An Impact Parameter Representation of the Scattering Problem

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概要

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• The new exact treatment of the scattering problem proposed by Adachi and Kotani is summarized in a more complete form. This impact parameter representation and the partial wave expansion are complementary. The former is more suitable in the short wavelength region, while the latter in the long wavelength region. By assuming a short wavelength approximation only, many formulae are simplified in the former expansion; in the case of the potential scattering, the simple relation between the scattering amplitude and the (optical) potential is obtained by applying this approximation to the correct solution in the complete form of the Born series. This result is identical with the form obtained under the eikonal or semiclassical approximation. It is proved that the total cross section in the high energy region is expressed accurately in this approximate form, but the angular distribution is less accurate for some cases. As examples, the scattering by a square well potential and the charge exchange scattering of protons by hydrogen atoms are discussed. The relations with the other impact parameter for-malisms proposed by Blankenbecler and Goldberger and others are discussed. The solution obtained by Blankenbecler and Goldberger for potential scattering is shown to be the simplest solution which satisfies the unitarity relation under the short wavelength approximation. The reason why their solution is different from the eikonal form is explored by deriving the exact dispersion relation. The Schrodinger equation in the impact parameter representation is derived.

• 理論物理学刊行会の論文
• 1968-02-25

著者

• Kotani Tsuneyuki

  Department Of Physics Faculty Of Science Osaka University

• Adachi Toshimi

  The Tokyo Metropolitan Technical

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