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Theory of band shape formation in Auger and autoionization decay in molecules is presented and numerically applied to spectra of the CO molecule. In particular, the role of lifetime vibrational interference in the various vibronic decay channels is elucidated. New high resolution Auger and autoionization spectra are presented. The calculated band shapes are compared with the experimental recordings. The vibronic spectra of the intermediate states in the Auger and autoionization decay are analyzed and compared with available ESCA and EELS spectra, respectively. The role of the electron correlation on the formation of the core state potential surfaces is investigated in that connection. The assignment problem of the outer part of the CO Auger spectrum is reinvestigated and the effect of interference due to hole mixing in the wave functions is pointed out. The time dependent Franck–Condon (FC) formalism used to derive the lifetime vibrational interference is shown to have a bearing on the analogy of the sudden approximation for electron ionization with the FC principle for vibronic excitations and makes possible a derivation of the lifetime for the vertical vibrational state in electron ionization.

Calculation including the electron correlation effects is reported for the ground 1 1S and lowest triplet 1 3S state energies of the confined helium atom placed at the center of an impenetrable spherical box. While the adopted wave-functional treatment involves optimization of three nonlinear parameters and 10, 20, and 40 linear coefficients contained in wave functions expressed in a generalized Hylleraas basis set that explicitly incorporates the interelectronic distance r12, via a Slater-type exponent and through polynomial terms entering the expansion, the Kohn-Sham model employed here uses the Perdew and Wang exchange-correlation functional in its spin-polarized version within the local-density approximation (LDA) with and without the self-interaction correction. All these calculations predict a systematic increase in the singlet-triplet energy splitting toward the high confinement regime, i.e., when the box radius is reduced. By using the variational results as benchmark, it is found that the LDA underestimates the singlet-triplet energy splitting, whereas the self-interaction correction overestimates such a quantity.