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HOMEWORK # 8
Physics 6572
Friday, 11/07/08; due 11/14/08
1. For low energy neutronproton 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 ² 116 [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).
 '08
 ELSER, V
 mechanics, Energy, Work, Neutron

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