Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 316 / 2 / vii

Table of contents
- Solution vii

Solution

The large-distance profile is proportional to

[2 β - 1, x]^{- 1}

. At

x = 2

, the exact profile is proportional to

(4 β - 1)^{- 1/2}

. Thus

\frac{Σ _{actual} ( 2 a _{p} )}{Σ _{r^{- 1} m e x t r a p o l a t i o n} ( 2 a _{p} )} = \frac{2 2 β - 1}{4 β - 1} ⟶ 2

β \to \infty

. The enhancement is the finite-radius remnant of the source-ring pile-up.

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