An Impact Parameter Formalism. II : High Energy Elastic Scattering

概要

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The mathematical structure of the impact parameter formalism proposed by Kotani and Adachi is discussed. The formalism is regarded as a counterpart of the partial wave expansion of the scattering amplitude. An impact parameter amplitude is defined as a function of impact parameter and total energy. This amplitude has two characteristic features, corresponding to particle-like and wave-like pictures. The latter nature has not been taken into account in previous impact parameter formalisms. In order to investigate the character of the impact parameter amplitude, our formalism is applied to high energy elastic scattering. A phenomenological analysis of the diffraction scattering is characterized by two parameters. Various expressions for the impact parameter amplitudes which are connected with the large angle proton-proton scattering are derived. The absorption coefficients for each partial waves are obtained. The Lommel function of two variables is widely used in the diffraction scattering, just as it has been employed in the diffraction theory of classical light waves.
理論物理学刊行会の論文
1966-03-25