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2.1 Scattering from an Atom

We can consider the scattering from an atom as the independent contributions due to the scattering from the distribution of electrons around the nucleus. The atomic scattering factor is measured in units of A0be where be is the scattering length of a single electron, and is given by

∫ f(s) = n(r)e-i2πsrdr

For a spherically symmetric n(r), f(s) is a function only of the magnitude of the scattering vector, s. The atomic scattering factor is given by a 3D Fourier transform [1] as

∫ ∞ 2 sin(2πsr) f(s) = 0 4πr n(r) 2πsr dr
(3)

At zero angle (s=0), all scattered waves are in phase and sum to give the atomic number of the atom. We shall see later on that in similar fashion, the zero angle scattered intensity in a light or x-ray scattering experiment is directly related to the molecular weight of the polymer under investigation.

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