Consider the case of low-energyscattering from a spherical delta function shell:
V(r) = αδ(r-a)
Where α and a are constants. Calculate the scattering amplitude, f(θ), the differenential cross-section, d(θ), and the total cross-section, σ. Assume ka « 1, so that only the l = 0 term contributes significantly. (To simplify matters, throw out all I ≠ 0 terms right from the start.) The main problem, of course, is to determine ao. Express your answer in terms of the dimensionless quantity ß ≡ 2maa/h2. Answer: σ = 4πa2ß2/(l + ß).
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