sumed no changes in the magnitude of the interaction strengths for the surface spins. The surface spin wave obtained in Ref. 7 splits off from the bulk spectrum from below, in contrast to the surface spin wave in the itinerant-electron model, which always lies above the bulk-spin-wave spectrum (even at g" = 0).It is clear that surface spin waves in itinerantelectron ferromagnets generally involve relatively high frequencies. Their study by microwave ferromagnetic resonance techniques would only be possible for small values of the exchange splitting. We have seen that in strong ferromagnets, the long-wave length surface modes are highly localized near the surfaces and thus an ideal probe would be by spin-polarized electron scattering or energy-loss measurements. Indeed, in such experiments, the large energies of longwavelength itinerant surface spin waves will be an advantage in removing energy resolution difficulties. More indirectly, the existence of these modes may show up by their effect on the rate of chemical reactions on ferromagnetic metal sur-Recent experimental studies of nigrogen-doped In^Ga^P * and GaAs^^Px 2 " 4 lead to a new interpretation of the previously observed 5 N-trap luminescence transitions in these materials. The broad luminescence band previously attributed to NN pairs arises from recombination between holes and electrons in single nitrogen bound states (labeled N x ) with a strong phonon sideband. 1 " 3 In addition, the transitions identified in early work as NN 3 pairs (x = 0.37, 0.38) 5fi and the A line (0.40 %x %> 0.53) 5 ' 7 in GaAs^P^N are faces. . 4 G. Gumbs and A. Griffin, to be published. ^We remark that in the complete absence of a finiterange interaction [i.e., I(q) =/ 0 ], one can show (see Ref. 2) that the poles of x+-for a slab are given by the zeros of € M (q\\ t q z ,<^), rather than the zeros of D defined in (9). The only way the boundaries come in in this case is to restrict the values of q z to multiples of TT/L , corresponding to bulk-mode standing waves. 6 S. C. Ying, L. M. Kahn, and M. T. Beal-Monod, Solid State Commun. 18, 359 (1976). 7 R. Fo Wallis, A. A. Maradudin, I. P. Ipatova, and A. A. Klochikhin, Solid State Commun. J5, 89 (1967). 8 See, for example, K. G. Petzinger and D. J. Scalapino, Phys. Rev. B 8, 266 (1973).actually an additional N-trap bound state (N r ) 2g4 with a smaller binding energy than N^. Hydrostatic-pressure experiments, in which the T and X energy gaps change with pressure and allow the continuous study of these states over a simulated composition range, demonstrate that the deep N x state is derived primarily from the X-conductionband minima for x <: 0.42 2 and that the shallow bound state, N r , follows the r minimum for 0.30 %x ^>0.45 and then bends and follows X for 0.45 %x ^0.53. In this latter range, as the present A new theory in which the observed electronic states in N-doped GaAs^P^ derive from the combination of a long-range disorder and strain-induced nitrogen-associated potential and the usual short-range isoelectronic nitrogen po...