Matrix-Shape Approach to Elastic Scattering

The theory and application of the matrix-shape (MS) approach is investigated for elastic scattering. Various aspects of the method, such as the choice of appropriate variables, the choice of basis-set functions as representations of the T matrix, and the use of a MS fit to the potential matrix that allows VG0+T-type integrals to be performed analytically, are considered. The method is applied to three-dimensional elastic scattering to ascertain if, on this widely studied problem, the MS approach can in fact produce the essential physics. Numerical calculations are presented to illustrate that reasonable results can be achieved. The numerical results were obtained using two special cases of the method of weighted residuals, which can be used with the MS approach to solve the Lippmann-Schwinger equation for T. The use of the MS approach in conjunction with variational principles is also discussed.