Relativistic core-potential calculations have been carried out on Omega states resulting from the interaction of Ar*(3p(5)4s, P-3, P-1) with ground state Ne atoms. The results yield the correct asymptotic limits for the atomic states of Ar while shallow minima (700-800 cm(-1)) at large internuclear distances, 7-8 bohr, are obtained for the excited states. Dipole transition moments between pairs of states have been calculated and strong radiative transitions are predicted from excited states to the ground state. The 1(I) state, correlating with the metastable P-3(2) state of Ar is found to have a small dipole transition moment at short and intermediate nuclear distances leading to a radiative lifetime for this state of 8.3 mu s.