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.
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.
In this thesis, two new types of solvable stochastic model are proposed and applied to light scattering phenomena. The theoretical framework for each model Is made based on a time-convolutlon-type equation In the damping theory. Each model Is used to develop a theory of line shape, in which the Influence of an environment for a relevant system is idealized so as to be represented with a stochastic process. Next, each model Is used to formulate a light scattering theory, especially focusing on the problem of "Raman versus Luminescence", or on a correlation among incident and scattered photons. For qualitative understanding of a problem like the light scattering, a stochastic approach such as employed here is really powerful. Recently, according to the development in experimental techniques of generating an ultra-short pulse excitation, various kinds of information upon relaxation phenomena have become obtainable in the real time domain. The models considered here may be of good use for phenomena in the ultra-short time domain. Two typical stochastic models are frequently used; one is the two-state-jump Markoff process and the other Is the Gaussian process. They are the opposite extremes with each other, whereas many real processes assume intermediate character between the two. Thus In part I a model (the first model) which bridges smoothly between these two extremes is introduced as a superposition of N two-state-jump Markoff processes. For a single two-state-jump Markoff process, the "partial cumulants" of higher than the second order vanish Identically, so that, its power spectrum can be expressed by the first order continued fraction. Because of this simple property, the general structure of the partial cumulants in case of an. arbitrary number N can be found. Thus, summing up contributions with the aid of a diagrammatic technique, the power spectrum of the proposed model is determined in a form of the N-step continued fraction. For a clear illustration of this model, a simple example of the random frequency modulation is considered, and then numerical calculations for its power spectra and its relaxation functions are given. This model is further adopted to analyze the stationary light scattering; a rigorous expression of the scattering Intensity is obtained. This result generalizes that of the stochastic model proposed by Takagahara, Hanamura and Kubo. According to an approach based on a generalized master (time-convolution-type) equation, It is found that the inhomogeneous term plays an essential role, whereas this term plays no important role In existing treatments of the relaxation. This Is due to the relaxation mechanism of the light scattering phenomena. Behavior of the light scattering spectrum is systematically investigated by the present theory with the aid of numerical calculations. It is shown how the spectrum changes from the "Raman" to the "Luminescence" under the Influence of environment. The multi-peak structure of the luminescence-like spectrum gradually disappears to become a smooth curve when the process is changed from the two-state-jump to the Gaussian. The transient response for a pulse excitation Is also considered with the use of this new model. From the above-mentioned result of the stationary light scattering, the expression for the time-resolved spectrum is readily obtained. This expression can be calculated numerically and a problem of the coherence is discussed. In part II, a further generalized model (the second model) is proposed. While the usual two-state-jump Markoff process assumes equal weight population for the two states, the newly introduced two-state-jump Markoff process Includes an asymmetric population. As a superposition of such constituent processes with asymmetric property, the new model becomes more flexible than the previous (first) model. In other words, the model Is composed of hopping processes among (N+1)-states with the binomial distribution in equilibrium. Namely, the distribution of the n-th state in equilibrium is given by p(n)=_NC_nx^ (1-x)^n, (O≤X≤1). This model is applied to various problems; the random frequency modulation, the stationary light scattering and the transient light scattering. The spectrum of this model is quite analogous to the one due to the phonon side bands, though the direct comparison must be done carefully. Our second model may be powerful in treating various systems except the ordinary light scattering, for Instance, γ-ray or X-ray scattering in solids. Moreover the formulation developed here may have wide range of applicability to various other phenomena. These remain to be solved in future.
The theory of resonance Raman effect, resonantly enhanced two-photon absorption, and resonance fluorescence---valid also for strong fields---is treated in a unified and simplified way. Dressed states, Bloch equations, and perturbation theory are used to calculate line positions, and integrated intensities both for steady state and transient excitation. The case of adiabatic following is solved explicitly; it occurs when an off-resonance incident pulse is turned on and off slowly. It leads to the identification of Raman scattering, two-photon absorption, and Rayleigh scattering with an adiabatic process while fluorescence and consecutive two-photon absorption with nonadiabaticity. Time-dependent spectra are defined in a rigorous way. Our formulas agree in the various limits with those that appear in the literature.
Light scattering by isolated small and intermediate-size molecules is studied theoretically. A quantum-mechanical model is developed that treats the molecule and the radiation field on equal terms and allows a nonperturbative solution for arbitrary wave forms and field strengths. The molecular states are described in terms of a basis set of zeroth-order states chosen so as to minimize the number of excited molecular states in the laser frequency range that combines radiatively with the initial (ground) state, i.e., that act as doorways for the field. Detailed calculations are restricted to the case of a single doorway. Closed-form expressions are obtained for the frequency-resolved scattering rates and time-resolved scattering spectra, including fluorescence and Rayleigh–Raman components, for a variety of conditions, including δ(t) excitation, excitation by a Lorentzian light pulse, by a coherent train of pulses and stationary excitation. The case of nonlinear scattering by very intense pulses is also investigated. Model calculations are reported for systems of 1–3 molecular levels. It is found that in general phase relations are maintained so that the coherence survives as long as the signal.
Abstract A practical approach to understanding light scattering processes in the condensed phase is presented. First a theoretical discussion of the various parameters in resonance light scattering is given and there is a special emphasis on our simplified approach to this question. As with other approaches the two level density matrix in association with a quantum regression theorem leads to two types of emission from an ensemble of molecules at finite temperature (T2 ≠ 2T1). We have called one of these fluorescence and the other sharper emission Raman scattering because it results directly from the presence of a coherent polarization in the medium. A brief discussion of time dependent scattering is also given. An experiment that reproduces the main features of the theory is described for resonance scattering from azulene in naphthalene at 30 K. For all values of the laser frequency (near resonance) both a sharp (Raman) and diffuse (fluorescent) component occurs in the emission spectrum. These spectra when interpreted by the simplified theory yield a value of T2 = 0.7 ps from fluorescence linewidth, and T2 = 0.8 ps from the incoherent to coherent scattering ratio, for the 0–0 two level system of azulene in naphthalene. A discussion of practical aspects of the influence of inhomogeneous line broadening is also presented.
A theory for the resonance light scattering in a molecular system interacting with the heat bath is developed, taking into account the multilevel structure of the molecular system. An expression for the cross section of the resonance light scattering process is derived by using the Liouville operator method in the Markoff approximation; the cross section consists of three terms: resonance Raman scattering, resonance fluorescence, and their mixing. The mixing term vanishes in the limit of the zero vibrational dephasing constant. Analytical expressions for the resonance Raman scattering and resonance fluorescence cross sections are derived in the displaced harmonic oscillator model. Model calculations of the vibrational band structure in the resonance light scattering cross section are performed by using the expressions derived. Differences of the band intensity distribution in the resonance fluorescence from that in the resonance Raman scattering are illustrated.
A thermal Green function theory of resonance long-laser-pulse scattering is developed, correctly taking account of the uncertainty-relation between the time-resolved and the energy-resolved experiments and the effect of the sample surface. The transient scattering efficiency can be calculated by folding the retarded Green's functions which are given by the thermal average of the chronological products of the pulse-current (or -density) and current operators into an uncertainty-principle broadening function. The theory is applied to resonance light scattering from a simple molecule in gas for steady and transient cases, where all the collision processes are treated quantum-statistically. At low pressure, the resonance scattering is mainly composed of Raman scattering (RS), final-state redistribution scattering (FRS), final-state transfer scattering (FTS) and collision-induced redistribution scattering (CIRS). In the steady state, it is shown that ordinary resonance Raman scattering is equivalent to RS in collisionless case, that absorption followed by emission contains RS, FRS and FTS, and that absorption followed by redistribution followed by emission is the same phenomenon as CIRS which is weighted by rotational population of excited molecules. Moreover, recent laser-pulse data by Roussea, Patterson and Williams are satisfactorily explained. Connection between this theory and other work is discussed.