Influence of relaxation phenomena in the unified description of resonant and nonresonant radiative transitions

A comprehensive quantum-mechanical description of resonant and nonresonant radiative transitions in complex electronic systems is developed, using a density-matrix approach. Specific applications are made to the unified treatment of radiative and dielectronic recombination of electrons with many-electron ions in high-temperature plasmas and to the unified treatment of transverse bound-bound and free-bound radiative transitions of energetic electrons channeled in crystal lattices. Both time-independent (resolvent-operator) and time-dependent (equation-of-motion) formulations of the density-matrix approach are presented. Liouville-space projection-operator techniques, which have been developed in the nonequilibrium quantum-statistical-mechanics description of relaxation phenomena, are employed. Self-consistent treatments are achieved for the excited-level populations and the spectral-line shapes. Applications are discussed for the broadening of atomic spectral lines by autoionization processes, radiative transitions, charged-particle collisions, and the action of the plasma electric microfields, and also for electron-channeling-radiation broadening by electron-electron, electron-photon, and electron-phonon interactions in a crystal lattice. The unified treatment of resonant and nonresonant radiative transitions is accomplished by means of a partition of the “relevant” Liouville space into separate subspaces corresponding to discrete resonance and nonresonant continuum states of the electronic system of interest. Although only single-photon processes are considered and only lowest-order quantum-electrodynamical perturbation theory is explicitly evaluated for the electron interaction with the radiation field, the general resolvent-operator and propagator formulations that are presented in this investigation can be applied to the description of multiphoton processes and, with the adoption of a suitable renormalization program, to the incorporation of radiative corrections to the transition probabilities.