Matrix methods in optical model - Spherical nuclei

The calculable R matrix theory developed by Lane and Robson by using the Bloch boundary condition operator L is shown to be useful in the frame of practical aspects of the optical model. The general formalism is recalled and applied to spherical nuclei. Practical methods are developed for constructing all the elements of the matrices which are to be inverted. A non local nuclear potential of the folding type is examined as a possible alternative or improvement of the conventional phenomenological Woods-Saxon potential. From a more fundamental point of view, matrix methods are also shown to be adapted to the treatment of Hartree-Fock type real parts. Finally the applicability of such matrix methods for practical evaluation purposes is illustrated with some simple examples. Other possible developments are suggested