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Unformatted text preview: 253a/Schwartz Due September 28, 2010 Problem Set 3 Problems marked with a * are optional, but strongly recommended. 1. We found for e + e → μ + μ that the cross section was proportional to 1 + cos 2 θ . a) Work out the Lorentz invariant quantities s = ( p e + + p e ) 2 , t = ( p μ p e ) 2 and u = ( p μ + p e ) 2 in terms of E cm and cos θ (still assuming m μ = m e = 0 ) b) Derive a relationship between s, t and u . c) Rewrite the differential cross section in terms of s, t and u . d) Now assume m μ and m e are nonzero. Derive a relationship between s, t and u and the masses (hint: do NOT choose coordinates). We will use this a lot . 2. One of the most important scattering experiments ever was Rutherford’s gold foil experiment. a) What is the formula for the classical Rutherford scattering cross section ( αparticle/nucleus scattering: αN → αN )? What are the assumptions go into its derviation?...
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This note was uploaded on 02/04/2012 for the course PHYS 253A at Harvard.
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