Laser-induced fluorescence experiments carried out using linearly polarized photons from a pulsed laser on a He(2s S-3 --> 4p P-3) excitation-detection scheme in electrical discharges at 0.04-0.6 Torr, show that light emitted during the interaction and in the subsequent decay manifests anisotropy in its angular distribution and polarization. A rate equation approach is used to:discuss the general features of the interaction between polarized light and atoms observed experimentally. The incident electromagnetic field is decomposed into multipolar components that may interact with the atom through an appropriate coupling. Defining the Einstein coefficients for each coupling, it is possible to introduce the equations for the dynamics of the atomic populations. For each direction and polarization, the temporal profile of the intensity during the transition is calculated. The theoretical prediction explains the outcome of the He experiment satisfactorily, providing that the role of the quenching and of the collision mixing within the manifold of the 4(3)P state is duly taken into account. Fitting of the model calculations to the experimental data then allows one to deduce the value of the 'thermally averaged' cross section for collision-induced transitions between fine-structure and degenerate components of the 4(3)P sublevel, sigma(4(3)P)(J,M-->J',M') = 15.8 Angstrom(2), for each J, M in the manifold.