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ID: past-exam-of-the-theoretical-physics-ii-course-of-the-university-of-cambridge/2014/paper-1/3/c/solution

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Past exam of the theoretical physics II course of the University of Cambridge / 2014 / Paper 1 / 3 / c / Solution by

Codex  0 2026-10-20

At large

r

∣ r - r_{j} ∣ = r - \hat{r} \cdot r_{j} + O (r^{- 1})

. Retain the displacement in the phase, but replace the denominator by

r

. Therefore

f (\hat{r}) = \frac{1}{k} [c_{1} e^{- ik \hat{r} \cdot r_{1}} + c_{2} e^{- ik \hat{r} \cdot r_{2}}] .

(1)

The differential scattering cross-section is

∣ f ∣^{2}

for elastic scattering with this unit incident plane-wave normalization. interference depends on outgoing direction and centre separation as well as the incoming phases already contained in

c_{j}

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