We have studied at room temperature (RT) and at near liquid-nitrogen temperature [low temperature (LT)], the adsorption of cesium on clean gallium-rich GaAs(001) prepared by sulfide passivation, and annealing in ultrahigh vacuum. We monitor the optical transitions of gallium surface dimers, using reflectance anisotropy spectroscopy (RAS), and the changes of work function and cesium sticking coefficient. The clear correlations between these three quantities allow us to distinguish three adsorption phases : (i) At LT and up to 0.7 ML coverage, cesium adsorption induces a decrease of the RA signal, which perfectly corresponds with the work function decrease. The RA decrease is, therefore, caused by the surface dipole due to charge transfer from cesium to the solid. (ii) At RT, for a coverage smaller than 0.15 ML, both the RA signal and the work function change are different from their LT behavior, so that a distinct adsorption process occurs. This indicates that cesium diffuses to specific surface sites at which the bonding is different. (iii) At a coverage larger than 0.7 ML, and independently on adsorption temperature, no charge transfer to the solid occurs, since no change of RA spectrum and work function is observed. The cesium sticking coefficient is reduced by a factor of 2. Comparison with results obtained on As-decapped GaAs(001) Shows the similarity of the formation of the interface for the two surfaces. However, the results are clearer for the surface prepared by sulfide passivation, which seems to be of higher quality.