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Calculations of Raman scattering intensities in spin 1/2 square-latticeHeisenberg model, using the Fleury-Loudon-Elliott theory, have so far beenunable to describe the broad line shape and asymmetry of the two magnon peakfound experimentally in the cuprate materials. Even more notably, thepolarization selection rules are violated with respect to theFleury-Loudon-Elliott theory. There is comparable scattering in $B_{1g}$ and$A_{1g}$ geometries, whereas the theory would predict scattering in only$B_{1g}$ geometry. We review various suggestions for this discrepency andsuggest that at least part of the problem can be addressed by modifying theeffective Raman Hamiltonian, allowing for two-magnon states with arbitrarytotal momentum. Such an approach based on the Sawatzsky-Lorenzana theory ofoptical absorption assumes an important role of phonons as momentum sinks. Itleaves the low energy physics of the Heisenberg model unchanged butsubstantially alters the Raman line-shape and selection rules, bringing theresults closer to experiments.Comment: 7 pages, 6 figures, revtex. Contains some minor revisions from  previous versio

Two-magnon Raman scattering in insulating cuprates: Modifications of the effective Raman operator