hw8 - ground state of the hydrogen atom in Born...

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HOMEWORK # 8 Physics 6572 Friday, 11/07/08; due 11/14/08 1. For low energy neutron-proton scatterings, it is a good approximation to assume that they interact by a spherical square well potential V ( ~ r ) = ± - V 0 for 0 < r < a 0 for r > a . a) Determine in the Born approximation the differential scattering cross section. b) Plot the differential cross section as a function of cos θ for ka = 0, 1 and 10. Ignore the overall normalization. 2. a) Show that the differential cross section for the elastic scattering of a fast electron by the
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Unformatted text preview: ground state of the hydrogen atom in Born approximation is given by d σ d ω = m 2 e 4 4 π 2 ¯ h 4 q 4 ² 1-16 [4 + ( qa ) 2 ] 2 ³ 2 , where q 2 = ( ~ k-~ k ) 2 = 4 k 2 sin 2 θ/ 2 is the momentum transfer squared and a is the Bohr radius. Ignore the identity of the two electrons. b) Verify that the differential cross section is finite in the forward direction ( θ = 0) in contrast with the case of Coulomb scattering. Explain why this is so....
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This note was uploaded on 03/27/2011 for the course PHYS 6572 at Cornell University (Engineering School).

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