  Diluted magnetic semiconductors (DMS) like Ga$_{1-x}$Mn$_{x}$As are described
by a realistic tight-binding model (TBM) for the (valence) bands of GaAs, by a
Zener (J-)term modeling the coupling of the localized Mn-spins to the spins of
the valence band electrons, and by an additional potential scattering (V-) term
due to the Mn-impurities. We calculate the effective (Heisenberg) exchange
interaction between two Mn-moments mediated by the valence electrons. The
influence of the number of bands taken into account (6-band or 8-band TBM) and
of the potential (impurity) scattering V-term is investigated. We find that for
realistic values of the parameters {\DH} the indirect exchange integrals show a
long-range, oscillating (RKKY-like) behavior, if the V-term is neglected,
probably leading to spin-glass behavior rather than magnetic order. But by
including a V-term of a realistic magnitude the exchange couplings become short
ranged and mainly positive allowing for the possibility of ferromagnetic order.
Our results are in good agreement with available results of ab-initio
treatments.
