Calculate θ (as a function of the impact parameter) for Rutherford scattering, in the impulse approximation. Show that your result is consistent with the exact expression (Problem 1), in the appropriate limit.
Problem 1
Rutherford scattering. An incident particle of charge q1 and kinetic energy E scatters off a heavy stationary particle of charge q2.
(a) Derive the formula relating the impact parameter to the scattering angle.
Answer: b = (q1q2/8π∑0E) cot(θ/2).
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