Diffraction theory for very-high-energy scattering

Abstract

In the simple diffraction theory, or black-sphere model, of Bethe and Placzek, it is assumed that partial wave with ℓ ≦ L are completely absorbed and partial waves with ℓ > L do not interact at all. (The projectile and target are assumed to have no spin or charge, so that ℓ represents orbital angular momentum; L is a critical value of ℓ usually related to the radius of the black sphere.) We improve this primitive but useful model by taking into account (a) the gradual, rather than sharp, transition from maximum to zero absorption, (b) the generally small but important deviation from complete absorption, and (c) finite values for the real part of the scattering amplitude. By adoption of appropriate forms for these improvements, closed-form expressions for the various cross sections are obtained. Whenever necessary, systematic approximation methods are developed which allow estimates of errors to be made. The results are shown to be model-independent, i.e., independent of the detailed way in which the above generalizations are made. Further simple improvements for the Coulomb field and spin- 1 2 projectiles are also discussed. Finally, these methods are applied to the scattering of neutrons from nuclei for neutron energies in the range from 0.3 to 5.0 Bev.