The nuclear shell model: Simplicity from complexity

The shell model of atomic nuclei has been in intensive use since the middle of the previous century. This simple model of very complex nuclei, offers a quantitative description of its many features. Other features follow from small deviations from the extreme picture. Our friend and colleague Akito Arima made seminal contributions to this field starting with his famous paper with Horie on the magnetic moments of nuclei [ Prog. Theor. Phys. 11, 509 (1954)]. In the following, a detailed description of a simple example is considered. It is the 1 f 7/2 shell of the neutrons in the nuclei between 40Ca and 48Ca and of the protons in the nuclei between 48Ca and 56Ni. The results demonstrate the power and elegance of the shell model. They show how simplicity arises out of complexity. It is also shown how small deviations from the simple shell model lead to effects, in which valence neutrons act as if they carry electric charge.