Abstract
A time-dependent description of the dissociative-attachment process is formulated within the framework of the projection-operator formalism of scattering theory. A generally applicable computational scheme for the solution of the resulting integro-differential equation of motion is developed. The concepts and computational techniques are illustrated for a model of a d-wave shape resonance as well as for the p-wave $^{2}\mathrm{\ensuremath{\Sigma}}_{\mathit{u}}^{+}$ shape resonance in electron-${\mathrm{H}}_{2}$ collisions. It is shown that the time-dependent wave-packet picture yields qualitative insight into the dynamics of the dissociative-attachment reaction. The origin of the complete failure of the local-complex-potential approximation for the $^{2}\mathrm{\ensuremath{\Sigma}}_{\mathit{u}}^{+}$ resonance in e+${\mathrm{H}}_{2}$ becomes apparent in the time-dependent picture.
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