In this paper, we present a detailed theoretical description for the coherent electron-impact excitation, the subsequent time evolution, and the cascading decay process of the singlet-triplet mixed 1s4f state of helium. The excitation amplitude and phase of each sublevel of this state are related to measurable coincidence intensities and polarizations of the emitted photons. It is found that the intensity and polarization of the emitted photons are time modulated due to the singlet and triplet mixing in the 1s4f state
