The study of optical forces exerted by off-axis Bessel beams on Rayleigh particles in the framework of generalized Lorenz-Mie theory demonstrated the existence of extra-forces named axicon forces, complementing the classical scattering and gradient forces already discussed extensively in the literature. The present paper revisits the same issue but in the more restricted case of on-axis beams. Results obtained in the case of off-axis beams are then confirmed but, computations being carried out in an easier framework, their meaning is displayed more clearly. Beside, we may easily distinguish between dark and non dark beams, a distinction which was not carried out in the off-axis study. A question at stake is to know whether the generalized Lorenz-Mie theory for Rayleigh particle identifies or not with the usual dipole theory.