Abstract
The time-dependent first-order Bethe-Goldstone theory is defined by using the Hartree-Fock approximation in the Bethe-Goldstone equation with the external field fully coupled in. Starting from this equation and using the Gell-Mann and Low projection technique various amplitude equations are obtained. Finally an equation is obtained in differential form for the excited-state pair amplitude. This can be used to calculate transition moments between the ground and excited states of atomic or molecular systems which incorporate short-range correlation effects.

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