.

Second, I turn to the question of Rydberg electrons in the presence of both an
ionic core and a neutral perturbing particle, extending certain basic features of the
above philosophy to a two-center geometry. This system is predicted to give rise to
a potential well that supports bound states, with a potential curve minimum existing
at many hundreds or thousands of Bohr radii. The problem is first handled at the
level of a zero-range potential approximation, where the solution can be written by
means of degenerate perturbation theory. This approach is compared to a more robust,
but computationally expensive, description of the interaction in terms of a finite range
model potential, requiring diagonalization of the Hamiltonian with respect to an L²
basis. Some properties of these states are also noted. Next, a more powerful but
difficult formulation using the Coulomb Green's function, subject to limiting boundary
conditions at the position of the core and perturber, is derived. Finally, a semiclassical
interpretation, corresponding to the trajectories of a point particle electron moving
classically in a Coulombic field, is examined in detail.

Third, I return to the case of the diatomic Rydberg spectrum, this time extending
the solution to accommodate dissociation pathways through the use of a Siegert
pseudostate basis. Previously developed methods of treating the competition between
ionization and dissociation are reviewed and evaluated. The Siegert basis is defined,
together with an efficient procedure for its calcuation, and some of its unconventional
properties are explicitly noted. The Siegert-MQDT method is applied to several reactive
scattering or half-scattering processes, including photodissociation, dissociative
ionization, and dissociative recombination.