Theory of Radiationless Transitions, Light Scattering and Fluorescence
Jacqueline O. Berg
In the first part of this thesis a purely electronic mechanism by which ~ 20 eV excitations in condensed non-metallic phases relax to lower energy states is described. The mechanism utilizes an "energy fission" process whereby an ionic or excitonic state splits into two lower energy states, at least one being of the Frenkel exciton variety. These relaxation processes should be important in the pre-chemical stage in the radiation chemistry of condensed phases. The mechanism explains not only the known rapidity of such processes but also suggests an explanation for the proportionation of the chemistry between ionic and electronically excited states. In the second part of this thesis, Green's functions are used to discuss the time and frequency dependence of light scattering and fluorescence from model systems. In the first section of this part, time-dependent scattering from a single resonance using an uncertainty-limited light pulse is described. Three terms occur in the time dependence--one which decays as the resonance, one which decays like the light source and a beat term between them which beats at the frequency difference between the exciting pulse and the resonance. In the next section the model is extended to scattering from a two-level system. The frequency dependence of the Rayleigh and Raman scattering is described, again using excitation from an uncertainty- limited light pulse. The effects of the two-photon states, which lead to the antiresonance terms in time-independent light scattering, have been evaluated for time-dependent light scattering in the next section. Thus a unified theory is obtained for time-dependent light scattering of an uncertainty-limited pulse from far off-resonance into the resonance region. The theory reduces to the conventional Kramers-Heisenberg second-order results if a monochromatic light source is used. The two-photon states' contribution to the scattering cross section has the same time dependence as the light source while the zero-photon state has the timede-pendence previously calculated for near-resonance light scattering. In the next section excitation profiles for Rayleigh and Raman cross sections have been calculated using the formalism of the previous section for an actual diatomic molecule from over 8000 cm-1 off resonance into the resonance region. Several interference effects are discussed. The usual formula for the scattering cross sections is shown to lead to errors off resonance if the basis set is truncated. Finally, a new method of calculating the zero-order density function directly from the absorption spectrum has been found and applied to the origin region of naphthalene's second excited singlet state. Results are in good agreement with previous trial-and-error methods. Mathematical appendices are given which derive the key formulae needed in the second part of this thesis.
•Dec 10, 2025•0 citations