  Liquid argon is used as active medium in a variety of neutrino and Dark
Matter experiments thanks to its excellent properties of charge yield and
transport and as a scintillator. Liquid argon scintillation photons are emitted
in a narrow band of 10~nm centered around 127 nm and with a characteristic time
profile made by two components originated by the decay of the lowest lying
singlet and triplet state of the excimer Ar$_2^*$ to the dissociative ground
state. A model is proposed which takes into account the quenching of the long
lived triplet states through the self-interaction with other triplet states or
through the interaction with molecular Ar$_2^+$ ions. The model predicts the
time profile of the scintillation signals and its dependence on the intensity
of an external electric field and on the density of deposited energy, if the
relative abundance of the unquenched fast and slow components is know. The
model successfully explains the experimentally observed dependence of the
characteristic time of the slow component on the intensity of the applied
electric field and the increase of photon yield of liquid argon when doped with
small quantities of xenon (at the ppm level). The model also predicts the
dependence of the pulse shape parameter, F$_{prompt}$, for electron and nuclear
recoils on the recoil energy and the behavior of the relative light yield of
nuclear recoils in liquid argon, $\mathcal{L}_{eff}$
