An analysis of diffraction formulae

In this paper various diffraction formulae deseribing elastie scattering of spinless uncharged particles are analysed. Expressions for the l-dependence of the S-matrix elements of boundary condition models are derived and compared with direct S-matrix models. Some incompatibility between the two different approaches, which are supposed to describe the same phenomenon, are found. In the derivation of Kirchhoff's diffraction formula there exists an incompatibility of the boundary conditions. Namely, for its derivation one should know both the values of the wave function and the normal component of the gradient of the wave function on the absorbing sphere. The solutions to bo both boundary problems are separately presented. The reflection from the absorbing sphere is treated and new formulae are derived. The differential and total cross-sections of the described models are analysed.