Discussion
In the Born approximation, the effective cross-section of scattering depends :
Answer: C
The cross-section depends on p sin θ/2.
In the first Born approximation the scattering amplitude is the Fourier transform of the potential with respect to the momentum transfer \(\vec{q} = \vec{p}' - \vec{p}\). For elastic scattering \(|\vec{p}'| = |\vec{p}| = p\), so
\[ q = 2p\sin\frac{\theta}{2} \]
For a central potential the amplitude, and so the cross-section \(|f|^{2}\), is a function of q alone, that is of \(p\sin(\theta/2)\). It is therefore not linear in \(\theta\), not a function of \(p\sin^{2}\theta\), and not of the momentum alone, since it varies with angle.
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