Part one: application of averaging to spontaneous radiation processes for one- and two-atom systems. Part two: a theoretical investigation of vibrational energy relaxation in solids

(I) In an effort to place the Wigner-Weisskopf approximation on a firm mathematical basis, the time-dependent Schroedinger equation for the fundamental problem of the radiative linewidth is solved by an approximation method for systems of integro-differential equations known as averaging. This method yields simply and rigorously the Dirac zeta function, which is vital to a proper description of the radiative damping of an atom. Moreover, the technique is readily extended to an N-atom system. In particular, the coherence effect brought about by the presence of a second atom is examined by averaging. (II) A quantum-mechanical model which accounts for the dynamical participation of orientational motions in vibrational energy relaxation of diatomic impurities isolated in rare-gas solids is developed. A simple closed expression for the VER rate constant is derived upon the following principal assumptions: the lattice is a rigid two-dimensional array, the diatomic, a plane vibrator; and participation of local translational modes is neglected. Results for the systems NH and ND in Ar, OH, and OD in Ne, HCl and DCl in Ar, and CO in Ar are in reasonable agreement with experiment. In particular, observed isotopic effects seem to be well described by the model. For the systems NH, ND/Kr and HCl, DCl/Ar there are a couple of discrepancies between calculated and observed vibrational energy relaxation rate constants. It is surmized that these discrepancies are due to features not included in the model, e.g., lattice imperfections, van der Waals molecule formation and/or rotational-translational coupling. A general theory for the participation of pseudo-local indes in vibrational energy relaxation of molecules in solids is developed. A closed expression for the relaxation rate at 00K is derived which includes details of proper lattice dynamics and depends only on the interaction potentials between the system constituents