So this is the lecture where you applied degenerate perturbation theory to the divalent, 2-dimensional metal? Q5, 2011?
OK, so  can't scatter to [-100] because the structure factor disappears for .  can't scatter to [-111] for the same reason, I found that the structure factor also disappears for  so it seems  can't scatter to [-1-1-1] either. BUT, scattering occurs for  so [1,1,1] can scatter to [1,-1,-1], [-1,1,-1] and [-1,-1,1], so the states are split and it's NOT degenerate, is that the right idea?
So the fact that the question specifies 'longitudinal modes' doesn't have any relevance to the calculation?
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