Many-Body Theory of Atomic Transitions

This dissertation presents a systematic approach to the derivation of transition widths and cross sections for atomic radiative and/or nonradiative processes. By applying the transition theory of Goldberger and Watson ^1, all transition properties are derived from proper solutions of the time-dependent Schrodinger equation. The focus is on situations where initial and final wave functions are nonorthogonal functions that belong to different self-consistent fields. This approach is particularly useful in the treatment of ionizing transitions where the outgoing free electron sees a different atomic potential from that of the initial bound state. Transition amplitudes are expressed as perturbation expansions in which singularities have been removed algebraically. These singularities are due to states which are degenerate with the initial and final states and represent the competing transition channels. The perturbation expansions show clearly the role of the nonorthogonality of the participating states leading to terms representing "shake" processes competing with higher-order electron correlation processes. Transition amplitudes including all second-order processes, are derived for the following transitions: X-ray, Auger, photoionization, radiative recombination, dielectronic recombination, radiative -Auger. Comparisons are made with the expressions frequently used by other workers. Using a Hartree-Fock-Slater model K- and L-shell X-ray and Auger transition widths are calculated for the range 5 <= Z <= 36. These calculations show the effects of initial/final state overlap. ftn^1M. L. Goldberger and K. M. Watson, Collision Theory, (John Wiley & Sons, New York, 1964), Chapter 8, page 424.