Generalized fresnel model for very heavy ion scattering (I)

Abstract

A generalization of the simple Fresnel diffraction formula for the angular distribution of elastic heavy ion scattering is presented. This is derived from the leading term of a closed-form asymptotic expression for the elastic scattering amplitude in the limit of large angular momentum and Sommerfeld parameters. It is shown that the generalized formula gives a quantitative description of very heavy ion data and provides a simple method of determining grazing angular momenta, interaction radii, diffusenesses, and total reaction cross sections. This method may be used as an alternative to optical model analyses because it will be shown that, despite its much greater simplicity, it gives equivalent information about the interaction of very heavy ions.