A particle is scattered by a potential at sufficiently low energy so that the phase shifts...
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A particle is scattered by a potential at sufficiently low energy so that the phase shifts & =() for 1>1. Assume rotational symmetry. (a) Show that the differential scattering cross section has the form (0, $) = A + B cos 0+C cos² 0. and determine A, B, and C in terms of phase shifts. (b) Determine the total cross section in terms of A, B, and C. (c) Assume that the differential cross section is known for 0=90° (o=a²); 0=180° (o=B2), and 0=45° (o = y²). Determine σ(0, 4) for 0 = 0° in terms of a, ß, and y. (d) Obtain the imaginary part of the forward scattering amp- litude in terms of a, ß, and y. A particle is scattered by a potential at sufficiently low energy so that the phase shifts & =() for 1>1. Assume rotational symmetry. (a) Show that the differential scattering cross section has the form (0, $) = A + B cos 0+C cos² 0. and determine A, B, and C in terms of phase shifts. (b) Determine the total cross section in terms of A, B, and C. (c) Assume that the differential cross section is known for 0=90° (o=a²); 0=180° (o=B2), and 0=45° (o = y²). Determine σ(0, 4) for 0 = 0° in terms of a, ß, and y. (d) Obtain the imaginary part of the forward scattering amp- litude in terms of a, ß, and y.
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Related Book For
Probability & Statistics for Engineers & Scientists
ISBN: 978-0130415295
7th Edition
Authors: Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying
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