The shell model-simplicity from complexity: some of my best nuclei are spherical

This article presents shell model applications to spherical nuclei with strong emphasis on semi-magic ones. A successful description of their low lying levels is obtained by applying to them the spherical shell model. These spherical nuclei are rather different from nuclei which exhibit collective phenomena, like rotational spectra. In the present article, several applications of the shell model to nuclei are presented. Only simple cases are considered which do not involve complicated calculations. These cases are sufficient to demonstrate the power of the shell model and to find the important ingredients of the mutual interactions of nucleons. The latter are limited to two-body interactions and it seems that they are the important ones in determination of the structure of nuclei. The interaction which should be used in the shell model (effective interaction) is a highly renormalized version of the bare interaction, between free nucleons. In the absence of a reliable many-body theory of the nucleus, matrix elements of the effective interaction are determined from energies of actual nuclei. General features of these are discussed, with particular attention to matrix elements which lead to nuclear deformation and rotational spectra.