A central force potential frequently encountered in nuclear physics is the rectangular wel...

A central force potential frequently encountered in nuclear physics is the rectangular well, defined by the potential

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

(This equivalence demonstrates why it was possible to explain refraction phenomena both by Huygen’s waves and by Newton’s mechanical corpuscles.) Show also that the differential cross section is

What is the total cross section?