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Scattering in a spherical well

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A particle moves in a spherical finite well

Show that the scattering produced by such a potential is identical with the reflection of light rays in a sphere of radius a and relative refracting index of

n = sqrt(1+V/E)

Show that the differential cross section is (see attachment for expression)

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The 8 pages file contains a detailed derivation (including a figure) that explains the scattering in a spherical finite well.

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