  We investigate the contributions of the Cartan generators in the static
potentials for various representations in the framework of the domain model of
center vortices for SU(3) gauge theory. Using the center domains with the cores
corresponding to only one Cartan generator H8, already given as a particular
proposal, leads to some concavities in the potentials for higher
representations. Furthermore, the string tension of the fundamental
representation is the same at Casimir scaling and N-ality regimes. We add the
contribution of the other Cartan generator H3 to the potentials and therefore
these shortcomings can be eliminated. However, we discuss that at intermediate
range of distances the potentials induced by only H8 agree with the Casimir
scaling better than those corresponding to both Cartan generators.
