The classification of states of the nuclear f -shell

Abstract
Following the methods of Racah and of Jahn, the orbital states arising from the nuclear configuration f n in Russell-Saunders coupling are classified by means of group theory. States are classified according to the irreducible representations of the permutation group, and of the rotation group in the seven-dimensional space spanned by the orbital states of a single f -particle. On the assumption of short-range attractive forces, this classification allows predictions regarding the ordering of levels in the f -shell; and, in particular, the lowest states of nuclei which contain only the simple f n configuration (apart from closed shells) may be predicted as a function of the isotopic number. Numerical values of the Slater integrals for the f -shell with a Gauss interaction are given as a function of the range of the interaction.