Posted by Steve Simon on April 27, 2014, 12:05 pm, in reply to "Relation scattering potential and form factors"
The two equations (First and last equation on page 145) are consistent with each other.
If the scattering potential of some atom is approximately a delta function then we would write
V(x) = f delta(x)
assuming this atom is at position 0. Plugging this into Eq. 9 just tells us that f = f (the integral kills the delta function) !
The reason this is not always trivial is because scattering potentials are not usually delta functions (at least in the case of X-rays). Eq. 14.8 and 14.9 will always hold true. But the expression
V= sum f_j delta(x - x_j)
is only true if the scattering potentials are very short ranged (you have a bunch of atoms each giving a delta function at its own position x_j and each having a strength f_j).
Does this help?
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