Percolation threshołds, pc , for site diluted spin systems on the fcc lattice are determined for exchange interactions extending up to the shell of the fourth nearest neighbors. If the interactions include the nearest, second, third, and fourth neighbors, pc is equal to 0.198, 0.136, 0.061, and 0.05 respectively. These results agree with the Roberts approximate formula for p c . Estimation o f p c t o e v e n l o n g e r -r a n g e d c o u p l i n g s i s p r e s e n t e d . F o r i n s t a n c e f o r p c = 0.01 the range of the couplings should extend at 1east to the eight shell of neighbors.PACS numbers: 75.40. Mg, 75.50.Pp In many diluted magnetic semiconduction (DMS) [1] the magnetic ions occupy randomly selected sites on the fcc lattice. The properties of such systems are governed by the site occupational probability x of the magnetic ions. For large enough x one observes ordered magnetic stuctures, like antiferromagnetism of the III kind seen in Cd1-xMnxTe [2]. For intermediate values of x the systems show features typical of spin glasses. The fustration here is due to an interplay between randomness and the fcc lattice geometry. Existence of any magnetic ordering, such as occuring in spin glasses, requires that the exchange interactions span the system in a percolating fashion. Otherwise the system would consist of isolated and thus paramagnetic magnetic clusters. The percolation threshold p c is defined here as the lowest value of x such that one observes a cluster which spans an infinite system. The effective value of x depends on the range of interactions in the system. For instance, if only the nearest neighbor interactions are present, i.e. the coordination number z = 12, pc = 0.195 [3]. Thus one would expect that for x (461)

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Assuming that the shallow-impurity wave function is composed of the states of a single Landau subband, an effective one-dimensional wave equation is derived and discussed in detail, allowing for the band anisotropy. The optical transitions from the bound impurity states to both, bound and free-carrier states are considered. For strong effective-mass anisotropy, e.g. for acceptors in semimagnetic semiconductors, the energies and wave functions are explicitly given for all impurity states.