Theoretical studies in nuclear structure I. Enumeration and classification of the states arising from the filling of the nuclear d -shell

Using a simple method due to Racah, the orbital states arising from the filling of the nuclear d -shell in Russell-Saunders coupling are enumerated and, again following Racah, a new classification of the states introduced according to their transformation properties under the group of rotations in the five-dimensional space of the orbital states of a single d -particle. This new classification acquires significance from the short-range nature of nuclear forces and permits of predictions relating to the order of the levels with attractive forces of short range.