THE existence of the shell structure of nuclei has been derived from a considerable variety of empirical facts (stability and abundance of nuclei, spin, magnetic moment, quadrupole moment, isomerism and β-decay)1. The closed shells of neutrons as well as of protons correspond to the numbers 2, 8, 20, 28, 50, 82, 126. Several theories2 have been put forward, based on the model of a single nucleon moving in an average field of the rest. As it is not easy to conceive how a single particle embedded in matter of nuclear density could move in its own orbit without being disturbed by the others, we have searched for a more general explanation*. This is obtained with the help of a well-known relation first derived by Fermi, connecting the density ρ(r) of a degenerate system of spin-half particles to the numbers of particles with angular momentum quantum number l. If one assumes that the formation of a closed shell is associated with the filling up of states of definite angular momentum, it follows that the closed shells are characterized by .