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